Mathematics
http://events.berkeley.edu/index.php/calendar/sn/math.html
Upcoming EventsCombinatorics Seminar, Oct 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=111854&date=2017-10-02
A partition of a positive integer n is a non-increasing sequence of positive integers whose sum is n. A Rogers-Ramanujan type partition identity is a theorem stating that for all n, the number of partitions of n satisfying some difference conditions equals the number of partitions of n satisfying some congruence conditions. In 1993 Alladi and Gordon introduced the method of weighted words to find refinements of Schur's theorem and other partition identities. After explaining their original method which relies on q-series identities, we will present a new version using q-difference equations and recurrences. It allows one to prove refinements and generalisations of identities with intricate difference conditions for which the classical method is difficult to apply, such as identities of Primc and Siladic which arose in representation theory.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=111854&date=2017-10-02Differential Geometry Seminar, Oct 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112168&date=2017-10-02
Given a smooth compact hypersurface in Euclidean space, one can show that there exists a unique smooth evolution starting from it, existing for some maximal time. But what happens after the flow becomes singular? There are several notions through which one can describe weak evolutions past singularities, with various relationship between them. One such notion is that of the level set flow. While the level set flow is almost by definition unique, it has an undesirable phenomenon called fattening: Our "weak evolution" of n-dimensional hypersurfaces may develop (and does develop in some cases) an interior in \( \mathbb R^{n+1} \). This fattening is, in many ways, the right notion of non-uniqueness for weak mean curvature flow.<br />
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As was alluded to above, fattening can not occur as long as the flow is smooth. Thus it is reasonable to say that the source of fattening is singularities. Permitting singularities, it is very easy to show that fattening does not occur if the initial hypersurface, and thus all the evolved hypersurface, are mean convex. Thus, singularities encountered during mean convex mean curvature flow should be of the kind that does not create singularities (i.e, the local structure of the singularities should prevent fattening, without any global mean convexity assumption). To put differently, it’s reasonable to conjecture that: "An evolving surface cannot fatten unless it has a singularity with no spacetime neighborhood in which the surface is mean convex".<br />
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In this talk, we will phrase a concrete formulation of this conjecture, and describe its proof. This is a joint work with Brian White.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112168&date=2017-10-02String-Math Seminar, Oct 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112199&date=2017-10-02
Okounkov's quantum K-theory is defined via virtual counting of parameterized quasimaps. In this talk I will consider explicit computations in the case of hypertoric varieties, where the quantum K-theory relation will arise from analysis of the bare vertex function.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112199&date=2017-10-02Northern California Symplectic Geometry Seminar, Oct 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112014&date=2017-10-02
I will explain a connection between the symplectic topology of Liouville domains and the Lagrangian enumerative geometry inside their compactifications. The enumerative invariants in question are the Landau-Ginzburg potentials and their higher Maslov index versions which I will introduce. I will explain the mirror context of the story as well as some applications, including a relationship between higher disk potentials and the ring structure on the symplectic cohomology of an anticanonical divisor complement.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112014&date=2017-10-02Probabilistic Operator Algebra Seminar, Oct 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112198&date=2017-10-02
We will discuss the non-commutative analogue of Fisher information, how it motivates the definition of a "non-microstates" free entropy and the various properties and applications of these two quantities.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112198&date=2017-10-02Arithmetic Geometry and Number Theory RTG Seminar, Oct 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=111590&date=2017-10-02
In 1981, Sansuc obtained a formula for Tamagawa numbers of reductive groups over number fields, modulo some then unknown results on the arithmetic of simply-connected groups which have since been proven, particularly Weil's conjecture on Tamagawa numbers over number fields. One easily deduces that this same formula holds for all linear algebraic groups over number fields. Sansuc's method still works to treat reductive groups in the function field setting, thanks to the recent resolution of Weil's conjecture in the function field setting by Lurie and Gaitsgory. However, due to the imperfection of function fields, the reductive case is very far from the general one; indeed, Sansuc's formula does not hold for all linear algebraic groups over function fields. We propose a modification of Sansuc's formula that recaptures it in the number field case and also gives a correct answer over number fields. We have proven this formula for all pseudo-reductive groups in characteristic greater than 3, as well as for all commutative groups (in any characteristic). The commutative case (which is essential even for the general pseudo-reductive case) is a corollary of a vast generalization of the Poitou-Tate nine-term exact sequence, from finite group schemes to arbitrary affine commutative group schemes of finite type.<br />
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Seminar Format: The seminar consists of two 50-minute talks, a pre-talk (3:10-4:00) and an advanced talk (4:10-5:00), with a 10-minute break (4:00-4:10) between them. The advanced talk is a regular formal presentation about recent research results to general audiences in arithmetic geometry and number theory; the pre-talk (3:10-4:00) is to introduce some prerequisites or background for the advanced talk to audiences consisting of graduate students.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=111590&date=2017-10-02Nick Sahinidis — ALAMO: Machine learning from data and first principles, Oct 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=111022&date=2017-10-02
We have developed the ALAMO methodology with the aim of producing a tool capable of using data to learn algebraic models that are accurate and as simple as possible. ALAMO relies on (a) integer nonlinear optimization to build low-complexity models from input-output data, (b) derivative-free optimization to collect additional data points<br />
that can be used to improve tentative models, and (c) global optimization to enforce physical constraints on the mathematical structure of the model. We present computational results and comparisons between ALAMO and a variety of learning techniques, including Latin hypercube sampling, simple least-squares regression, and the lasso. We also describe results from applications in CO 2 capture that motivated the development of ALAMO.<br />
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Nick Sahinidis<br />
Department of Chemical Engineering<br />
Carnegie Mellon University<br />
http://archimedes.cheme.cmu.edu<br />
Sahinidis@cmu.eduhttp://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=111022&date=2017-10-02Northern California Symplectic Geometry Seminar, Oct 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112015&date=2017-10-02
Families of moduli spaces in symplectic Gromov-Witten theory and gauge theory are often manifolds that have "thin" compactifications, in the sense that the boundary of the generic fiber has codimension at least two. In this talk I will discuss a notion of a relative fundamental class for such thinly compactified families. It associates to each fiber, regardless whether it is regular or not, an element in its Cech homology in a way that is consistent along paths. We give several examples of this construction, discuss some of its properties, and its benefits. This talk is based on joint work with Tom Parker.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112015&date=2017-10-02Analysis and PDE Seminar, Oct 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112197&date=2017-10-02
The thresholding scheme is a time discretization for mean curvature flow. Recently, Esedoglu and Otto showed that thresholding can be interpreted as minimizing movements for an energy that Gamma-converges to the total interfacial area. In this talk I'll present new convergence results, in particular in the multi-phase case with arbitrary surface tensions. The main result establishes convergence to a weak formulation of (multi-phase) mean curvature flow in the BV-framework of sets of finite perimeter. Furthermore, I will present a similar result for the vector-valued Allen-Cahn equation.<br />
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This talk encompasses joint works with Felix Otto, Thilo Simon, and Drew Swartz.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112197&date=2017-10-02Seminar 217, Risk Management: Nonparametric Risk Attribution for Factor Models of Portfolios, Oct 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112150&date=2017-10-03
Factor models are used to predict the future returns of a portfolio with known positions in many assets. These simulations yield a distribution of future returns and various measures of the risk of the portfolio. Clients would often like to identify sources of risk in their portfolios, but this is difficult when factors influence the portfolio in nonlinear ways, such as when returns are measured on a log scale and when the portfolio contains nonlinear instruments. We develop a two-step method to partition risk among factors in a portfolio which accounts for these nonlinearities: first, model the relationship between factors and portfolio returns, and second, estimate the risk contribution of each factor as the increase in portfolio risk due to increasing the factor's weight. Both of these steps can be done using nonparametric regressions, which make no assumptions about the distribution of factors or their functional relationship with the portfolio returns. This research was done at State Street GX Labs.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112150&date=2017-10-033-Manifold Seminar, Oct 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112226&date=2017-10-03
The profinite completion of the fundamental group $G$ of a 3-manifold $M$ is an assemblage of the possible finite quotients of $G$. If a $G$ has profinite completion different from that of any distinct $\pi _1 N$, $N$ a 3-manifold, then we say that $G$ is profinitely rigid. We will see some positive and negative results in the study of profinite rigidity, and review some open questions in this area. Highlights include Hempel's construction of non-homeomorphic surface bundles with all the same finite covers, and Bridson-Reid-Wilton's proof that punctured torus bundles over the circle are profinitely rigid among 3-manifold groups.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112226&date=2017-10-03Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Oct 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112126&date=2017-10-03
To a lattice polytope P one can associate a graded semigroup algebra K[P]. A well-known theorem due to Hochster implies that K[P] is Cohen-Macaulay, and since the 1970's there has been a fruitful interaction between combinatorics and commutative algebra using this construction. In this talk I will discuss (1) several open problems regarding the Hilbert series of K[P] (often referred to as the Ehrhart series of P) and (2) recent joint work with my student Brian Davis regarding free resolutions of K over K[P] and rationality of the associated Poincare series for a specific family of lattice polytopes.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112126&date=2017-10-03Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Oct 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112127&date=2017-10-03
Two curves X and Y are linked if their union is a complete intersection in $P^3$. The equivalence relation generated by linkage is called liaison. We survey the results on free resolution of curves, classification of liaison classes and minimal curves, and mention the relevance to the study of the Hilbert scheme of curves in $P^3$.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112127&date=2017-10-03Topology Seminar (Introductory Talk), Oct 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112249&date=2017-10-04
We will briefly review the definition and basic properties of closed and finite-volume hyperbolic 3-manifolds, and take a few minutes to place them in context of 3-manifolds more generally. Then we will outline the speaker’s work with Vladimir Markovic, constructing nearly geodesic surfaces in every closed hyperbolic 3-manifold.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112249&date=2017-10-04Chaining, interpolation, and convexity, Oct 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112141&date=2017-10-04
Classical estimates on the suprema of random processes in terms of metric<br />
entropy have found widespread use in probability theory, statistics,<br />
computer science, and other areas. Such estimates are powerful and easy to<br />
use, but often fail to be sharp. To obtain sharp bounds, one must replace<br />
these methods by a multiscale analogue known as the generic chaining that<br />
was developed by Talagrand. Unfortunately, the latter is notoriously<br />
difficult to use in any given situation. In this talk, I will exhibit a<br />
surprisingly simple construction, inspired by real interpolation of Banach<br />
spaces, that is readily amenable to explicit computations. Despite its<br />
simplicity, the method proves to be sufficiently powerful to recover the<br />
central results in Talagrand's theory in a very simple way. The talk will<br />
focus on some basic ideas and will be illustrated by specific examples; I<br />
will not assume prior familiarity with the topic. If time permits, I will<br />
briefly outline applications to the majorizing measure theorem and randommatrices, as well as some embarrassing open problems.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112141&date=2017-10-04Applied Math Seminar, Oct 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=111858&date=2017-10-04
Data assimilation or filtering of nonlinear dynamical systems combines numerical models and observational data to provide the best statistical estimates of the systems. Ensemble-based methods have proved to be indispensable filtering tools in atmosphere and ocean systems that are typically high dimensional turbulent systems. In operational applications, due to the limited computing power in solving the high dimensional systems, it is desirable to use cheap and robust reduced-order forecast models to increase the number of ensemble for accuracy and reliability. This talk describes a multiscale data assimilation framework to incorporate reduced-order multiscale forecast methods for filtering high dimensional complex systems. A reduced-order model for two-layer quasi-geostrophic equations, which uses stochastic modeling for unresolved scales, will be discussed and applied for filtering to capture important features of geophysical flows such as zonal jets. If time permits, a generalization of the ensemble-based methods, multiscale clustered particle filters, will be discussed, which can capture strongly non-Gaussian statistics using relatively few particles.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=111858&date=2017-10-04Heterogeneity: opportunities for causal inference and prediction, Oct 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112005&date=2017-10-04
Heterogeneity in potentially large-scale data can be beneficially exploited for causal inference and more robust prediction. The key idea relies on invariance and stability across different heterogeneous regimes or sub-populations. What we term as "anchor regression" opens some novel insights and connections between causality and protection (robustness) against worst case interventions in prediction problems. The resulting new procedures offer (possibly conservative) confidence guarantees. We will discuss the methodology as well as some applications.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112005&date=2017-10-04EECS Colloquium: Mathematical Explorations and Visualizations with Code, Oct 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112203&date=2017-10-04
The world of digital/algorithmic/generative art is blooming, and creative coding is becoming more and more popular. This talk is a part of a family of talks I give, where I try to highlight the connections between computer science, mathematics, and art. For the EECS Colloquium I will go more in depth and focus on the interplay between mathematical structures and programming, with many of my own examples. Programming not only enables beautiful expression, art and engaging visualizations and explanations, but also, more importantly, opens up the world of mathematics to insightful exploration and deeper understanding. With only a few lines of code, we can parameterize and experiment with mathematical structures and learn more about them. Keywords: Math, Art, Creative Coding, Geometry, Curves, Envelopes, Primes, Permutations, Card Shuffling, Partitions, Flocking, Cellular Automata, and Celtic Knots<br />
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Biography<br />
Roger Antonsen is an Associate Professor of Computer Science at the University of Oslo. He is a mathematician, logician, computer scientist, philosopher, researcher, author, lecturer, artist, and public speaker, with a PhD in mathematical logic and proof theory. Roger is currently a Visiting Scholar at UC Berkeley, California. Home page: http://rantonse.no/enhttp://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112203&date=2017-10-04Topology Seminar (Main Talk), Oct 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112250&date=2017-10-04
We will describe the new work with Alexander Wright, building on the speaker’s work with Vladimir Markovic, on constructing nearly geodesic surfaces in cusped hyperbolic 3-manifolds.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112250&date=2017-10-04Mathematics Department Colloquium, Oct 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112086&date=2017-10-05
In 1979, Richard Stanley made the following conjecture: Every Cohen-Macaulay simplicial complex is partitionable. Motivated by questions in the theory of face numbers of complexes, the conjecture sought to bridge a combinatorial condition and an algebraic condition. Recent work of the speaker and collaborators resolves the conjecture in the negative. I will discuss the history and context of the conjecture, the counterexamples, the consequences, and the new questions we are now asking.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112086&date=2017-10-05Talking About Combinatorial Objects Student Seminar, Oct 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112278&date=2017-10-06
**Note unusual time**<br />
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This talk is intended to expose the audience to a variety of important concepts or constructions in matroid theory that may reappear in later talks.<br />
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Theo will discuss the greedy characterization of matroids. Kruskal's greedy algorithm finds the minimum or maximum weight of a spanning tree of a weighted graph. If I is a collection of subsets of E, we will show how this algorithm successfully finding a maximal member of I with maximum weight for any weight function is equivalent to (E,I) being a matroid.<br />
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Mario will introduce the lattice of flats of a matroid and characterize which lattices arise in this way. Then, he'll define the characteristic polynomial of a matroid and show that this polynomial encodes some interesting properties of combinatorial objects.<br />
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Time permitting, Chris will do the following in order: 1. give a M2 demonstration of the matroids package that our very own Justin Chen wrote, 2. discuss what a Bergman fan of a matroid is, and 3. discuss an important invariant of a matroid called the Tutte polynomial.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112278&date=2017-10-06Student Probability/PDE Seminar, Oct 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112084&date=2017-10-06
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112084&date=2017-10-06Logic Colloquium, Oct 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112166&date=2017-10-06
Analytic sets enjoy a classical representation theorem based on well-founded relations. I will explain a similar representation theorem for Sigma^1_2 sets due to Marcone which is based on an intriguing topological graph: the Shift Graph. The chromatic number of this graph is 2, but its Borel chromatic number is infinite. We use this representation theorem to show that the Shift Graph is not minimal among the graphs of Borel functions which have infinite Borel chromatic number. While this answers negatively the primary outstanding question from (Kechris, Solecki and Todorcevic; 1999), our proof unfortunately does not construct any explicit example of a Borel function whose graph has infinite Borel chromatic number and admits no homomorphism from the Shift Graph.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112166&date=2017-10-06Student / postdoc PDE seminar, Oct 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112200&date=2017-10-06
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112200&date=2017-10-06Differential Geometry Seminar, Oct 9
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=111313&date=2017-10-09
A Ricci flow exhibits a Type I singularity if the curvature blows up at a certain rate near the singular time. Type I singularities are abundant and in fact it is conjectured that they are the generic singular behaviour for the Ricci flow on closed manifolds.<br />
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In this talk, I will describe some new integral curvature estimates for Type I flows, valid up to the singular time. These estimates partially extend to higher dimensions an estimate that was recently shown to hold in dimension three by Kleiner-Lott, using Ricci flow with surgery.<br />
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In this work we use the monotonicity formula available for Type I Ricci flows, adapting the technique of quantitative stratification of Cheeger-Naber to this setting.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=111313&date=2017-10-09BLISS Seminar: Optimal Experimental Design via Regret Minimization, Oct 9
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112326&date=2017-10-09
The experimental design problem concerns the selection of k points from a potentially very large design pool of p-dimensional vectors, so as to maximize the statistical efficiency regressed on the selected k design points.<br />
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We achieve 1+varepsilon approximations to all popular optimality criteria for this problem, including A-optimality, D-optimality, T-optimality, E-optimality, V-optimality and G-optimality, with only k = O(p/varepsilon^2) design points.<br />
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In contrast, to the best of our knowledge, previously (1) no polynomial-time algorithm exists for achieving any 1+varepsilon approximations for DTEG-optimality, and (2) the algorithm achieving 1+varepsilon approximation for AV-optimality require $k geq Omega(p^2/varepsilon)$http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112326&date=2017-10-09Probabilistic Operator Algebra Seminar, Oct 9
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=111746&date=2017-10-09
The theory of smooth operators by Kato and Krein's trace formula are combined to obtain the Helton-Howe trace formula. In the second part, some results towards a trace formula in two variables ( a kind of extension of Krein's formula) will be discussed.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=111746&date=2017-10-09Arithmetic Geometry and Number Theory RTG Seminar, Oct 9
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112085&date=2017-10-09
Let $G$ be a finite group and Π an irreducible complex representation of $G$ whose character is valued in the number field $k$. There is a canonical class in the Brauer group of $k$ that describes the obstruction to descending $G$ to a representation on a $k$-vector space. The question of determining this class (or its order in the Brauer group, known as the Schur index of Π) is very classical, dating to the turn of the 20th century. I will describe a new approach to computing the local Brauer obstructions at places above p (for special cases of $G$), based on using Colmez's Montreal functor (for $\mathrm {GL}_2(\mathbf Q_p)$) to transport the problem to an equivalent one about Galois representations. This also motivates a generalization of the Montreal functor to the setting of $\mathrm {SL}_2(\mathbf Q_p)$, which I will also discuss.<br />
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Seminar Format: The seminar consists of two 50-minute talks, a pre-talk (3:10-4:00) and an advanced talk (4:10-5:00), with a 10-minute break (4:00-4:10) between them. The advanced talk is a regular formal presentation about recent research results to general audiences in arithmetic geometry and number theory; the pre-talk (3:10-4:00) is to introduce some prerequisites or background for the advanced talk to audiences consisting of graduate students.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112085&date=2017-10-09Student Algebraic Geometry Seminar, Oct 9
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112375&date=2017-10-09
We will discuss at least one of the close relationships between symplectic geometry and algebraic geometry other than curve counting (Gromov-Witten theory) and mirror symmetry. In particular, we will discuss how symplectic packing of the projective plane is related to Nagata's conjecture and (time-permitting) discuss an application of Seidel's symplectic Picard-Lefschetz theory.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112375&date=2017-10-09Analysis and PDE Seminar, Oct 9
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112373&date=2017-10-09
To understand the behavior of waves at a fluid surface in configurations where the surface and the bottom meet (islands, beaches…), one encounters a difficulty: the presence in the bulk of the fluid of an edge, at the triple line. To solve the Cauchy problem, we need to study elliptic regularity in such domains, understand the linearized operator around an arbitrary solution, and construct an appropriate procedure to quasi-linearize the equations. Using those tools, I will present some a priori estimates, a first step to a local existence result.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112373&date=2017-10-09Seminar 217, Risk Management: Advances in Basketball Analytics Using Player Tracking Data, Oct 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=110436&date=2017-10-10
In the 2013-2014 season, the National Basketball League, in conjunction with STATS LLC, implemented a league-wide program to collect player-tracking data for all NBA games. The data feed now provides 25-FPS records of all players' XY coordinates on the court, as well as XYZ coordinates for the ball. This data source has opened up new lines in inquiry into the quantitative analysis of basketball that have previously been hamstrung by a reliance on spatially naive box-score and play-by-play statistics. In this talk I will discuss several projects undertaken by myself and the XY Research group that use newly-available spatial data to work toward answering fundamental questions about basketball. Topics covered will include expected (EPV, or a stock-ticker for a possession), defensive shot charts, the impact of ball movement, and play detection.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=110436&date=2017-10-103-Manifold Seminar, Oct 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112377&date=2017-10-10
I will introduce the notion of a ribbon category. I will show how such categories can be used to recover and generalize the ribbon graph invariants that were introduced in prior talks.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112377&date=2017-10-10Student Harmonic Analysis and PDE Seminar (HADES), Oct 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112376&date=2017-10-10
Kakeya-type questions ask how much tubes that point to different directions overlap. Such problems are central in harmonic analysis, due to their connection with restriction theory, geometric measure theory, PDE and number theory. Over the years there was some indication that Kakeya-type problems have an underlying algebraic structure, but it was only a decade ago that a tool was introduced in the area to reveal such structure, leading to important advances in the field. This tool is the polynomial method. During this talk we will explain the method and see applications to Kakeya-type problems.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112376&date=2017-10-10Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Oct 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112201&date=2017-10-10
For a fixed integer \(r\), Serre's condition \(S_r\) is a condition on the depth of a ring at various localizations. It can be viewed as a weakening of the Cohen-Macaulay condition. In this talk, we focus on Serre's condition for Stanley-Reisner rings. The first main topic will be the relationship between Serre's \(S_2\) condition and Hirsch type bounds on the diameter of the dual graph. The second topic is some homological properties of Stanley-Reisner rings with \(S_r\) condition using higher nerves.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112201&date=2017-10-10Topology Seminar (Introductory Talk), Oct 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112304&date=2017-10-11
The cohomology jumping loci of a space come in two basic flavors: the characteristic varieties, which are the jump loci for homology with coefficients in rank 1 local systems, and the resonance varieties, which are the jump loci for the homology of cochain complexes arising from multiplication by degree 1 classes in the cohomology ring. The geometry of these varieties, and the interplay between them sheds new light on the topology of the original space.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112304&date=2017-10-11Statistical estimation under group actions: The Sample Complexity of Multi-Reference Alignment, Oct 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112319&date=2017-10-11
Many problems in signal/image processing, and computer vision amount to estimating a signal, image, or tri-dimensional structure/scene from corrupted measurements. A particularly challenging form of measurement corruption are latent transformations of the underlying signal to be recovered. Many such transformations can be described as a group acting on the object to be recovered. Examples include the Simulatenous Localization and Mapping (SLaM) problem in Robotics and Computer Vision, where pictures of a scene are obtained from different positions and orientations; Cryo-Electron Microscopy (Cryo-EM) imaging where projections of a molecule density are taken from unknown rotations, and several others.<br />
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One fundamental example of this type of problems is Multi-Reference Alignment: Given a group acting in a space, the goal is to estimate an orbit of the group action from noisy samples. For example, in one of its simplest forms, one is tasked with estimating a signal from noisy cyclically shifted copies. We will show that the number of observations needed by any method has a surprising dependency on the signal-to-noise ratio (SNR), and algebraic properties of the underlying group action. Remarkably, in some important cases, this sample complexity is achieved with computationally efficient methods based on computing invariants under the group of transformations.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112319&date=2017-10-11Split-Sample Strategies for Avoiding False Discoveries, Oct 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=110881&date=2017-10-11
Preanalysis plans (PAPs) have become an important tool for limiting false discoveries in field experiments. We evaluate the properties of an alternate approach which splits the data into two samples: An exploratory sample and a confirmation sample. When hypotheses are homogeneous, we describe an improved split-sample approach that achieves 90% of the rejections of the optimal PAP without requiring preregistration or constraints on specification search in the exploratory sample. When hypotheses are heterogeneous in priors or intrinsic interest, we find that a hybrid approach which prespecifies hypotheses with high weights and priors and uses a split-sample approach to test additional hypotheses can have power gains over any pure PAP. We assess this approach using the community-driven development (CDD) application from Casey et al (2012) and find that the use of a hybrid split-sample approach would have generated qualitatively different conclusions.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=110881&date=2017-10-11Topology Seminar (Main Talk), Oct 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112251&date=2017-10-11
A recurring theme in topology is to determine the geometric and homological finiteness properties of spaces and groups. A fruitful approach is to compare these finiteness properties to those of differential graded algebras that model topological objects of this sort. I will discuss several concrete questions that arise in this context, and explain how the cohomology jump loci help answer some of those questions.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112251&date=2017-10-11Representation Theory and Mathematical Physics Seminar, Oct 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112374&date=2017-10-11
We review the representation of $SL(2,Z)$ - the mapping class group of the torus - by automorphisms of a simple algebra of difference operators. The algebra, known as spherical double affine Hecke algebra (DAHA) plays an important role in many developments in modern representation theory and mathematical physics. We will define a new algebra which is a direct analogue of spherical DAHA for a genus two surface, and sketch the proof of the corresponding mapping class group action. Time permitting, we will explain the connection to the Reshetikhin-Turaev construction, and possible generalizations to higher genus.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112374&date=2017-10-11Applied Math Seminar, Oct 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112409&date=2017-10-11
This presentation begins with a review of the asynchronous Spacetime Discontinuous Galerkin (aSDG) method. In its original context, the aSDG method exploits the characteristic structure of hyperbolic PDEs and special asynchronous spacetime meshes to generate solution schemes with linear computational complexity in the number of spacetime finite elements. In lieu of conventional time marching, the solution advances through local implicit solutions on patches (small clusters of spacetime elements) to combine the stability of implicit schemes with the linear complexity and locality of explicit methods. Remeshing operations can be similarly localized to obtain adaptive solutions that are exceptionally responsive to solution dynamics. In addition, aSDG solution schemes are rich in embarrassingly parallel structure that is ripe for exploitation on HPC platforms. Mathematical underpinnings of the method, such as the use of exterior calculus and differential forms in objective spacetime formulations, as well as an advanced application to dynamic fracture complete the review.<br />
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The latter part of the presentation describes ongoing research on a new parallel–adaptive aSDG scheme. We set aside established techniques and abstractions, such as the domain decomposition method (DDM) and the bulk synchronous parallel (BSP) model of parallel computation. The result is a novel parallel finite element method that is free of synchronization barriers (major obstacles to effecient use of exascale platforms) and that vastly simplifies load-balancing in response to dynamic adaptive meshing. Other current research directions, including prospects for applying aSDG methods to elliptic and parabolic systems and extensions of spacetime meshing to three spatial dimensions will be covered in brief.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112409&date=2017-10-11Mathematics Department Colloquium, Oct 12
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112128&date=2017-10-12
The classical theorem of Edouard Helly (1913) is a masterpiece of geometry. In the simplest original form it states that if a finite family $\Gamma$ of convex sets in $R^n$ has the property that every $n+1$ of the sets have a non-empty intersection, then all the convex sets must intersect. This theorem has since found applications in many areas of mathematics, most particularly convex analysis, discrete geometry, optimization, computational geometry, number theory, algebraic geometry, etc. My lecture will begin explaining the basics and proceed with a selection of lovely applications of Helly's theorem and some of its many generalizations and variations. The last part of the talk I will present our new work about discrete versions of Helly’s theorem. This part of the story originated in the 1970’s with work of Doignon, Bell, and Scarf (arising in Economics theory). I present joint work with Aliev and Louveaux and with La Haye, Oliveros, Roldan-Pensado. I promise I will provide several open questions and students (including undergrads) are guaranteed to understand a big portion of this talk.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112128&date=2017-10-12Mirror Symmetry and Symplectic Geometry Seminar, Oct 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112196&date=2017-10-13
I will first recall the definition of an invariant that assigns to any compact subset $K$ of a closed symplectic manifold $M$ a module $SH_M(K)$ over the Novikov ring. I will go over the case of $M=S^2$ to illustrate various points about the invariant. Finally I will state the Mayer-Vietoris property and explain under what conditions it holds.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112196&date=2017-10-13Visualizing Gate-tunable Nanoscale Chladni Patterns in Dirac Billiards, Oct 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112115&date=2017-10-13
Dirac fermions have coexisting electron-hole states and exhibit angular anisotropy when transmitting through a potential barrier. Because of these attributes, electrostatically confined Dirac fermions are fundamentally different from similarly trapped Schrödinger fermions. In particular, these confined charge carriers are predicted to exhibit new states with properties that depend strongly on their angular momentum, the integrability of their confinement potential, and whether they are massless or massive. <br />
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Several recent experiments have investigated confined states within integrable structures for massless Dirac fermions. However, the spatial behavior of states with high angular momentum and within non-integrable structures remains unexamined. In addition, experiments on confined massive Dirac fermions are lacking despite numerous intriguing theoretical predictions for these charge carriers.<br />
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In this talk I will discuss experiments that use scanning tunneling microscopy (STM) to map the behavior of electrostatically confined Dirac fermions at the nanoscale. Our confinement potentials were realized by manipulating defect charge within boron nitride (BN) crystals to create pn junctions on graphene (or bilayer graphene)/BN heterostructures. <br />
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First, for circular graphene pn junctions we resolved Chladni-like figures by accessing high angular momentum states. Subsequently, by merging three of these circular pn junctions we realized a stadium structure and observed quantum interference patterns that are vastly different from circularly confined Dirac fermions. Finally, by using pn junctions on bilayer graphene/BN heterostructures, we imaged the response of electrostatically confined massive Dirac fermions. <br />
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The techniques and findings presented here open the door to highly controlled studies on the ergodicity of confined Dirac fermions—gate tunable Dirac billiards.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112115&date=2017-10-13Student Probability/PDE Seminar, Oct 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112323&date=2017-10-13
In 2015, Ziliotto constructed the first example of a non-convex Hamilton-Jacobi equation in random media which fails to homogenize almost surely. We discuss a generalization of this result by Feldman and Souganidis who extend the non-homogenization result to a class of Hamiltonians with a saddle-point non-convexity.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112323&date=2017-10-13Student / postdoc PDE seminar, Oct 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112378&date=2017-10-13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112378&date=2017-10-13Julia Robinson Math Festival, Oct 14
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112411&date=2017-10-14
Julia Robinson Mathematics Festivals inspire students to explore the richness and beauty of mathematics through activities that encourage collaborative, creative problem-solving. Named for the UC Berkeley math professor and sponsored by the Math Department, this festival is for 6th-10th grade students. The Museum of Math will be bringing some of its traveling exhibits to this festival, which is a treat for anyone who hasn’t it made it to the Museum of Math in New York City!http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112411&date=2017-10-14Combinatorics Seminar, Oct 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112407&date=2017-10-16
T-systems are certain discrete dynamical systems associated with quivers. Keller showed in 2013 that the T-system is periodic when the quiver is a product of two finite Dynkin diagrams. We prove that the T-system is periodic if and only if the quiver is a finite ⊠ finite quiver. Such quivers correspond to pairs of commuting Cartan matrices which have been classified by Stembridge in the context of Kazhdan-Lusztig theory. We show that if the T-system is linearizable then the quiver is necessarily an affine ⊠ finite quiver. We classify such quivers and conjecture that the T-system is linearizable for each of them. Next, we show that if the T-system has algebraic entropy zero then the quiver is an affine ⊠ affine quiver, and classify them as well. We pay special attention to the tropical version of the problem. This is joint work with Pavlo Pylyavskyy.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112407&date=2017-10-16Differential Geometry Seminar, Oct 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112167&date=2017-10-16
Consider a projective hyperkähler manifolds with a surjective holomorphic map with connected fibers onto a lower-dimensional manifold. In the case the base must be half-dimensional projective space, and the generic fibers are holomorphic Lagrangian tori. I will explain how hyperkähler metrics on the total space with volume of the torus fibers shrinking to zero, collapse smoothly away from the singular fibers to a special Kähler metric on the base, whose metric completion equals the global collapsed Gromov-Hausdorff limit, which has a singular set of real Hausdorff codimension at least 2. The resulting picture is compatible with the Strominger-Yau-Zaslow mirror symmetry, and can be used to prove a conjecture of Kontsevich-Soibelman and Gross-Wilson for large complex structure limits which arise via hyperkähler rotation from this construction. This is joint work with Yuguang Zhang.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112167&date=2017-10-16String-Math Seminar, Oct 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112554&date=2017-10-16
I’ll describe a variant of the geometric Langlands program that has more of the topological flavor of some physical accounts. I’ll explain how it fits into broader patterns in mirror symmetry, and also the form it takes in some examples. A key quest is for a “categorical Verlinde formula” to reduce the case of high genus curves to nodal configurations. (Joint work in parts with D. Ben-Zvi and Z. Yun.)http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112554&date=2017-10-16BLISS Seminar: Kannan-Lovasz-Simonovitz Conjecture, Oct 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112457&date=2017-10-16
Kannan-Lovasz-Simonovitz (KLS) conjecture asserts that the isoperimetric constant of any isotropic convex set is uniformly bounded below.<br />
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It turns out that this conjecture implies several well-known conjectures from multiple fields: (Convex Geometry) Each unit-volume convex set contains a constant area cross section. (Information Theory) Each isotropic logconcave distribution has O(d) KL distance to standard Gaussian distribution. (Statistics) A random marginal of a convex set is approximately a Gaussian distribution with 1/sqrt(d) error in total variation distance. (Measure Theory) Any function with Lipschitz constant 1 on an isotropic logconcave distribution is concentrated to its median by O(1).<br />
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In this talk, we will discuss the latest development on the KLS conjecture.<br />
Joint work with Santosh Vempala.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112457&date=2017-10-16Arithmetic Geometry and Number Theory RTG Seminar, Oct 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112433&date=2017-10-16
For any fixed odd integer $n \geq 3$, we study the 2-torsion of the ideal class groups of certain families of degree $n$ number fields. We show that (up to a tail estimate) the average size of the 2-torsion in these families matches the predictions given by the Cohen-Lenstra-Martinet-Malle heuristics, which predict the distribution of class groups of number fields. As a consequence, we find that for any odd $n\geq 3$, there exist infinitely many number fields of degree $n$ and associated Galois group $S_n$ whose class number is odd. This talk is based on joint work with Arul Shankar and Ila Varma.<br />
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Seminar Format: The seminar consists of two 50-minute talks, a pre-talk (3:10-4:00) and an advanced talk (4:10-5:00), with a 10-minute break (4:00-4:10) between them. The advanced talk is a regular formal presentation about recent research results to general audiences in arithmetic geometry and number theory; the pre-talk (3:10-4:00) is to introduce some prerequisites or background for the advanced talk to audiences consisting of graduate students.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112433&date=2017-10-16Philip Protter - Issues of Incomplete Markets, Oct 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112204&date=2017-10-16
Abstract: In a complete market, there is a unique risk neutral measure, unique prices, and all contingent claims can be (at least theoretically) perfectly hedged. In an incomplete market, in contrast, there is an infinite number of risk neutral measures, a continuum of “fair” prices, and contingent claims can in general not be perfectly hedged, even theoretically. Unfortunately, there seems to be plenty of evidence markets in actuality are incomplete.<br />
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We are interested in trying to understand this a priori confusing situation. To make things concrete, we address the following question: Suppose a sequence of incomplete markets “converges” to a complete market in an appropriate sense (to be defined), do the major objects also converge? Mostly, this is false: the ranges of option prices do not converge, for example. We work out some simple examples that illustrate some of the issues, and we indicate when one might have some kind of reasonable convergence of the markets, and what such a convergence might be.<br />
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The talk is back on joint work with Jean Jacod. <br />
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Light refreshments will be served.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112204&date=2017-10-16CANCELED: Special Topology Seminar, Oct 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112334&date=2017-10-16
There seem to be 5 broad theorems whose conclusion is an embedded two dimensional disk (perhaps with additional structures). The five are about mapping a disk into manifolds of dimension: 2,3,4,higher, and symplectic manifolds, respectively. Each is worth knowing. The theorem about mapping a disk into a three manifold is called Dehn’s lemma. It is 60 years old, but I will explain a new wrinkle which is joint work with Marty Scharlemann.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112334&date=2017-10-16Analysis and PDE Seminar, Oct 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112477&date=2017-10-16
I will present a new explanation of the connection between the fractal uncertainty principle of Bourgain–Dyatlov, a statement in harmonic analysis, and the existence of zero free strips for Selberg zeta functions, which is a statement in geometric scattering/dynamical systems. The connection is proved using (relatively) elementary methods via the Ruelle transfer operator which is a well known object in thermodynamical formalism of chaotic dynamics. (Joint work with S Dyatlov.)http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112477&date=2017-10-16Seminar 217, Risk Management: Backtest overfitting, stock fund design and forecast performance, Oct 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=110437&date=2017-10-17
Backtest overfitting means the usage of backtests (historical market data) to construct an investment strategy, fund or portfolio, when the number of variations explored exceeds limits of statistical reliability. We show that backtest overfitting is inevitable when computer programs are employed to explore millions or even billions of parameter variations (as is typical) to select an optimal variant. We illustrate this by showing that while it is a simple matter to design a stock fund, based only on a weighted collection of S&P500 stocks, that achieves any desired performance profile, these funds typically perform erratically at best when confronted with new, out-of-sample data. Similarly, we present results of a recent study of market forecasters, most of whom employ some sort of historical market data analysis, and show that few, if any, have a positive long-term record.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=110437&date=2017-10-173-Manifold Seminar, Oct 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112642&date=2017-10-17
Modular tensor categories are certain tensor categories that lead to 3d TQFTs and, hence, to invariants of 3-manifolds. I will describe two kinds of modular tensor categories: those coming from Drinfeld centers, and those coming from quantum groups.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112642&date=2017-10-17Student Harmonic Analysis and PDE Seminar (HADES), Oct 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112557&date=2017-10-17
In this talk we will introduce the gravity water waves equations, which describe the motion of a fluid influenced by gravity, under a free interface with a vacuum. We will discuss various formulations of the problem, and in particular a paradifferential reduction due to Alazard, Burq, and Zuily. From this formulation we can exhibit the dispersive properties of the water waves system by establishing Strichartz estimates.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112557&date=2017-10-17Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Oct 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112549&date=2017-10-17
The resolution of the coordinate ring of a canonically embedded curve has been studied since the beginnings of algebraic geometry. In the 80s, Mark Green famously predicted that the length of the linear strand could be given in terms of a particular invariant of the curve (the Clifford index). A conjecture of Schreyer gives a proposed explanation for this conjecture via the Eagon-Northcott resolution of the scroll associated to a “minimal pencil”. I will explain what all this means and outline a proof of an extension of Schreyer’s conjecture, stating that all syzygies at the end of the linear resolution comes from such scrolls, provided there are only finitely many minimal pencils and up to explicit generality hypotheses. This is joint work with Gavril Farkas.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112549&date=2017-10-17Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Oct 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112550&date=2017-10-17
In the first talk I will give an introduction the notion of a deformation, give examples and explain why deformations can fail to exist. This will include deformations of k-algebras (varieties) and modules over a fixed algebra (coherent sheaves). I will end by describing how deformation theory is used to understand the global geometry of the Hilbert Scheme. In particular, motivate why the Hilbert scheme parameterizing nice objects can be badly behaved.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112550&date=2017-10-17Topology Seminar (Introductory Talk), Oct 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112305&date=2017-10-18
The notion of a trisection of a four-manifold was introduced by Gay and Kirby in 2012 and can be described as a decomposition of the four-manifold into three simple pieces. Trisections are the natural analogue in dimension four of Heegaard splittings of three-manifolds; in both cases, all of the topological complexity of the manifold is described by suitable collections of curves on surfaces. Since 2012, the theory of trisections has been rapidly developed and adapted to a number of new settings: most notably, the setting of knotted surfaces in four-manifolds.<br />
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In this talk, which will be accessible to any graduate student with some familiarity of low-dimensional manifolds (surfaces, Heegaard splittings, knots and links, etc.), I'll give an introduction to trisections and bridge trisections and describe the advances that have been made in the theory of trisections since its inception.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112305&date=2017-10-18Large deviation and entropic optimality in sparse settings, Oct 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112417&date=2017-10-18
The so called upper tail problem in the Erdos-Renyi random graph comes up naturally in the study of exponential random graph models and related graph ensembles with prescribed subgraph densities. The problem is broadly twofold:<br />
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(1) To estimate the probability that the number of copies of a graph H in a random graph is atypically large. <br />
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(2) To describe the structure of the random graph, in particular its clustering properties, in this situation.<br />
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This is a canonical example of a non-linear large deviation problem where the statistic of interest is a polynomial of independent bits. In this talk, I will describe some recent progress regarding the upper tail problem in the sparse setting, i.e., when the edge density decays to zero, involving solutions of certain entropic optimization problems. <br />
Results in other related settings and open problems will also be presented.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112417&date=2017-10-18Applied Math Seminar, Oct 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=111859&date=2017-10-18
Historically, engineers have tried to avoid working with materials and structures under conditions where instabilities are likely to occur. Classical stability analyses have focused on predicting the onset of instability for use as an upper bound on allowable loads or as a design constraint. More recently it is becoming common to take advantage of these instabilities in order to design materials and structures with new and improved properties. Examples include, the remarkable properties and applications of shape memory alloys, phase transforming materials for solid state computer memory, and flexible high aspect-ratio airplane wings (providing improved manoeuvrability) designed to operate under flutter conditions and actively controlled against dynamic instability. Physical models (of materials, structures, aircraft, etc.) capable of predicting such instabilities are highly nonlinear. Thus, it is often extremely difficult to explore and understand all of the behavior predicted by a model. This presentation will review the theory and numerical implementation of Branch-Following and Bifurcation (BFB) techniques for exploring and understanding instabilities in physical systems. These techniques provide a systematic approach to the identification and interpretation of a model's behavior. The application of these techniques will be illustrated through examples: (i) atomistic modeling of shape memory alloys; (ii) finite element modeling of periodic structural materials such as honeycombs; and (iii) atomistic modeling of nano-structures such as nano-pillars.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=111859&date=2017-10-18Topology Seminar (Main Talk), Oct 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112306&date=2017-10-18
The theory of knotted surfaces in four-manifolds (the natural analogue of knot theory to dimension four) is one of the richest and least-explored domains of low-dimensional topology. In this talk, I'll outline some of the most intriguing open problems in this area, and I'll discuss a new approach to four-dimensional knot theory that is inspired by the theory of trisections, which was introduced by Gay and Kirby in 2012. Particular focus will be placed on the setting of complex curves in the simplest complex manifolds: \(\mathbb {CP}^2\) and \(S^2\times S^2\). In this setting, the theory of bridge trisections has produced surprisingly beautiful pictures, which intriguing implications to the study of exotic smooth structures on (complex) four-manifolds.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112306&date=2017-10-18Humans Enter the Robot Equation, Oct 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112449&date=2017-10-18
Robots are becoming increasingly more capable of optimizing objective functions for physical tasks, from navigation, to dexterous manipulation, to flight. The ultimate goal is to perform these tasks for us, in our environments. We want cars driving on our roads, or personal robots assisting us with activities of daily living as we age in our own homes. Right now, we tend to be merely obstacles to these robots. I believe we need to be more -- humans need to enter the robot equation in two fundamental ways. First, we are agents who take actions in the same spaces, putting a burden on robots that their actions are <em>well-coordinated</em> with ours. Second, and perhaps more importantly, we hold the key to what the robot's objective function be in the first place -- robots need to optimize for what <em>we</em> want, for <em>our</em> values, for what helps <em>us</em>. In this talk, I will summarize my lab's journey into making robots formally reason about people in these two ways.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112449&date=2017-10-18Theoretically Speaking Series — Black Holes, Firewalls, and the Limits of Quantum Computers, Oct 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112043&date=2017-10-18
Quantum computers are proposed devices that would exploit quantum mechanics to solve certain specific problems dramatically faster than we know how to solve them with today's computers. In the popular press, quantum computers are often presented not just as an exciting frontier of science and technology (which they are), but as magic devices that would work by simply trying every possible solution in parallel. However, research over the past 25 years has revealed that the truth is much more subtle and problem-dependent: for some types of problems, quantum computers would offer only modest speedups or no speedups at all. These limitations are entirely separate from the practical difficulties of building quantum computers (such as "decoherence"), and apply even to the fully error-corrected quantum computers we hope will be built in the future. In this talk, I'll give a crash course on what computer science has learned about both the capabilities and the limitations of quantum computers. Then, in a final section, I'll describe a remarkable and unexpected connection – made just within the last five years – where the conjectured limitations of quantum computers have been applied to issues in fundamental physics. These include Hawking's black-hole information puzzle (in its modern incarnation as the "firewall paradox"), and understanding the growth of wormholes in the so-called gauge/gravity duality that emerged from string theory.<br />
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Theoretically Speaking is a lecture series highlighting exciting advances in theoretical computer science for a broad general audience. Events are held at the David Brower Center in Downtown Berkeley, and are free and open to the public. No special background is assumed.<br />
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Light refreshments will be served before the lecture, at 5:30 p.m.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112043&date=2017-10-18Paris/Berkeley/Bonn/Zürich Analysis Seminar, Oct 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112408&date=2017-10-19
For the focusing energy critical wave equation in 5D, we construct a solution showing the inelastic nature of the collision of any two solitons, except the special case of two solitons of same scaling and opposite signs. Beyond its own interest as one of the first rigorous studies of the collision of solitons for a non-integrable model, the case of the quartic gKdV equation being partially treated by the authors in previous works, this result can be seen as part of a wider program aiming at establishing the soliton resolution conjecture for the critical wave equation. This conjecture has already been established in the 3D radial case and in the general case in 3, 4 and 5D along a sequence of times by Duyckaerts, Kenig and Merle. The study of the nature of the collision requires a refined approximate solution of the two-soliton problem and a precise determination of its space asymptotics. To prove inelasticity, these asymptotics are combined with the method of channels of energy. Joint work with Frank Merle<br />
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(Please note the change of room.)http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112408&date=2017-10-19Mathematics Department Colloquium, Oct 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112641&date=2017-10-19
Spacetime and Quantum Mechanics form the pillars of our understanding of modern physics, but there are several indications that these concepts are approximate and must emerge from deeper principles, undoubtedly involving new mathematics. In this talk I will describe some emerging ideas along these lines, and present a new formulation of some very basic physics– fundamental to particle scattering and to cosmology–not following from quantum evolution in space-time, but associated with simple new mathematical structures in "positive geometry". In these examples we can concretely see how the usual rules of space-time and quantum mechanics can arise, joined at the hip, from fundamentally geometric and combinatorial origins.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112641&date=2017-10-19GraphXD Seminar, Oct 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=111915&date=2017-10-19
Many important properties of an undirected graph manifest themselves spectrally in the eigenvalues or quadratic forms of matrices related to the graph. For instance, the connectivity structure, electrical properties, and random walk behavior of a graph are determined by its Laplacian matrix. A spectral sparsifier of a graph G is a sparse graph H on the same set of vertices such that the Laplacians of H and G are close, so that H captures the spectral behavior of G while being much cheaper to store and perform computations on. We survey a line of work showing that spectral sparsifiers with constant degree exist for every graph and can be computed efficiently.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=111915&date=2017-10-19Talking About Combinatorial Objects Student Seminar, Oct 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112653&date=2017-10-20
In this talk I will introduce the theory of Hopf algebras as an abstraction of the notion of composition and decomposition. I will focus mainly on a Hopf algebra that arises from matroids and use this view point to understand the more general and abstract constructions. As an application of this theory, we will study a few polynomial invariants of matroids and the strange phenomenon that is combinatorial reciprocity. No prior knowledge of Hopf algebras required!http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112653&date=2017-10-20Student Probability/PDE Seminar, Oct 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112733&date=2017-10-20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112733&date=2017-10-20Logic Colloquium, Oct 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112552&date=2017-10-20
The aim of this talk will be to convey some of the ways that familiar ideas and tools from randomized and probabilistic computation might bear on issues of philosophical interest, focusing especially on questions about cognition, representation, and reasoning. A first question is when it would ever make sense for an agent to employ randomization in the course of decision making. Drawing on ideas from game theory, reinforcement learning, and statistics, we tentatively propose a unified answer to the question. A second set of questions revolves around the idea of characterizing an agent’s implicit causal knowledge of the world by appeal to the explicit causal structure of a probabilistic algorithm. This second topic raises novel questions about the logic of counterfactuals beyond the usual propositional setting. Much of this is work in progress.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112552&date=2017-10-20Student / postdoc PDE seminar, Oct 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112555&date=2017-10-20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112555&date=2017-10-20Science at Cal Lecture - Leave election integrity to chance, Oct 21
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112163&date=2017-10-21
There’s no perfect way to count votes. To paraphrase Ulysses S. Grant and Richard M. Nixon, “Mistakes will be made.” Voters don’t always follow instructions. Voting systems can be mis-programmed. Ballots can be misplaced. Election fraud is not entirely unknown in the U.S. And the more elections depend on technology, the more vulnerable they are to failures, bugs, and hacking–domestic and foreign.<br />
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How can we protect elections against honest mistakes and nation states that want to influence our political system? If we vote on paper ballots and keep track of them well, we can double-check election results by inspecting a random sample of ballots. If the results are right, a very small random sample can suffice to confirm the results; if the results are wrong, a full manual count may be required to set the record straight.<br />
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“Risk-limiting audits” (RLAs), developed in 2007, guarantee that if the outcome is wrong, there is a large chance that the audit will correct the record before the results are official. They have been tested in California, Colorado, Ohio, and Denmark. Colorado will be the first state to routinely conduct RLAs, starting in November, 2017, and Rhode Island just passed a law requiring RLAs starting in 2018. An immediate national push for RLAs could give the public justified confidence in the 2018 midterm elections and the 2020 presidential election. But time is short.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112163&date=2017-10-21Combinatorics Seminar, Oct 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112453&date=2017-10-23
Descents in permutations and tableaux arise frequently in combinatorics. More recently, cyclic notions of descents have come up for permutations, and for standard tableaux of certain shapes. I'll talk about recent work resolving the question of exactly which shapes have such a notion of cyclic descents for their tableaux. This leads to a connection with Postnikov's work on toric shapes, and to several questions.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112453&date=2017-10-23Differential Geometry Seminar, Oct 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112742&date=2017-10-23
In 1993, Almgren, Taylor and Wang introduced an implicit time discretization for mean curvature flow which comes as a family of variational problems. The a priori estimate yields weak convergence of the approximations. In the talk I will show that this convergence is in fact strong if the initial conditions are mean convex. In particular, following the work of Luckhaus and Sturzenhecker, the scheme converges to a BV-solution of mean curvature flow. The talk is basic and should be understandable for anybody with some background in geometric analysis.<br />
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This is joint work with Guido de Philippis.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112742&date=2017-10-23Probabilistic Operator Algebra Seminar, Oct 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112452&date=2017-10-23
We recall the notion of free entropy dimension of a finite set of selfadjoint operators in a noncommutative probability space introduced by Voiculescu. We then provide a new definition of the above notion due to Kenley Jung and discuss its ramifications and survey some of its applications.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112452&date=2017-10-23BLISS Seminar: Sparsity, variance, and curvature in multi-armed bandits, Oct 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112689&date=2017-10-23
In (online) learning theory the concepts of sparsity, variance and curvature are well-understood and are routinely used to obtain refined regret and generalization bounds. In this work we further our understanding of these concepts in the more challenging limited feedback scenario. We consider the adversarial multi-armed bandit and linear bandit problems and solve several open problems pertaining to the existence of algorithms with good regret bounds under the following assumptions: (i) sparsity of the individual losses (open problem by Kwon and Perchet), (ii) small variation of the loss sequence (open problem by Kale and Hazan), and (iii) curvature of the action set (open problem by Bubeck, Cesa-Bianchi and Kakade). <br />
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Joint work with Michael B. Cohen and Yuanzhi Li.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112689&date=2017-10-23Arithmetic Geometry and Number Theory RTG Seminar, Oct 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112556&date=2017-10-23
Given a smooth projective variety over an algebraically closed field of positive characteristic, can we always dominate it by another smooth projective variety that lifts to characteristic 0? We give a negative answer to this question.<br />
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Seminar Format: The seminar consists of two 50-minute talks, a pre-talk (3:10-4:00) and an advanced talk (4:10-5:00), with a 10-minute break (4:00-4:10) between them. The advanced talk is a regular formal presentation about recent research results to general audiences in arithmetic geometry and number theory; the pre-talk (3:10-4:00) is to introduce some prerequisites or background for the advanced talk to audiences consisting of graduate students.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112556&date=2017-10-23Seminar 217, Risk Management: Submodular Risk Allocation, Oct 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=110438&date=2017-10-24
We analyze the optimal allocation of trades to portfolios when the cost associated with an allocation is proportional to each portfolio's risk. Our investigation is motivated by changes in the over-the-counter derivatives markets, under which some contracts may be traded bilaterally or through central counterparties, splitting a set of trades into two or more portfolios. A derivatives dealer faces risk-based collateral and capital costs for each portfolio, and it seeks to minimize total margin requirements through its allocation of trades to portfolios. When margin requirements are submodular, the problem becomes a submodular intersection problem. Its dual provides per-trade margin attributions, and assigning trades to portfolios based on the lowest attributed costs yields an optimal allocation. As part of this investigation, we derive conditions under which standard deviation and other risk measures are submodular functions of sets of trades. We compare systemwide optimality with individually optimal allocations in a market with multiple dealers.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=110438&date=2017-10-24Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Oct 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112551&date=2017-10-24
We witness a phenomenon of so-called Murphy's law in the context of Hilbert schemes. After a brief review of Hilbert schemes and their basic properties, we use the liaison theory to construct Mumford's example of a non-reduced component of the Hilbert scheme of smooth curves in $P^3$.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112551&date=2017-10-24Applied Math Seminar, Oct 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=111860&date=2017-10-25
The design and optimization of the next generation of materials and applications strongly hinge on our understanding of the processing-microstructure-performance relations; and these, in turn, result from the collective behavior of materials’ features at multiple length and time scales. Although the modeling and simulation techniques are now well developed at each individual scale (quantum, atomistic, mesoscale and continuum), there remain long-recognized grand challenges that limit the quantitative and predictive capability of multiscale modeling and simulation tools. In this talk we will discuss three of these challenges and provide solution strategies in the context of specific applications. These comprise (i) the homogenization of the mechanical response of materials in the absence of a complete separation of length and/or time scales, for the simulation of metamaterials with exotic dynamic properties; (ii) the collective behavior of materials’ defects, for the understanding of the kinematics of large inelastic deformations; and (iii) the upscaling of non-equilibrium material behavior for the modeling of phase change materials.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=111860&date=2017-10-25Topology Seminar (Main Talk), Oct 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112644&date=2017-10-25
Let M be a closed oriented 3-manifold not diffeomorphic to the 3-sphere, and suppose that there is a strongly irreducible Heegaard splitting H. Previously, Rubinstein announced that either there is a minimal surface of index at most one isotopic to H or there is a non-orientable minimal surface such that the double cover with a vertical handle attached is isotopic to H. He sketched a natural outline of a proof using min-max, however some steps are non-trivially incomplete and we will explain how to justify them. The key point is a version of min-max theory producing interior minimal surfaces when the ambient manifold has minimal boundary. Some corollaries of the theorem include the existence in any \(RP^3\) of either a minimal torus or a minimal projective plane with stable universal cover. Several consequences for metric with positive scalar curvature are also derived.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=112644&date=2017-10-25Seminar 217, Risk Management:, Oct 31
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=110439&date=2017-10-31
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=110439&date=2017-10-31