Mathematics
http://events.berkeley.edu/index.php/calendar/sn/math.html
Upcoming EventsCombinatorics Seminar, Apr 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116251&date=2018-04-02
Parking functions are basic objects of combinatorics. In joint work with Angela Hicks, we ask 'What does a typical parking function look like? What's the chance that $\pi (i)=j$? How about the number of ones or the area $\pi (1)+ ...+\pi (n)$?' These questions lead to new probability (Airey processes) and new results about parking functions. I will try to explain both the combinatorics and the probability 'in English'.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116251&date=2018-04-02Probabilistic operator Algebra Seminar, Apr 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116443&date=2018-04-02
Ben Arous and Voiculescu started the study of non-commutative extreme values in 2006, proving that in the free setting the limiting distributions (max-stable laws) are generalized Pareto distributions. In this talk I will present my joint work with Voiculescu on the study of Boolean extreme values. I will show that the Boolean max-convolution is in a sense isomorphic to the classical max-convolution. This result enables us to transfer what is known about the classical max-convolution to the Boolean case, in which the max-stable laws happen to be the previously known Dagum distributions (also called log-logistical distributions).http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116443&date=2018-04-02Differential Geometry Seminar, Apr 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116572&date=2018-04-02
We discuss general compactness results for Kahler-Einstein manifolds with negative first Chern class and geometric Kahler-Einstein metrics on smoothable log canonical models.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116572&date=2018-04-02Northern California Symplectic Geometry Seminar, Apr 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116612&date=2018-04-02
In real dimension two, the symplectic mapping class group of a surface agrees with its ``classical'’ mapping class group, whose properties are well-understood. To what extent do these generalise to higher-dimensions? We consider specific pairs of symplectic manifolds $(S, M)$, where $S$ is a surface, together with collections of Lagrangian spheres in $S$ and in $M$, say $v_1, ...,v_k$ and $V_1, ...,V_k$, that have analogous intersection patterns, in a sense that we will make precise. Our main theorem is that any relation between the Dehn twists in the $V_i$ must also hold between Dehn twists in the $v_i$. Time allowing, we will give some corollaries, such as embeddings of certain interesting groups into auto-equivalence groups of Fukaya categories.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116612&date=2018-04-02Arithmetic Geometry and Number Theory RTG Seminar, Apr 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116657&date=2018-04-02
Title (re-talk): An introduction to metaplectic groups<br />
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Abstract (re-talk): In his 1964 Acta paper, André Weil introduced metaplectic groups. For Weil, these were groups generated by certain unitary operators on a space of $L^2$ functions. His paper brought together harmonic analysis and number theory, yielding new results on quadratic forms and a proof of quadratic reciprocity. Within about 10 years, Shimura had carried out a deep study of modular forms of half-integer weight and Gelbart and Piatetski-Shapiro linked half-integer weight modular forms to automorphic forms on Weil's metaplectic groups.<br />
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The metaplectic groups are central extensions of symplectic groups by a group of order 2. Soon after Weil's analytic construction, Steinberg and Matsumoto studied central extensions of Chevalley groups (like $SL_n(F)$) over arbitrary fields, finding a link to algebraic K-theory. This provided an algebraic approach to metaplectic groups, and a broader class of groups to study with applications to automorphic forms and number theory.<br />
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In this talk, I will give a historical introduction to the metaplectic group and its generalizations, focusing on algebraic aspects and motivating Brylinski and Deligne's category of "central extensions of reductive groups by K2". No familiarity with algebraic groups, K-theory, or automorphic forms is required. The style will be comparable to a "What is..." paper in the Notices. <br />
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Title (advanced talk): Extending the Langlands program to covering groups.<br />
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Abstract (advanced talk): Among the very first modular forms, studied by Jacobi, were modular forms of half-integer weight. In modern terms, these can be viewed as automorphic forms on the metaplectic group. Since the metaplectic group is not an algebraic group, the conjectures of Langlands do not apply -- Langlands did not conjecture a relationship between automorphic representations of metaplectic groups and Galois representations, for example. <br />
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I will describe recent efforts to close this basic gap in the Langlands program, by constructing an "L-group" for a broad class of covering groups (including the metaplectic group). This L-group allows one to reformulate Langlands' conjectures for covering groups. I will discuss the classification of covering groups (after Brylinski-Deligne), the construction of this L-group, and evidence for an extension of the Langlands program.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116657&date=2018-04-02Agostino Capponi - Columbia University, Apr 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=115026&date=2018-04-02
Agostino Capponi joined Columbia University's IEOR Department in August 2014, where he is also a member of the Institute for Data Science and Engineering.<br />
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His main research interests are in the area of networks, with a special focus on systemic risk, contagion, and control. In the context of financial networks, the outcome of his research contributes to a better understanding of risk management practices, and to assess the impact of regulatory policies aimed at controlling financial markets. He has been awarded a grant from the Institute for New Economic Thinking for his research on dynamic contagion mechanisms.<br />
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His research has been published in top-tier journals of Operations Research, Mathematical Finance, and Financial Economics, including Operations Research, Mathematics of Operations Research, Management Science, Review of Asset Pricing Studies, and Mathematical Finance. His work has also been published in leading practitioner journals and invited book chapters. Agostino is a frequently invited speaker at major conferences in the area of systemic risk. He has on-going collaborations with several governmental institutions that are tasked with the analysis of financial networks data, in particular the US Commodity Futures Trading Commission and the Office of Financial Research. Agostino holds a world patent for a target tracking methodology in military networks.<br />
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Agostino received his Master and Ph.D. Degree in Computer Science and Applied and Computational Mathematics from the California Institute of Technology, respectively in 2006 and 2009.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=115026&date=2018-04-02Northern California Symplectic Geometry Seminar, Apr 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116613&date=2018-04-02
I will try to argue that cooperads provide a useful way to organize the construction of various algebraic structures in Floer theories.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116613&date=2018-04-02Student Harmonic Analysis and PDE Seminar (HADES), Apr 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116748&date=2018-04-03
The GBO equation has the quasilinear property. The derivative in the nonlinearity is strong enough to insure that the nonlinearity is non-perturbative, and that only countinuous dependence on the initial data may hold, even at high regularity. The proof of local well-posedness is given by Herr, Ionescu, Kenig and Koch. Following the work of Ifrim and Tataru, we may prove the local well-posedness of GBO in a much simpler way.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116748&date=2018-04-03Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Apr 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116704&date=2018-04-03
We examine effective divisors on a smooth cubic surface in $\mathbf {P^3}$. By means of Zariski decomposition, we reveal the interplay between the geometry of secant lines and cohomologies of line bundles. We also describe the degrees of the generators of the Hartshorne-Rao modules. Finally we determine the free resolutions of the curves. The work is a simplification, correction and generalization of the work of Giuffrida and Maggioni.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116704&date=2018-04-03Solving composite minimization problems arising in statistics and engineering, with applications to phase retrieval, Apr 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116452&date=2018-04-03
We consider minimization of stochastic functionals that are compositions of a (potentially) non-smooth convex function h and smooth function c. We develop two stochastic methods--a stochastic prox-linear algorithm and a stochastic (generalized) sub- gradient procedure--and prove that, under mild technical conditions, each converges to stationary points of the stochastic objective. Additionally, we analyze this problem class in the context of phase retrieval and other nonlinear modeling problems, showing that we can solve these problems (even with faulty measurements) with extremely high probability under appropriate random measurement models. We provide substantial experiments investigating our methods, indicating the practical effectiveness of the procedures.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116452&date=2018-04-03Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Apr 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116703&date=2018-04-03
We give a gentle introduction to liaison of algebraic varieties following Peskine-Szpiro. We will carefully go through the basic definitions and properties, along with various examples, in preparation for subsequent talks on the linkage of space curves.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116703&date=2018-04-03Topology Seminar (Introductory Talk), Apr 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116674&date=2018-04-04
We will go over some background material for the research talk.<br />
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**This talk starts at 2:45 PM, not 10 minutes after that.**http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116674&date=2018-04-04Poisson-Dirichlet interval partition evolutions related to the Aldous diffusion, Apr 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116660&date=2018-04-04
We construct diffusions on a space of interval partitions of [0,1] that<br />
are stationary with Poisson-Dirichlet laws. The processes of ranked<br />
interval lengths of our partitions are diffusions introduced by Ethier and<br />
Kurtz (1981) and Petrov (2009). Specifically, we decorate the jumps of a spectrally positive stable process with independent squared Bessel<br />
excursions. In the spirit of Ray-Knight theorems, we form a process<br />
indexed by level, in our case by extracting intervals from jumps crossing the level. We show that the fluctuating total interval lengths form another squared Bessel process of different dimension parameter. By interweaving two such constructions, we can match dimension parameters to equal -1. We normalize interval partitions and change time by total interval length in a de-Poissonisation procedure. These interval partition diffusions are a key ingredient to construct a diffusion on the space of real trees whose existence has been conjectured by David Aldous. This is joint work, partly in progress, with Noah Forman, Soumik Pal and Douglas Rizzolo.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116660&date=2018-04-04Applied Math Seminar, Apr 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=115860&date=2018-04-04
Mechanical behavior, specifically plastic deformation at low and high temperatures in metal alloys is governed by the motion of dislocations: topological line defects in a crystal. Dislocations in crystalline materials were hypothesized nearly eighty years ago, and their experimental and theoretical study has provided powerful tools for modern materials engineering. While the long-range elastic field of a dislocation is known and straight-forward to compute, many of the strongest effects of dislocations occur in the "core"–the center of the dislocation–where elasticity breaks down, and new chemical bonding environments can often make even empirical potential descriptions suspect. Hence, there is much effort to use the accuracy of modern quantum mechanical methods (like density-functional theory) to study dislocation cores accurately, as well as their interaction with other defects, such as solutes and boundaries. While there are a variety of possible coupling or "multiscale" techniques available, I will focus on flexible boundary conditions, which use the lattice Green function to couple electronic structure to an infinite harmonic bulk; this approach greatly simplifies many "hand-shaking" problems, and generally provides a computationally efficient approach. We recently developed a new numerical approach that accounts for the topology change of a dislocation. This methodology has explained solid-solution softening in molybdenum (explaining a 50-year-old mystery of metallurgy), dislocation cores in aluminum, titanium, and iron, and provided a wide range of mechanical behavior predictions for magnesium alloys, and recently the dislocation core structures for a 1/2< 110 > Ni screw dislocation and a < 110 > Ni3Al screw superdislocation.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=115860&date=2018-04-04Topology Seminar (Main Talk), Apr 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116675&date=2018-04-04
The mapping class group $\rm {Mod}_g$ of a genus $g$ closed oriented $2$-manifold has virtual cohomological dimension $4g-5$, by a theorem of John Harer, and therefore its cohomology groups $H^i(\rm {Mod}_g;\mathbb Q)$ vanish for $i > 4g-5$. For $i=4g-5$ it also vanishes, by work of Morita-Sakasai-Suzuki, Church-Farb-Putman, and unpublished results of Harer. The highest remaining interesting cohomological degree is therefore $i = 4g-6$. I will discuss joint work with Melody Chan and Sam Payne, in which we prove that the cohomology in this degree is usually non-zero and in fact its dimension grows quite fast as a function of $g$.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116675&date=2018-04-04Center for Computational Biology Seminar, Apr 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114977&date=2018-04-04
Title: Modeling the Complex Impact of Genetic Variation on Gene Expression<br />
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Abstract:<br />
Non-coding and regulatory genetic variation plays a significant role in human health, but the impact of regulatory variants has proven difficult to predict from sequence alone. Further, genetic effects can be modulated by context, such as cell type and environmental factors. We have developed machine learning approaches to model the effects of regulatory variation, including predicting the impact of rare regulatory variants on gene expression, modeling the interaction between environmental factors and genetic variation, and detecting regulatory effects that vary over time. I will present recent results evaluating the complex impact of both rare and common genetic variation on gene regulation in diverse contexts including changes in genetic effects evident across cellular differentiation.<br />
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Bio: <br />
Alexis Battle’s research focuses on unraveling the impact of genetics on the human body, using machine learning and probabilistic methods to analyze large scale genomic data. She is interested in applications to personal genomics, genetics of gene expression, and gene networks in disease, leveraging diverse data to infer more comprehensive models of genetic effects on the cell. She earned her Ph.D. and Masters in Computer Science in 2014 from Stanford University in 2014, where she also received her Bachelors in Symbolic Systems (2003). Alexis also spent several years in industry as a member of the technical staff at Google. Prior to joining Hopkins, Alexis spent a year as a postdoc with Jonathan Pritchard with HHMI and the Genetics Department at Stanford. She joined John's Hopkins in July 2014.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114977&date=2018-04-04Seminar 217, Risk Management: The Securitization and Solicited Refinancing Channel of Monetary Policy, Apr 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114356&date=2018-04-05
I document the “securitization and solicited refinancing channel,” a novel transmission mechanism of monetary policy and its heterogenous regional effects. The mechanism predicts that mortgage lenders who sell their originations to Government Sponsored Enterprises or into securitizations no longer hold the loan’s prepayment risk, and when rates drop, these lenders are more likely to signal to their borrowers to refinance, resulting in more borrower refinancing. A regression analysis finds that in response to a decline in mortgage-backed security yields, regions where originate-to-sell-or-securitize lenders operate see more refinancing activity than regions where originate-to-hold lenders operate. The findings have important implications for (i) the efficacy of policy to increase refinancing, lower mortgage payments, and stimulate demand, (ii) the distributional consequences of monetary policy, and (iii) how the Government Sponsored Enterprises and securitization may play a key role in the pass-through to the housing market.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114356&date=2018-04-05Mathematics Department Colloquium, Apr 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116252&date=2018-04-05
The asymmetric simple exclusion process (ASEP) is an interacting particle system introduced in 1970 by Frank Spitzer in Interaction of Markov Processes. Many articles have been published on it in the physics and mathematics literature since then, and it has become a paradigm in modeling and analyzing non-equilibrium traffic systems. In this talk, I will show that beautiful combinatorics emerge from studying this model on a finite line with open boundaries.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116252&date=2018-04-05Talking About Combinatorial Objects Student Seminar, Apr 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116702&date=2018-04-06
In their seminal 1979 paper, Kazhdan and Lusztig introduced a collection of polynomials for any Coxeter group that have (surprising?) connections to a myriad of topics in algebra, combinatorics, and geometry. We will attempt to survey this program, starting from the Hecke algebra, working our way through to computing Kazhdan-Lusztig polynomials, and ending at the construction of the representations of the associated Coxeter system. We will then specialize to Type A to hopefully see the interactions with already established tableau combinatorics. If time permits, I will mention a modification in Type B, as well as applications of Kazhdan-Lusztig polynomials. No prior knowledge of representation theory is strictly needed.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116702&date=2018-04-06Student Probability/PDE Seminar, Apr 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116543&date=2018-04-06
In this talk, I'll prove metastability of the zero range process on a finite set without using capacity estimates. The proof is based on the existence of certain auxiliary functions. One such function is inspired by Evans and Tabrizian's article, "Asymptotics for the Kramers-Smouchowski equations". This function is the solution of a certain equation involving the infinitesimal generator of the zero range process. Another relevant auxiliary function is from a work of Beltran and Landim. We also use martingale problems to characterize Markov processes. Let $p$ be the jump rates of a random walk on a finite set $S$. Assume that the uniform measure on $S$ is an invariant measure of this random walk for simplicity (we expect that our method is applicable for an arbitrary invariant measure $m$). Consider the zero range process on $S$, where the rate the particle jumps from a site $x$ to $y$ with $k$ particles at the site $x$ is given by $g(k) p(x, y).$ Here $g(0) = 0$, $g(1) = 1$, and $g(k) = (k/ k-1)^\alpha , k > 1$ for some $\alpha > 1$. As total number of particles $N \rightarrow \infty $, most of the particles concentrate on a single site. In the time scale $N^{1+\alpha }$, the site of concentration evolves as a Markov chain whose jump rates are proportional to the capacities of the underlying random walk. This talk based on the joint work with F. Rezakhanlou.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116543&date=2018-04-06Student / postdoc PDE seminar, Apr 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116751&date=2018-04-06
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116751&date=2018-04-06Student Arithmetic Geometry Seminar, Apr 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116845&date=2018-04-06
I will discuss Kestutis Cesnavicius' recent preprint https://arxiv.org/abs/1711.06456 in which he proves a purity conjecture due to Grothendieck and Auslander–Goldman, which predicts that if $X$ is a regular Noetherian scheme and $Z \subseteq X$ is a closed subscheme of codimension $\ge 2$, then the restriction map on the cohomological Brauer groups $H^2_{\operatorname {\text {ét}}}(X , \mathbb G_m) \to H^2_{\text {ét}}(X \setminus Z , \mathbb G_m)$ is an isomorphism. The combination of several works by Gabber, including his proof of the absolute purity conjecture, settles the equi-characteristic case; Cesnavicius treats the mixed characteristic case using the tilting equivalence for perfectoid rings.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116845&date=2018-04-06Combinatorics Seminar, Apr 9
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116468&date=2018-04-09
A cluster algebra is a commutative ring determined by an initial "seed," which consists of A-variables, X-variables, and some additional data. Given a seed, one can produce new seeds via a combinatorial process called mutation. The cluster algebra is generated by the variables obtained from all possible sequences of mutations. In this talk, we will focus on cluster algebras of finite type, which are those with finitely many A- and X-variables. The classification of finite type cluster algebras, due to Fomin and Zelevinsky, coincides with the classification of reduced crystallographic root systems. For classical types, the combinatorics of the A-variables and their mutations are encoded by triangulations of marked surfaces associated to each type. In this talk, we will discuss how the X-variables fit into this combinatorial framework. Namely, we will show that in cluster algebras of classical types over the universal semifield, the X-variables are in bijection with the quadrilaterals (with a choice of diagonal) appearing in triangulations of the surface of the appropriate type. Using this bijection, we also give the number of X-variables in each type.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116468&date=2018-04-09Arithmetic Geometry and Number Theory RTG Seminar, Apr 9
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116747&date=2018-04-09
A well-known conjecture (often attributed to Serre) asserts that any motive over any number field has infinitely many ordinary primes, in the sense of the Newton Polygon coinciding with the Hodge Polygon. We will present a few methods for producing more ordinary primes in the case of modular Jacobians — and more generally the part of the (intersection) cohomology of Hilbert modular varieties cut out by cusp forms. If time permits, we will also discuss examples in which our methods fall short.<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=116747&date=2018-04-093-Manifold Seminar, Apr 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116928&date=2018-04-10
We'll discuss Kronheimer-Mrowka's twisted instanton invariant of webs and foam cobordisms. The rank of this invariant for planar webs gives the number of Tait colorings, but the torsion can contain more information (in particular, admits a spectral sequence to their previous untwisted invariant).http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116928&date=2018-04-10Student Harmonic Analysis and PDE Seminar (HADES), Apr 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116846&date=2018-04-10
The Falconer distance problem asks what the smallest Hausdorff dimension of a compact set E in $R^d$ can be such that its distance set D(E) has positive Lebesgue measure. It is conjectured that if dim E is greater than d/2, then dim D(E) is at least 1. We will discuss the relationship between this problem and spherical averages of Fourier transforms of measures and present a result of Wolff that any set of Hausdorff dimension at least 4/3 in the plane has a distance set of positive Lebesgue measure.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116846&date=2018-04-10Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Apr 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116930&date=2018-04-10
Randomness is an important tool in algebra, especially from an algorithmic perspective. I will discuss our recent work looking at the random behavior of monomial ideals. We describe several random models, inspired by earlier models for random graphs and random simplicial complexes, and give results on properties such as Hilbert function and Krull dimension. We also prove "threshold behavior" in the model parameters. In this talk I'll focus on properties related to the minimal free resolutions of random monomial ideals, in particular projective dimension, Cohen-Macaulayness, and genericity/the Scarf complex. I'll also discuss some open problems and ongoing work.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116930&date=2018-04-10Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Apr 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116892&date=2018-04-10
In this talk we will study the equivalence relation generated by linked curves in $ \mathbf P^3 $. In particular we will define the Rao module and show that (up to shifts and duals) it determines the equivalence class. Time permitting we will study curves that are cut out by three surfaces.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116892&date=2018-04-10Topology Seminar (Introductory Talk), Apr 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116890&date=2018-04-11
Evidence of deep connections between contact geometry and Heegaard Floer theory has steadily mounted since the latter theory first appeared a little over a decade ago. In one direction, Heegaard Floer homology supports an invariant which is capable of distinguishing contact structures and detecting tightness. In the other, much of the algebraic structure Heegaard Floer possesses reflects appropriate geometric properties and constructions arising in contact geometry. In this talk, we’ll explore some of these correspondence and connections. In particular, we’ll show how to interpret much of the algebraic structure present in knot Floer homology in contact-geometric terms.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116890&date=2018-04-11A unifying framework for constructing MCMC algorithms from irreversible diffusion processes, Apr 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116700&date=2018-04-11
In this talk, I will first present a general recipe for constructing MCMC algorithms from diffusion processes with the desired stationary distributions. The recipe translates the task of finding valid continuous Markov processes into one of choosing two matrices. Importantly, any diffusion process with the target stationary distribution (given an integrability condition) can be represented in our framework. To simulate the irreversible diffusion processes and correct for bias from discretization error, I will turn to MCMC techniques based on jump processes. Generalization of the Metropolis Hastings algorithm will be introduced---with the same ease of implementation---but allowing for the benefits of irreversible dynamics.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116700&date=2018-04-11Using visualisation to understand R theory, Apr 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116680&date=2018-04-11
In this talk, I will introduce the lobstr package which provides tools to visualise R's data structures on the command line. I'll show three R functions ast(), cst(), and ref() and use them to discuss three important components of R's theory:<br />
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1. All R code possesses a tree like structure, known as the abstract<br />
syntax tree.<br />
2. R's lazy evaluation introduces a tree-like structure into the call stack<br />
3. R's copy on modify semantics<br />
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Together, these three topics make R special compared to other programming languages, and have surprisingly practical implications.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116680&date=2018-04-11Applied Math Seminar, Apr 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116746&date=2018-04-11
A major challenge in materials science is to understand and control the properties of materials based on the microstructure evolution at the mesoscale. For a wide range of materials, the relevant microstructures consist of a network of line objects. In this talk, I will use three examples to illustrate how the study of geometric/topological features of line networks can help us understand the microstructure-property relationship of materials. The first example deals with dislocation line networks in crystals (such as metals) under plastic deformation. Over the last two decades, much effort has been placed on the prediction of stress-strain curve of single crystals through large-scale dislocation dynamics (DD) simulations. Our DD simulations reveal that the dislocation line lengths follow an exponential distribution in a dislocation microstructure of single crystal Cu under uniaxial loading along the [001] direction. A Boltzmann-type theory developed to explain this exponential distribution also reveals the new insights on the origin of strain hardening. In the second example, we consider a coarse-grained molecular dynamics (CGMD) model of an elastomer in which the cross-link bonds can be broken. It is found that bond breaking caused by uniaxial loading does not occur at random locations in the polymer chain network. Instead they occur on shortest paths connecting far away beads (monomers). The evolution of the length distribution of shortest paths is found to control the stress-strain response of the elastomer. The third example is concerned with a planar network of carbon nanotubes (CNTs) on an elastic substrate, acting as a stretchable electrode. The electrical resistance of the CNT network is measured during cyclic loading to progressively larger maximum strains. The hysteretic behavior of the resistance R as a function of strain ε is explained through the evolution of a microstructural parameter, β, the relative coverage of single tubes, with strain. Analytical expressions are obtained for the relation between β and strain ε, and between β and electrical resistance R, which are consistent with both coarse-grained molecular statics (CGMS) simulations and experiments.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116746&date=2018-04-11Topology Seminar (Main Talk), Apr 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116891&date=2018-04-11
We prove that the knot Floer homology of a fibered knot is nontrivial in its next-to-top Alexander grading. Immediate applications include a new proof that L-space knots prime and a classification of knots 3-manifolds with rank 3 knot Floer homology. We will also discuss a numerical refinement of the Ozsvath-Szabo contact invariant. This is joint work with John Baldwin.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116891&date=2018-04-11Seminar 217, Risk Management: The Long-lasting Effects of Propaganda on Financial Risk-Taking, Apr 12
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114357&date=2018-04-12
We argue that emotional coloring of experiences via political propaganda has long-term effects on risk taking. We show that living in an anti-capitalist system reduces individuals' willingness to invest in the stock market even decades later. Utilizing a large comprehensive data set of 300,000 clients of a German discount broker, we find that even today East Germans invest less in the stock market, both at the extensive and the intensive margin, are more likely to hold stocks of communist countries, and are less likely to hold stocks of capitalist institutions and countries. Effects are stronger for individuals for whom we expect stronger emotional priming under the communist regime, for example those living in “showcase cities" renamed after communist politicians and in cities of Olympic gold medalists. In contrast, effects are weaker in regions where people had a less positive experience, including areas with high levels of religiosity, areas that experienced significant environmental pollution, and areas where people did not have (Western) TV entertainment. We show that exposure to anti-capitalist propaganda is costly and results in less diversified portfolios, more expensive actively managed fund, and finally, lower risk-adjusted returns. The long-term effects of anti-capitalist propaganda appear to have significant welfare consequences.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114357&date=2018-04-12Mathematics Department Colloquium, Apr 12
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116887&date=2018-04-12
Most invariants of a symplectic manifold derive in some way from a count of J-holomorphic curves. However, in a general symplectic manifold one often cannot count curves directly in a robust way, i.e. so that the count is independent of the choice of perturbation. Instead one has to define a virtual count. This talk will try to give an elementary description of the problem and will describe some recent approaches to it.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116887&date=2018-04-12Talking About Combinatorial Objects Student Seminar, Apr 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116929&date=2018-04-13
Noncrossing partitions are a subset of partitions that behave nicely with respect to an underlying total order of the ground set. These simple to define objects appear in topics ranging from total positivity to noncommutative probability. In this talk, we will focus on the combinatorial aspects of noncrossing partitions and their relation with a few other topics in combinatorics. In the process of building noncrossing partitions of other types, we will be forced to think about Coxeter groups in a different way.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116929&date=2018-04-13Student Probability/PDE Seminar, Apr 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116976&date=2018-04-13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116976&date=2018-04-13Dissertation talk: Detection limits and fluctuation results in some spiked random matrix models, Apr 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116671&date=2018-04-13
In this talk, we will investigate the fundamental limits of detecting the presence of a structured low-rank signal buried inside a large noise matrix. This setting serves among other things as a simple model for principal component analysis: Given a set of data points in Euclidean space, find out whether there exists a distinguished direction (a "spike") along which these data points align. <br />
It is known from random matrix theory that the top eigenpair of the data matrix becomes indicative of the presence of the spike when and only when the strength of the spike is above a certain "spectral" threshold.<br />
A natural question is then whether it is possible to identify the spike, or even tell if it's really present in the data below this spectral threshold? <br />
I will show that the answer depends on the structure of this spike and then completely characterize the fundamental limits of its detection and estimation. <br />
The analysis leading to this characterization relies on a connection with the mean-field theory of spin glasses, more specifically the study of the Sherrington-Kirkpatrick spin-glass model. <br />
I will introduce the necessary tools and show how they can be used to obtain a precise control on the behavior of the posterior distribution of the spike as well as the fluctuations of the associated likelihood ratio process.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116671&date=2018-04-13CANCELED: Student / postdoc PDE seminar, Apr 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116927&date=2018-04-13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116927&date=2018-04-13Combinatorics Seminar, Apr 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116469&date=2018-04-16
The classical Arrow's Theorem answers "how can n voters obtain a collective preference on a set of outcomes, if they have to obey certain constraints?" We give an analogue of this theorem in the judgment aggregation framework of List and Pettit, answering "how can n judges obtain a collective judgment on a set of logical propositions, if they have to obey certain constraints?" We introduce the concept of "normal pairs" of functions on the Hamming cube, which we analyze with Fourier analysis and elementary combinatorics. We obtain judgment aggregation results and compare them with existing theorems in the literature. Amusingly, the non-dictatorial classes of functions that arise are precisely the classical logical functions OR, AND, and XOR, meaning that they have yet another special place in the nature of logic.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116469&date=2018-04-16Probabilistic Operator Algebra Seminar, Apr 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=115278&date=2018-04-16
Several different models exist for quantum strategies for non-local games (e.g. the graph coloring game ). Different sets correspond to different sets of correlation matrices. Open questions about these sets of correlation matrices remain, including some that are equivalent to Connes' Embedding Conjecture. One set of correlation matrices is the set arising from finite dimensional projections. The question of whether this set is always closed was solved by William Slofstra in early 2017.<br />
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In this talk we will briefly introduce the theory of quantum strategies for non-local games and the corresponding set of correlation matrices, and we will describe the current state of knowledge about them. Then we will discuss a newer proof of Slofstra's result, which actually works for games with fewer inputs and outputs than Slofstra required. The latter result is joint work with Vern Paulsen and Jitendra Prakash.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=115278&date=2018-04-16Arithmetic Geometry and Number Theory RTG Seminar, Apr 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=115572&date=2018-04-16
I discuss work with Cai, Ginzburg and Kaplan that allows us to establish liftings for spaces of automorphic forms (first proved by Arthur) without using the trace formula. The converse theorem has long been understood as an alternative to the trace formula for such liftings, but it requires information about Rankin-Selberg L-functions. Until recently it was not possible to obtain this information in general, but we are now able to do so.<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=115572&date=2018-04-163-Manifold Seminar, Apr 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117051&date=2018-04-17
Knots and spatial graphs can be represented as diagrams, which are planar graphs with special $4$-valent vertices for the crossings. Kauffman proposed considering diagrams on non-planar surfaces as well, and the corresponding objects are called virtual knots and virtual spatial graphs. In this talk, I will describe the Brauer category (a Tempereley-Lieb-like category for diagrams on surfaces), an extension of the flow polynomial to surface graphs, and an extension of the Yamada polynomial to virtual spatial graphs. Combined with another extension of the Yamada polynomial by Fleming and Mellor, I will describe a partial test for whether a virtual spatial graph is not virtually equivalent to a spatial graph.<br />
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This is joint work with Calvin McPhail-Snyder.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117051&date=2018-04-17Student Harmonic Analysis and PDE Seminar (HADES), Apr 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117011&date=2018-04-17
I will discuss some partial progress towards the construction of global in time solutions to the energy critical wave maps equation with $S^2$ target, in the 1 equivariance class.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117011&date=2018-04-17Rigid structures in the universal enveloping traffic space, Apr 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116832&date=2018-04-18
For a tracial $*$-probability space $(\mathcal{A}, \varphi)$, C\'{e}bron, Dahlqvist, and Male constructed an enveloping traffic space $(\mathcal{G}(\mathcal{A}), \tau_\varphi)$ that extends the trace $\varphi$. The CDM construction provides a universal object that allows one to appeal to the traffic probability framework in generic situations, prioritizing an understanding of its structure. We show that $(\mathcal{G}(\mathcal{A}), \tau_\varphi)$ comes equipped with a canonical free product structure, regardless of the choice of $*$-probability space $(\mathcal{A}, \varphi)$. If $(\mathcal{A}, \varphi)$ is itself a free product, then we show how this structure lifts into $(\mathcal{G}(\mathcal{A}), \tau_\varphi)$. Here, we find a duality between classical independence and free independence. We apply our results to prove the asymptotic freeness of a large class of dependent random matrices, generalizing results of Bryc, Dembo, and Jiang and of Mingo and Popa. The talk will be accessible to non-specialists in non-commutative probability. This is joint work with Camille Male.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116832&date=2018-04-18Global Testing Against Sparse Alternatives under Ising Models, Apr 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116985&date=2018-04-18
We study the effect of dependence on detecting sparse signals. In particular, we focus on global testing against sparse alternatives for the magnetizations of an Ising model and establish how the interplay between the strength and sparsity of a signal determines its detectability under various notions of dependence (i.e. the coupling constant of the Ising model). The impact of dependence can be illustrated under the Curie-Weiss model where one observes the effect of a "thermodynamic" phase transition. In particular, the critical state exhibits a subtle "blessing of dependence" phenomenon in that one can detect much weaker signals at criticality than otherwise. Furthermore, we develop a testing procedure that is broadly applicable to account for dependence and show that it is asymptotically minimax-separation optimal under some regularity conditions.<br />
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This talk is based on joint work with Sumit Mukherjee and Ming Yuan.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116985&date=2018-04-18Seminar 217, Risk Management: Could Probability of Informed Trading Predict Market Volatility?, Apr 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114388&date=2018-04-19
Significant market events such as Flash Crash of 2010 undermine the trust of the capital market system. An ability to forecast such events would give market participants and regulators time to react to such events and mitigate their impact. For this reason, there have been a number of attempts to develop early warning indicators. In this work, we explore one such indicator named Probability of Informed Trading (typically shorten as PIN) and its variants. In an earlier test, a variant known as VPIN was demonstrated to show a strong signal more than an hour before the Flash Crash of 2010. There have been a number of articles published on whether or not the VPIN signal is accidental. By employing a supercomputer, we are able to systematically examine the effectiveness of a number of variants of PIN. In this talk, we will discuss how the computing power helps us explore the parameters controlling the performance of PIN, leading us to find more effective way to use PIN.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114388&date=2018-04-19Mathematics Department Colloquium, Apr 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116893&date=2018-04-19
I will describe the mirror dual object to a Grassmannian, which was introduced in joint work with Robert Marsh, and explain two different aspects of mirror symmetry in this setting. In both applications Gromov-Witten invariants come up, in different ways.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116893&date=2018-04-19Topology Seminar (Introductory Talk), Apr 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116971&date=2018-04-20
I will give an overview of veering triangulations, a combinatorial tool introduced by Agol that describes hyperbolic manifolds with pseudo-Anosov bundle or flow structures.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116971&date=2018-04-20Student Probability/PDE Seminar, Apr 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117052&date=2018-04-20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117052&date=2018-04-20Topology Seminar (Main Talk), Apr 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116972&date=2018-04-20
Agol introduced veering triangulations of mapping tori, whose combinatorics are canonically associated to the pseudo-Anosov monodromy. Guéritaud and Agol generalised an alternative construction to any closed manifold equipped with a pseudo-Anosov flow without perfect fits. Using Mosher's dynamic pairs, we prove the converse, showing that veering triangulations are a perfect combinatorialisation of such flows.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116972&date=2018-04-20Student / postdoc PDE seminar, Apr 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117012&date=2018-04-20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117012&date=2018-04-20Combinatorics Seminar, Apr 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117191&date=2018-04-23
Despite the fact that it converges on no open subset of the complex plane, the Kontsevich-Zagier series has a number of interesting combinatorial, number-theoretic, and topological properties. I will discuss some of these properties, such as quantum modularity, Ramanujan-type congruences, q-identities, and a relation to the colored Jones polynomial of the trefoil knot, along with a program to extend them to the so-called generalized Kontsevich-Zagier series.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117191&date=2018-04-23Probabilistic Operator Algebra Seminar, Apr 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116750&date=2018-04-23
We explore the theory of Minoru Tomita (later polished and developed more by Masamichi Takesaki) on modular automorphisms of von Neumann algebras. This is a vast subject, and one cannot hope to cover it in one talk. As a result we will look at some basic notions and build a flavor for this subject in this presentation. The theory has led to some important classification results of Type III factors, which were once considered untamable beasts.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116750&date=2018-04-23Differential Geometry Seminar, Apr 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117050&date=2018-04-23
We discuss several (related) homogeneous fully nonlinear elliptic equations which originated from Kahler geometry and conformal geometry. We mainly focus on a class of equations introduced by Gursky and Streets. We discuss the existence and regularity of this equation and its application to the sigma-2 problem in conformal geometry.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117050&date=2018-04-23BLISS Seminar: Stabilizing Gradients for Deep Neural Networks, Apr 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117177&date=2018-04-23
Vanishing and exploding gradients are two main obstacles in training deep neural networks, especially when trying to capture long range dependencies in recurrent neural networks (RNNs). In this talk, I will present an efficient parametrization of the transition matrix of an RNN that stabilizes the gradients that arise in its training. Specifically, we parameterize the transition matrix by its singular value decomposition (SVD), which allows us to explicitly track and control its singular values. We attain efficiency by using tools that are common in numerical linear algebra, namely Householder reflectors for representing the orthogonal matrices that arise in the SVD. We present results on the Inline Search Suggestions (ISS) application at Amazon Search.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117177&date=2018-04-233-Manifold Seminar, Apr 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117174&date=2018-04-24
Following the paper of John Pardon of the same title, we will see that there does not exist a faithful action of the p-adic integers on any connected 3-manifold. This is equivalent to showing that any locally compact topological group that acts faithfully on a connected 3-manifold has to be a Lie Group.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117174&date=2018-04-24Topology Seminar (Introductory Talk), Apr 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117204&date=2018-04-25
Polyfold theory, as developed by Hofer, Wysocki, and Zehnder, is a relatively new approach to resolving transversality issues that arise in the study of J-holomorphic curves in symplectic geometry. In this talk I explain the polyfold theoretic approach to defining the Gromov-Witten invariants for all closed symplectic manifolds.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117204&date=2018-04-25The weak Pinsker property, Apr 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117180&date=2018-04-25
This talk is about the structure theory of measure-preserving systems: transformations of a finite measure space that preserve the measure. Many important examples arise from stationary processes in probability, and simplest among these are the i.i.d. processes. In ergodic theory, i.i.d. processes are called Bernoulli shifts. Some of the main results of ergodic theory concern an invariant of systems called their entropy, which turns out to be intimately related to the existence of `structure preserving' maps from a general system to Bernoulli shifts.<br />
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I will give an overview of this area and its history, ending with a recent advance in this direction. A measure-preserving system has the weak Pinsker property if it can be split, in a natural sense, into a direct product of a Bernoulli shift and a system of arbitrarily low entropy. The recent result is that all ergodic measure-preserving systems have this property. Its proof depends on a new theorem in discrete probability: a probability measure on a finite product space such as A^n can be decomposed as a mixture of a controlled number of other measures, most of them exhibiting a strong `concentration' property. I will sketch the connection between these results and the proof of the latter, to the extent that time allows.<br />
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I will assume a basic graduate-level background in real analysis and measure-theoretic probability, but little beyond that.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117180&date=2018-04-25Applied Math Seminar, Apr 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117189&date=2018-04-25
The numerical simulation of multiphysics problems is significant in many engineering and scientific applications, e.g., aircraft flutter in transonic flows, biomedical flows in heart and blood vessels, mixing and chemically reacting flows, reactor fuel performance, turbomachinery and so on. These problems are generally highly nonlinear, feature multiple scales and strong coupling effects, and require heterogeneous discretizations for the various physics subsystems. Due to dramatic improvement of single-physics solvers during the last two decades, partitioned procedures for multiphysics system become dominant, which exploit single-physics software components and facilitate mathematical modeling. However, these schemes are often low-order accurate (second order accuracy) and suffer from lack of stability (subiteration is needed).<br />
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To relieve these issues, we introduce a general framework for constructing high-order, linearly stable, partitioned solvers for multiphysics problems. The coupled ODE system of the multiphysics problems is taken as a monolithic system and discretized using an implicit-explicit Runge-Kutta (IMEX-RK) discretization based the concept of a predictor for the coupling term. We propose four coupling predictors inspired by basic ideas of weak/strong coupling effects, Jacobi method, and Gauss-Seidel method, which enable the monolithic system to be solved in a partitioned manner, i.e., subsystem-by-subsystem, and preserve the design order of accuracy of the monolithic scheme. We also analyze the stability on a coupled, linear model problem and show that one of the partitioned solvers achieves unconditional linear stability, while the others are unconditionally stable only for certain values of the coupling strength. Furthermore, a fully-discrete adjoint solver derived from our partitioned solvers, is applied for time-dependent PDE constraint optimization. (Joint work with Per-Olof Persson and Matthew J. Zahr)http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117189&date=2018-04-25Topology Seminar (Main Talk), Apr 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117205&date=2018-04-25
In 1994 Kontsevich and Manin stated the Gromov-Witten axioms, given as a list of formal relations between the Gromov-Witten invariants. In this talk I prove several of the Gromov-Witten axioms for curves of arbitrary genus for all closed symplectic manifolds.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117205&date=2018-04-25Seminar 217, Risk Management: Statistical Arbitrage, Apr 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116677&date=2018-04-26
Statistical arbitrage is a collection of trading algorithms that are widely used today but can have very uneven performance, depending on their detailed implementation. I will introduce these methods and explain how the data used as trading signals are prepared so that they depend weakly on market dynamics but have adequate statistical regularity. The trading algorithm itself will be presented and then a well calibrated version of it will be used on daily SP500 data from 2003-2014. Well calibrated means that the risk associated with this trading algorithm can be identified and controlled effectively. It also emerges from this study of statistical arbitrage algorithms that when tested with real data they can produce strong and steady returns that are essentially decoupled from overall market behavior. (Joint work with J. Yeo.)http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116677&date=2018-04-26Ribosomes, traffic jams, and phase transitions, Apr 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116986&date=2018-04-26
Since its introduction, the totally asymmetric simple exclusion process (TASEP) has been widely used to model transport phenomena in non-equilibrium interacting particle systems. Many mathematicians and physicists have studied this stochastic process under various conditions motivated by a broad range of applications. In biology, for example, the TASEP has been used to describe the dynamics of mRNA translation by ribosomes. Despite much progress, when particles have an extended size and hop at site-dependent rates, theoretically analyzing the behavior of the system and the associated phase transitions has remained challenging. In this talk, I will describe such an analysis, and present closed-form formulas for steady-state particle densities and currents. I will then discuss new biological insights resulting from this theoretical work. (Joint work with Dan Erdmann-Pham and Khanh Dao Duc.)http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116986&date=2018-04-26Mathematics Department Colloquium, Apr 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117053&date=2018-04-26
A K3 surface is a simply connected compact complex surface with trivial canonical bundle. Moduli space of K3 surfaces has been extensively studied in algebraic geometry and it can be characterized in terms of the period map by the Torelli theorem. The differential geometric significance is that every K3 surface admits a hyperkahler metric (a metric whose holonomy group is SU(2)), which is in particular Ricci-flat. The understanding of limiting behavior of a sequence of hyperkahler K3 surfaces gives prototype for more general questions concerning Ricci curvature in Riemannian geometry. In this talk I will survey what is known on this, and talk about a new glueing construction, joint with Hans-Joachim Hein, Jeff Viaclovsky and Ruobing Zhang, that shows a multi-scale collapsing phenomenon, and discuss the connection with the Kulikov classification in algebraic geometry.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117053&date=2018-04-26Probabilistic Operator Algebra seminar, Apr 27
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116656&date=2018-04-27
Nicolas Monod has in a recent paper introduced a new class of groups with the fixed-point property for cones, characterized by always admitting a non-trivial fixed-point whenever they act on cones (under some additional hypothesis). He showed that this class contains all groups of sub-exponential growth and is contained in the class of supramenable groups. (It is not known if these three classes are distinct). He proved a number of equivalent conditions to be a group with the fixed-point property for cones, and he established a list of permanence properties for this class of groups. Monod's results have applications for the existence of invariant traces on a (non-unital) C*-algebra equipped with an action of a group. The purpose of the talk will be to explain some of Monod's results and their applications to C*-algebras. As an example we describe traces on the Roe algebra.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116656&date=2018-04-27Probabilistic Operator Algebra Seminar, Apr 27
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116749&date=2018-04-27
In joint work with Haagerup, we established in 2015 a reformulation of the Connes embedding problem in terms of an asymptotic property of quantum channels posessing a certain factorizability property, introduced by Anantharaman-Delaroche in the setting of Markov maps between von Neumann algebras. I will discuss new results concerning the class of channels which exactly factor through matrix algebras, and a number of open problems. I will also discuss ongoing work, joint with Brown and Rordam, related to the remarkable recent breakthrough of Slofstra concerning sets of quantum correlations.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=116749&date=2018-04-27Talking About Combinatorial Objects Student Seminar, Apr 27
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117203&date=2018-04-27
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117203&date=2018-04-27Student Probability/PDE Seminar, Apr 27
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117230&date=2018-04-27
It has been known that even when the vector field has no regularity, if ODE is perturbed by non-degenerate Brownian motion, then one can construct a solution. In this talk, we discuss a similar phenomenon when generating Brownian motion is degenerate but hypoelliptic. I will introduce a basic theory of the analysis on Lie groups and how this theory can be applied to prove the probabilistic results.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117230&date=2018-04-27Differential Geometry Seminar, Apr 30
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117193&date=2018-04-30
Consider a compact Calabi-Yau manifold \(X\) with a holomorphic vibration \(F: X \rightarrow B\) over some base \(B\), together with a "collapsing" path of Kahler classes of the form \([F^*\omega _B] + t [\omega _X]\) for \(t \in (0,1]\). Understanding the limiting behavior as \(t \rightarrow 0\) of the Ricci-flat Kahler forms representing these classes is a basic problem in geometric analysis that has attracted a lot of attention since the celebrated work of Gross-Wilson (2000) on elliptically fibered K3 surfaces. The limiting behavior of these Ricci-flat metrics is still not well-understood in general even away from the singular fibers of \(F\). A key difficulty arises from the fact that Yau's higher-order estimates for the complex Monge-Ampere equation heavily depend on bounds on the curvature tensor of a suitable background metric, but such bounds are simply not available in this collapsing situation. I will explain recent joint work with Valentino Tosatti where we manage to bypass Yau's method in some cases, proving higher-order estimates even though the background curvature blows up.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117193&date=2018-04-30BLISS Seminar: Phase Transitions in Generalized Linear Models, Apr 30
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117178&date=2018-04-30
We consider generalized linear models (GLMs) where an unknown $n$-dimensional signal vector is observed through the application of a random matrix and a non-linear (possibly probabilistic) componentwise output function. <br />
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We study the models in the high-dimensional limit, where the observation consists of $m$ points, and $m/n \to \alpha > 0$ as $n \to \infty$. This situation is ubiquitous in applications ranging from supervised machine learning to signal processing.<br />
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We will analyze the model-case when the observation matrix has i.i.d.\ elements and the components of the ground-truth signal are taken independently from some known distribution.<br />
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We will compute the limit of the mutual information between the signal and the observations in the large system limit. This quantity is particularly interesting because it is related to the free energy (i.e. the logarithm of the partition function) of the posterior distribution of the signal given the observations. Therefore, the study of the asymptotic mutual information allows to deduce the limit of important quantities such as the minimum mean squared error for the estimation of the signal.<br />
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We will observe some phase transition phenomena. Depending on the noise level, the distribution of the signal and the non-linear function of the GLM we may encounter various scenarios where it may be impossible / hard (only with exponential-time algorithms) / easy (with polynomial-time algorithms) to recover the signal.<br />
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This is joint work with Jean Barbier, Florent Krzakala, Nicolas Macris and Lenka Zdeborova.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117178&date=2018-04-30Applied Math Seminar, Apr 30
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117190&date=2018-04-30
Many science and engineering applications necessitate the optimal control or design of systems described by partial differential equations (PDEs) with uncertain inputs such as coefficients, boundary conditions and initial conditions. In this talk, I formulate such problems as risk-averse optimization problems in Banach space. For many popular measures of risk such as coherent risk measures, the resulting risk-averse objective function is often nonsmooth and requires an enormous number of samples, and hence PDE solves, to accurately evaluate. Additionally, the nonsmooth objective function precludes the use of rapidly converging derivative-based optimization algorithms. To address these challenges, I present a general smoothing technique for risk measures based on the epigraphical calculus. I show that the resulting smoothed risk measures are differentiable and converge in a variational sense to the original nonsmooth risk measure. Moreover, under mild assumptions, I prove consistency of this smooth approximation for both minimizers and stationary points of the target optimization problem. Under slightly stronger assumptions, I further prove a convergence rate for the minimizers of the smoothed problem. I conclude with numerical examples confirming these results.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117190&date=2018-04-30Arithmetic Geometry and Number Theory RTG Seminar, Apr 30
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=117054&date=2018-04-30
Sen attached to each p-adic Galois representation of a p-adic field a multiset of numbers called generalized Hodge-Tate weights. In this talk, we regard a p-adic local system on a rigid analytic variety as a geometric family of Galois representations and show that the multiset of generalized Hodge-Tate weights of the local system is constant. The pretalk is designed to be a quick introduction to p-adic Hodge theory.<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=117054&date=2018-04-30Avraham Shtub -Technion, Apr 30
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=115031&date=2018-04-30
Professor Avraham Shtub holds the Stephen and Sharon Seiden Chair in Project Management. He has a B.Sc in Electrical Engineering from the Technion - Israel Institute of Technology (1974), an MBA from Tel Aviv University (1978) and a Ph.D in Management Science and Industrial Engineering from the University of Washington (1982). He is a certified Project Management Professional (PMP) and a member of the Project Management Institute (PMI-USA). <br />
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Professor Shtub is the recipient of the Institute of Industrial Engineering's 1995 "Book of the Year Award" for his Book "Project Management: Engineering, Technology and Implementation" (co- authored with Jonathan Bard and Shlomo Globerson), Prentice Hall, 1994. He is the recipient of the Production Operations Management Society's Wick Skinner Teaching Innovation Achievements Award for his book: "Enterprise Resource Planning (ERP): The Dynamics of Operations Management". His books on Project Management were published in English, Hebrew, Greek and Chinese. He is the recipient of the 2008 Project Management Institute Professional Development Product of the Year Award for the training simulator "Project Team Builder – PTB". Prof. Shtub was a Department Editor for IIE Transactions he was on the Editorial Boards of the Project Management Journal, The International Journal of Project Management, IIE Transactions and the International Journal of Production Research. <br />
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He was a faculty member of the department of Industrial Engineering at Tel Aviv University from 1984 to 1998 where he also served as a chairman of the department (1993-1996). He joined the Technion in 1998 and was the Associate Dean and head of the MBA program. He has been a consultant to industry in the areas of project management, training by simulators and the design of production-operation systems. He was invited to speak at special seminars on Project Management and Operations in Europe, the Far East, North America, South America and Australia. Professor Shtub visited and taught at Vanderbilt University, The University of Pennsylvania, Korean Institute of Technology, Bilkent University in Turkey, Otego University in New Zealand, Yale University, Universidad Politécnica de Valencia, University of Bergamo in Italy.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=115031&date=2018-04-30