Mathematics
http://events.berkeley.edu/index.php/calendar/sn/math.html
Upcoming EventsCombinatorics 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=2017-10-25