Mathematics
http://events.berkeley.edu/index.php/calendar/sn/math.html
Upcoming EventsCombinatorics 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=2018-04-27