Mathematics
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Upcoming EventsStudent Probability/PDE Seminar, Apr 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125045&date=2019-04-26
We revisit the [R. Jordan, D. Kinderlehrer, and F. Otto. The variational formulation of the Fokker-Planck equation (1998)] variational characterization of diffusion as entropic gradient flux, and provide for it a probabilistic interpretation based on stochastic calculus. It was shown by Jordan, Kinderlehrer, and Otto that, for diffusions of Langevin-Smoluchowski type, the Fokker-Planck probability density flow minimizes the rate of relative entropy dissipation, as measured by the distance traveled in terms of the quadratic Wasserstein metric. We obtain novel, stochastic-process versions of these features, valid along almost every trajectory of the diffusive motion in both the forward and, most transparently, the backward, directions of time, using a very direct perturbation analysis; the original results follow then simply by taking expectations. As a bonus, we derive the Cordero-Erausquin version of the so-called HWI inequality relating relative entropy, Fisher information and Wasserstein distance.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125045&date=2019-04-26Deformation Theory Seminar, Apr 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125466&date=2019-04-26
We will review the construction of generators in MF categories, following work of a Dyckerhoff, Orlov and othershttp://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125466&date=2019-04-26Representation Theory and Mathematical Physics Seminar, Apr 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125068&date=2019-04-26
Hurwitz numbers enumerate branched coverings of the Riemann sphere with specified branching profiles. \(\tau \)-functions of hypergeometric type for the KP and \(2D\)-Toda integrable hierarchies serve as combinatorial generating functions for weighted sums over Hurwitz numbers, with weights chosen as symmetric functions of a set of auxiliary parameters determined by a weight generating function. This talk will explain how multicurrent correlators may be used to explicitly generate weighted Hurwitz numbers as weighted polyonomials in the Taylor coefficients of the weight generating function, without any knowledge required either of symmetric group characters or the Kostka matrices relating different bases of the ring of symmetric functions. The case of rational weight generating functions will be the main illustrative example.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125068&date=2019-04-26Tarski Lecture, Apr 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125072&date=2019-04-26
In 1995, Kontsevich introduced a new form of integration, call motivic integration. From the start, the development of motivic integration has been guided by model theory, especially quantifier elimination. One particularly useful result has been a far-reaching generalization of the Ax-Kochen-Ersov transfer principle in logic to integration. This talk will give a gentle introduction to motivic integration and will highlight some applications to the Langlands program.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125072&date=2019-04-26Student 3-Manifold Seminar, Apr 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125514&date=2019-04-26
We will continue our discussion of spaces that are the complement of a knot or link in $S^3$, and then we will talk about Conway's normalization of the Alexander polynomial. If time permits, we will see the definition of the Jones polynomial via the Kauffman bracket.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125514&date=2019-04-26