Mathematics
http://events.berkeley.edu/index.php/calendar/sn/math.html
Upcoming EventsCombinatorics Seminar, Oct 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120823&date=2018-10-22
A Hopf monoid is an algebraic structure that many families of combinatorial objects share. The collection of multiplicative functions defined on a Hopf monoid forms a group, called the character group. Aguiar and Ardila (2017) proved that the character groups for the Hopf monoids of permutahedra and associahedra are exponential power series under multiplication and composition, respectively. In this talk I will introduce the Hopf monoid of orbit polytopes, and then I will discuss some of my recent work on determining the structure of the character group of this Hopf monoid.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120823&date=2018-10-22String-Math Seminar, Oct 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120980&date=2018-10-22
I will describe a construction which, for a given \(4d\), \(N=2\) Argyres-Douglas SCFT, seems to produce a three-dimensional TQFT, whose underlying modular tensor category coincides with that of a \(2d\) chiral algebra of the parent \(4d\), \(N=2\) theory.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120980&date=2018-10-22Arithmetic Geometry and Number Theory RTG Seminar, Oct 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120940&date=2018-10-22
Shimura varieties attached to unitary similitude groups are a well-studied class of PEL Shimura varieties (i.e., varieties admitting a moduli description in terms of abelian varieties endowed with a polarization, endomorphisms, and a level structure). There are also natural Shimura varieties attached to (honest) unitary groups; these lack a moduli interpretation, but they have other advantages (e.g., they give rise to interesting cycles of the sort that appear in the arithmetic Gan-Gross-Prasad conjecture). I will describe some variant Shimura varieties which enjoy good properties from both of these classes. This is joint work with M. Rapoport and W. Zhang.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120940&date=2018-10-22Differential Geometry Seminar, Oct 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120724&date=2018-10-22
The notion of a harmonic Z/2 spinor was introduced by Taubes as an abstraction of various limiting objects appearing in compactifications of gauge-theoretic moduli spaces. I will explain this notion and discuss an existence result for harmonic Z/2 spinors on three-manifolds. The proof uses a wall-crossing formula for solutions of generalized Seiberg-Witten equations in dimension three, a result itself motivated by Yang-Mills theory on Riemannian manifolds with special holonomy $G_2$. The talk is based on joint work with Thomas Walpuski.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120724&date=2018-10-22Mathematical Theories of Communication: Old and New, Oct 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120115&date=2018-10-22
Reliable and efficient digital communication is possible today largely due to some wonderful successes in mathematical modelling and analysis. A legendary figure in this space is Claude Shannon (1916-2001) who laid out the mathematical foundations of communication in his seminal 1948 treatise, where among other contributions he gave a mathematical definition of "entropy" and coined the now ubiquitous term "bit" (for binary digit). But Shannon's theory is not the last word in communication. Communication extends to settings well beyond the carefully designed full information exchange model explored in Shannon's work. In this talk I will try to describe some of the many extensions that have been explored in the interim period including communication complexity (Yao 1980) that explores how it might be possible to achieve effective communication without a full exchange; interactive communication (Schulman 1992) which explores how to cope with errors in an interactive setting, and some of our own work on uncertain communication, which explores how shared context can make communication more effective, even if the context is shared only loosely.<br />
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Light refreshments will be served before the lecture at 3:30 p.m.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120115&date=2018-10-22CANCELED: Analysis and PDE Seminar, Oct 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=121012&date=2018-10-22
I will discuss joint work with Cristian Gavrus and Daniel Tataru in which we study wave maps on a (1+2)-dimensional nonsmooth background. Our main result asserts that in this context, the wave maps system is locally wellposed at almost critical regularity.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=121012&date=2018-10-22Deformation Theory Seminar, Oct 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=121016&date=2018-10-22
In this talk we'll introduce operads and the interaction with sheaf theory. Parallel to the notion of Koszul algebras, we'll define Koszul operads and duality between them. In particular, connections with sheaves and Verdier duality will be explained in an example arising from the moduli spaces of genus zero stable curves with marked points.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=121016&date=2018-10-22