Abstract: We present a geometric condition which is sufficient and necessary for the existence of hyperbolic SRB measures on closed Riemannian manifolds.
Robin boundary conditions are used in heat conductance theory to interpolate between a perfectly insulating boundary, described by Neumann boundary conditions, and a temperature fixing boundary, described by Dirichlet boundary conditions. I have recently started to explore the statistics of these Robin eigenvalues for planar domains, and the fluctuations of the gaps between the Robin and Neumann spectrum, in part driven by numerical experimentation. Read more about Basic Notions: Zeev Rudnik "The Robin eigenvalue problem: statistics and arithmetic"
Repeats every week every Sunday until Sun Jan 17 2021 .
11:00am to 1:00pm
Abstract: A fundamental lemma is an identity relating p-adic integrals on two different groups. These pretty identities fit into a larger story of trace formulas and special values of L-functions. Our goal is to present recent work of Beuzart-Plessis on the Jacquet-Rallis fundamental lemma, comparing integrals on GL(n) and U(n).
Repeats every week every Sunday until Sun Jan 17 2021 .
2:00pm to 4:00pm
Abstract: Given a smooth and proper curve X and a reductive group G one can consider the stack Bun_{G,X} of principal G-bundles on X. This stack has an important role in Algebraic Geometry and Representation Theory especially with regard to the Langlands program. We shall study the geometry of Bun_{G,X} and the category D(G,X) of constructible sheaves on Bun_{G,X}. We shall be especially interested in the subcategory D_{nil}(G,X) of sheaves with nilpotent singular support.
Repeats every week every Sunday until Sun Jan 17 2021 .
4:00pm to 6:00pm
Abstract: We will discuss stability conditions on triangulated categories following the work of Douglas and Bridgeland. Concrete examples of stability conditions will be given from symplectic and algebraic geometry, which will also illustrate mirror symmetry. An effort will be made to give a gentle introduction to the relevant background material from category theory, symplectic geometry and algebraic geometry.
For everynumber field K, there is a finite abelian group C called the class group, which serves as an obstruction to unique factorization. Since Gauss, number theorists have tried to understand questions such as how often is C trivial, or how often C contains an element of fixed order (as K varies). In the 1970's, Cohen and Lenstra observed empirically that when the degree and signature of K is fixed, the isomorphism class of C adheres to a natural probability distribution. I'll discuss these Cohen-Lenstra heuristics and survey what is known, Read more about Basic Notions: Ari Shnidman "Randomness in arithmetic: class groups."
