One might say that there exist zeta functions of three kinds: the very well-known ones (whose stock example is Riemann's zeta function); some less familiar ones; and at least one type which has been totally forgotten for decades. We intend to mention instances of all three types. The first type is important, if not predominant, in algebraic number theory, as we will try to illustrate by (very few) examples. As examples of the second type we will discuss zeta functions of finite groups.
Abstract: Perturbation theoryworks well for the the discrete spectrum below the essential spectrum. Whathappens if a parameter of a quantum system is tuned in such a way that abound state energy (e.g. the ground state energy) hits the bottom of theessential spectrum? Does the eigenvalue survive, i.e., the correspondingeigenfunction stays $L^2$, or does it dissolve into the continuumenergies?
Abstract: I will review the research about dp-minimal expansions of (Z,+), and then present a recent result classifying (Z,+,<) as the unique dp-minimal expansion of (Z,+) defining an infinite subset of N. All the relevant notions will be defined in the talk.
Abstract: The rel foliation is a foliation of the moduli space of abelian differentials obtained by "moving the zeroes of the one form while keeping all absolute periods fixed". It has been studied in complex analysis and dynamics under different names (isoperiodic foliation, Schiffer variation, kernel foliation). Until recent years the question of its ergodicity was wide open. Recently partial results were obtained by Calsamiglia-Deroin-Francaviglia and by Hamenstadt. In our work we completely resolve the ergodicity question.
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 .
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).
A family of problems in Diophantine geometry has the following form: We fix a collection of "special" algebraic varieties among which the 0-dimensional are called "special points". Mostly, if V is a special variety then the special points are Zariski dense in V, and the problem is to prove the converse: If V is an irreducible algebraic variety and the special points are Zariski dense in V then V itself is special.
Particular cases of the above are the Manin-Mumford conjecture
Universal functions, strong colourings and ideas from PID
A construction of Shelah will be reformulated using the PID to provide alternative models of the failure of CH and the existence of a universal colouring of cardinality. The impact of the range of the colourings will be examined. An application to the theory of strong colourings over partitions will also be given.
