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.
In this talk, we consider the following problem: Given the source-to-solution map for a relativistic Boltzmann equation on a neighbourhood $V$ of an observer in a Lorentzian spacetime $(M,g)$ and knowledge of $g|_V$, can we determine (up to diffeomorphism) the spacetime metric $g$ on the domain of causal influence for the set $V$?
On generating ideals by additive subgroups of rings and an application to Bohr compactifications of some matrix groups
Abstract: I will present several fundamental results about generating ideals in finitely many steps inside additive groups of rings from my very recent joint paper with T. Rzepecki. I will also mention an application to computations of definable and classical Bohr compactifications of the groups of upper unitriangular and invertible upper triangular matrices
