## Huajie Li : On an infinitesimal variant of Guo-Jacquet trace formulae

- Uploaded by schrett ( 31 Views )A well-known theorem of Waldspurger relates central values of automorphic L-functions for GL(2) to automorphic period integrals over non-split tori. His result was reproved by Jacquet via the comparison of relative trace formulae. Guo-Jacquet抯 conjecture aims to generalise Waldspurger抯 result as well as Jacquet抯 approach to higher dimensions. In this talk, we shall first recall the background of Guo-Jacquet trace formulae. Then we shall focus on an infinitesimal variant of these formulae and try to explain several results on the local comparison of most terms. Our infinitesimal study is expected to be relevant to the study of geometric sides of the original Guo-Jacquet trace formulae.

## Oguz Savk : Bridging the gaps between homology planes and Mazur manifolds.

- Uploaded by ezy3 ( 36 Views )We call a non-trivial homology 3-sphere a Kirby-Ramanujam sphere if it bounds a homology plane, an algebraic complex smooth surface with the same homology groups of the complex plane. In this talk, we present several infinite families of Kirby-Ramanujam spheres bounding Mazur type 4-manifolds, compact contractible smooth 4-manifolds built with only 0-, 1-, and 2-handles. Such an interplay between complex surfaces and 4-manifolds was first observed by Ramanujam and Kirby around nineteen-eighties. This is upcoming joint work with Rodolfo Aguilar Aguilar.

## David Herzog : Hypocoercivity for Langevin dynamics

- Uploaded by schrett ( 27 Views )This will be the last in his sequence of an introductory lecture on Hypocoercivity for Langevin dynamics. For those who have not attended the previous lectures and are familiar with Langevin dynamics, the talk should be accessible. We will continue our discussion on convergence to equilibrium for second-order Langevin dynamics using the Poincare approach. We'll recap convergence in H^1(\mu) and then we'll talk about the direct L^2(\mu) method of Dolbeault, Mouhot, and Schmeiser, also called the DMS approach.

## Edna Jones : The Kloosterman circle method and weighted representation numbers of positive definite quadratic forms

- Uploaded by schrett ( 29 Views )We develop a version of the Kloosterman circle method with a bump function that is used to provide asymptotics for weighted representation numbers of positive definite integral quadratic forms. Unlike many applications of the Kloosterman circle method, we explicitly state some constants in the error terms that depend on the quadratic form. This version of the Kloosterman circle method uses Gauss sums, Kloosterman sums, Sali茅 sums, and a principle of nonstationary phase. If time permits, we may discuss a potential application of this version of the Kloosterman circle method to a proof of a strong asymptotic local-global principle for certain Kleinian sphere packings.

## Benedict Morrissey : Regular quotients and Hitchin fibrations (joint work with Ng么 B.-C.)

- Uploaded by schrett ( 35 Views )Orbital integrals for the Lie algebra can be analyzed using the Hitchin fibration. In turn the Hitchin fibration can be analyzed via the morphism g^{reg} ----> g//G from the regular elements of the Lie algebra, to the GIT quotient by the adjoint action. In trying to generalize this story by replacing the action of G on g by the action of G on some sufficiently nice variety M, we must replace the GIT quotient with what we call the regular quotient. This talk will look at the reasons for this, and the difference between the GIT and regular quotients in the case of G acting on G by conjugation (when the derived group of G is not simply connected), G acting on the commuting scheme, and G acting on the Vinberg monoid.