Nguyen Viet Dang (Paris): Value at zero of Poincaré series of surfaces
Abstract: We will discuss an identity, found with Gabriel Rivière, which expresses the value at 0 of Poincaré series of any surface with negatively curved metric in terms of the Euler characteristic of the surface. Hence a Dirichlet series which depends on geodesic length has a zero value which is topological.
Yagna Dutta (Leiden): D-modules in Hyperkähler geometry
Abstract: D-modules are omnipresent in various branches of mathematics. For example, M. Saito has used this framework in vastly generalising the study of the variation of Hodge structures arising from families of varieties. This theory has recently seen interesting applications in studying Lagrangian fibrations of Hyperkähler manfolds, a very special kind of degenerating family of abelian varieties that mimics elliptic fibrations of K3 surfaces in higher dimensions. In this talk, I will focus on an application of M. Saito's theory, that among other things, allows us to construct an interesting group scheme on the base of the Lagrangian fibrations. The talk will be partially based on a joint work in progress with Dominique Mattei and Evgeny Shinder.
Jessica Fintzen (Bonn): The category of representations of p-adic groups and Hecke algebras
Abstract: An explicit understanding of the category of all (smooth, complex) representations of p-adic groups provides an important tool in the construction of an explicit and a categorical local Langlands correspondence and also has applications to the study of automorphic forms. The category of representations of p-adic groups decomposes into
subcategories, called Bernstein blocks. I will give an overview of what we know about the structure of the Bernstein blocks. In particular, I will discuss a joint project with Adler, Mishra and Ohara in which we show that general Bernstein blocks are equivalent to much better understood depth-zero Bernstein blocks. This is achieved via an isomorphism of Hecke
algebras and allows to reduce a lot of problems about the (category of) representations of p-adic groups to problems about representations of finite groups of Lie type, where answers are often already known or easier to achieve.
Sharmila Gunasekaran (Nijmegen): Quasi Einstein manifolds
Abstract: A quasi-Einstein manifold is a triplet (M,g,X) where (M,g) is a closed Riemannian manifold and X is a one form. In this talk, I will elaborate the connection between quasi-Einstein manifolds and extreme black holes (these are black holes at ‘zero temperature’). I will then provide an overview of concepts and key results that help us understand these manifolds better. The results mentioned are a collaborative effort with Eric Bahuaud, Hari Kunduri, and Eric Woolgar.
Clover May (Trondheim): Classifying modules of equivariant Eilenberg-MacLane spectra
Abstract: Cohomology with Z/p-coefficients is represented by a stable object, an Eilenberg-MacLane spectrum HZ/p. Classically, since Z/p is a field, any module over HZ/p splits as a wedge of suspensions of HZ/p itself. Equivariantly, cohomology and the module theory of G-equivariant Eilenberg--MacLane spectra are much more complicated.
For the cyclic group G=C_p and the constant Mackey functor Z/p, there are infinitely many indecomposable HZ/p-modules. Previous work together with Dugger and Hazel classified all indecomposable HZ/2-modules for the group G=C_2. The isomorphism classes of indecomposables fit into just three families. By contrast, we show for G=C_p with p an odd prime, the classification of indecomposable equivariant HZ/p-modules is wild. This is joint work in progress with Grevstad.
Thomas Rot (VU Amsterdam): Differential topology in infinite dimensions
Abstract: Infinite dimensional manifolds, and mappings between them, play an important role in the study of non-linear PDE's. In this talk I will discuss work, together with Alberto Abbondandolo, Lauran Toussaint and Michael Jung, extending classical ideas from differential topology to the infinite dimensional setting.
David Schwein (Bonn): Tame supercuspidals at very small primes
Abstract: Supercuspidal representations are the elementary particles in the representation theory of reductive p-adic groups. Constructing such representations explicitly, via (compact) induction, is a longstanding open problem, solved when p is large. When p is small, the remaining supercuspidals are expected to have an arithmetic source: wildly ramified field extensions. In this talk I’ll discuss ongoing work joint with Jessica Fintzen that identifies a second, Lie-theoretic, source of new (tame!) supercuspidals: special features of root systems at very small primes.
Boris Vertman (Oldenburg): Microlocal Analysis on manifolds with fibered boundaries
Abstract: We discuss spectral geometric questions on on some non-compact manifolds with fibered boundaries. Main examples include non-compact complete hyper-Kähler 4-manifolds and scattering spaces. We discuss how such spaces naturally arise in the analysis of analytic torsion under degeneration of a smooth compact manifold to a space with conical singularities.
