12:00
12:00
12:00
Macroscopic temperature profiles in non-equilibrium stationary states
Abstract
Systems that have more than one conserved quantity (i.e. energy plus momentum, density etc.), can exhibit quite interesting temperature profiles in non-equilibrium stationary states. I will present some numerical experiment and mathematical result. I will also expose some other connected problems, always concerning thermal boundary conditions in hydrodynamic limits.
12:00
Patlak-Keller-Segel equations
Abstract
Patlak-Keller-Segel equations
ut−Lu=−div(u∇v)vt−Δv=u,
where L is a dissipative operator, stem from mathematical chemistry and mathematical biology.
Their variants describe, among others, behaviour of chemotactic populations, including feeding strategies of zooplankton or of certain insects. Analytically, Patlak-Keller-Segel equations reveal quite rich dynamics and a delicate global smoothness vs. blowup dichotomy.
We will discuss smoothness/blowup results for popular variants of the equations, focusing on the critical cases, where dissipative and aggregative forces seem to be in a balance. A part of this talk is based on joint results with Rafael Granero-Belinchon (Lyon).
12:00
A variational perspective on wrinkling patterns in thin elastic sheets
Abstract
14:00
A Ringel duality formula inspired by Knörrer equivalences for 2d cyclic quotient singularities
Abstract
We construct triangle equivalences between singularity categories of
two-dimensional cyclic quotient singularities and singularity categories of
a new class of finite dimensional local algebras, which we call Knörrer
invariant algebras. In the hypersurface case, we recover a special case of Knörrer’s equivalence for (stable) categories of matrix factorisations.
We’ll then explain how this led us to study Ringel duality for
certain (ultra strongly) quasi-hereditary algebras.
This is based on joint work with Joe Karmazyn.
Euclidean lattices of infinite rank and Diophantine applications
Abstract
I will discuss the definitions and the basic properties of some infinite dimensional generalizations of Euclidean lattices and of their invariants defined in terms of theta series. Then I will present some of their applications to transcendence theory and Diophantine geometry.
Minimal weights of mod-p Hilbert modular forms
Abstract
I will discuss results on the characterization of minimal weights of mod-p Hilbert modular forms using results on stratifications of Hilbert Modular Varieties. This is joint work with Fred Diamond.
P-adic representations attached to vector bundles on smooth complete p-adic varieties
Abstract
We discuss vector bundles with numerically stable reduction on smooth complete varieties over a p-adic number field and sketch the construction of associated p-adic representations of the geometric fundamental group. On projective varieties, such bundles are semistable with respect to every polarization and have vanishing Chern classes. One of the main problems in the construction consisted in getting rid of infinitely many obstruction classes. This is achieved by adapting a theory of Bhatt based on de Jongs's alteration method. One also needs control over numerically flat bundles on arbitrary singular varieties over finite fields. The singular Riemann Roch Theorem of Baum Fulton Macpherson is a key ingredient for this step. This is joint work with Annette Werner.
A logarithmic interpretation of Edixhoven's jumps for Jacobians
Abstract
Let A be an abelian variety over a strictly henselian discretely valued field K. In his 1992 paper "Néron models and tame ramification", Edixhoven has constructed a filtration on the special fiber of the Néron model of A that measures the behaviour of the Néron model with respect to tamely ramified extensions of K. The filtration is indexed by rational numbers in [0,1], and if A is wildly ramified, it is an open problem whether the places where it jumps are always rational. I will explain how an interpretation of the filtration in terms of logarithmic geometry leads to explicit formulas for the jumps in the case where A is a Jacobian, which confirms in particular that they are rational. This is joint work with Dennis Eriksson and Lars Halvard Halle.
Finding Arithmetic Implications of Mirror Symmetry
Abstract
Mirror symmetry is a duality from string theory that states that given a Calabi-Yau variety, there exists another Calabi-Yau variety so that various geometric and physical data are exchanged. The investigation of this mirror correspondence has its roots in enumerative geometry and hodge theory, but has been later interpreted by Kontsevich in a categorical setting. This exchange in data is very powerful, and has been shown to persist for zeta functions associated to Calabi-Yau varieties, although there is no rigorous statement for what arithmetic mirror symmetry would be. Instead of directly trying to state and prove arithmetic mirror symmetry, we will instead use mirror symmetry as an intuitional framework to obtain arithmetic results for special Calabi-Yau pencils in projective space from the Hodge theoretic viewpoint. If time permits, we will discuss work in progress in starting to find arithmetic implications of Kontsevich's Homological Mirror Symmetry.