I will give a complete description of all groups definable in Presburger arithmetic, up to finite index subgroups. This builds on previous work on bounded groups in Presburger arithmetic by Mariana Vicaria and Alf Onshuus.
The notion of ampleness captures essential properties of projective spaces over fields. It is natural to ask whether any sufficiently ample strongly minimal set arises from an algebraically closed field. In this talk I will explain the question and present recent results on ample strongly minimal structures.
Any algebraic stack X can be represented by a groupoid object in the category of schemes: that is, a pair of schemes Ob, Mor and morphisms source, target: Mor → Ob, inversion: Mor → Mor, composition: Mor ×_{Ob} Mor → Mor and identity: Ob → Mor that satisfy certain axioms. Yet this description of the stack X might be misleading. Namely, given a field F which is not algebraically closed, we have a natural functor between the groupoid (Ob(F),Mor(F)) and the groupoid X(F). While this functor is fully faithful, it […]
Based on mirror symmetry considerations, Hausel and Thaddeus conjectured an equality between `stringy' Hodge numbers for moduli spaces of SL_n/PGL_n Higgs bundles. With Michael Groechenig and Paul Ziegler we prove this conjecture using non-archimedean integrals on these moduli spaces, building on work of Denef-Loeser and Batyrev. Similar ideas also lead to a new proof of the geometric stabilization theorem for anisotropic Hitchin fibers, a key ingredient in the proof of the fundamental lemma by Ngô.In my talk I will outline the main arguments of the proofs and discuss the adjustments […]
JG: In this talk, I will discuss fundamental properties of the solutions to the incompressible Navier–Stokes equations in three dimensions. After reviewing the classical local well-posedness results, I will explain how numerical simulations suggest local ill-posedness at the borderline of the known results. I will discuss a plausible scenario of non-uniqueness from smooth initial data through finite-time blow-up. Finally, I will describe how this scenario is actually happening in a model equation sharing the same fundamental properties as the Navier–Stokes equations.KM: Singularities of the Navier-Stokes equations occur when some derivative […]
14.00-14.45 Stefan Witzel (Ecole Polytehchnique)15.00-15.45 Katie Vokes (IHES)15.45-16.15 coffee break16.15-16.45 Adrien Le Boudec (ENS Lyon)Stefan Witzel, Arithmetic approximate groups and their finiteness propertiesI will talk about approximate groups, a geometric generalization of groups. Approximate groups were discovered independently in various contexts and I will describe how they arise very naturally in the context of arithmetic groups. I will then explain how to extend topological finiteness properties of groups to approximate groups. This allows to make a connection betweenarithmetic groups in positive characteristic and arithmetic approximate groups in characteristic zero. The […]
