Jonathan Gruber (Erlangen)
Centers and centralizers in (double) affine Hecke algebras. abstract
Abstract:
The affine Hecke algebra and its center are important objects of study in combinatorial, geometric and categorical representation theory. In this talk, I will discuss a new commutative subalgebra of the affine Hecke algebra of type A, which arises from a centralizer construction in the double affine Hecke algebra. This subalgebra contains the center, and it admits a canonical basis akin to the Kazhdan-Lusztig basis of the affine Hecke algebra. I will explain how the canonical basis can be used as a tool to compute composition multiplicities in Gaitsgory\'s central sheaves on affine flag manifolds.
10:15 • EPF Lausanne, CM 1 517
Mathias Braun (EPFL)
Abstract:
We present a distributional notion of d\'Alembertian of Lorentz distance functions in spacetimes which may be smooth or nonsmooth. We derive comparison estimates and precise representation formulas. This expands on a recent elliptic interpretation of this operator (e.g. enabling us to give a simplified proof of the classical Lorentzian splitting theorem); even in the Lorentzian case, our results seem to pioneer its interpretation across the timelike cut locus. Two central ingredients our work unifies are the localization paradigm of Cavalletti-Mondino and our recent Lorentzian Sobolev calculus. Partly in collaboration with Robert McCann (University of Toronto), Nicola Gigli, Felix Rott (SISSA Trieste), Clemens Sämann (University of Oxford), Argam Ohanyan, Tobias Beran, Matteo Calisti (University of Vienna).
Jeremy Feusi (ETH Zürich)
Complex abelian varieties and their moduli II abstract
Abstract:
Toroidal compactifications and their cone stacks
13:30 • UZH Irchel
Prof. Dr. Roman Sauer (Karlsruhe Institute for Technology)
The Kazhdan property donates an extra dimension abstract
Abstract:
The waist inequality for the sphere by Gromov is wonderful result of geometric measure theory. Formulated appropriately for families of spaces, a (uniform) waist inequality for a family of Riemannian manifolds is the Riemannian analog of higher dimensional expanders. We formulate a conjectural picture for locally symmetric spaces. Finally, we show that the Kazhdan property alone gives rise not only to expanders, which is classical, but also to 2-dimensional expanders. An extra dimension for free! This is joint work with Uri Bader.
13:45 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H 28
Lyne Moser (Universität Regensburg)
New methods to construct model categories abstract
Abstract:
Model categories provide a good environment to do homotopy theory. While weak equivalences are the main players in a model category and encode how two objects should be thought of as being ``the same\'\', the additional data of cofibrations and fibrations typically facilitates computations of homotopy (co)limits and derived functors. However, because of their robust structure, model categories are usually hard to construct. In joint work with Guetta, Sarazola, and Verdugo, we develop new techniques for constructing model structures from given classes of cofibrations, fibrant objects, and weak equivalences between them. The requirement that one only needs to provide a class of weak equivalences between fibrant objects seems more natural in practice as the fibrant objects are often the ``well-behaved\'\' objects and so weak equivalences should only be expected to exhibit a good behavior between these objects. As a straightforward consequence of our result, we obtain a more general version of the usual right-induction theorem along an adjunction, where fibrations and weak equivalences are now only right-induced between fibrant objects. If time permits, I will mention some applications of these new methods.
Prof. Dr. Sobhan Seyfaddini (ETH Zürich, Switzerland)
On the algebraic structure of area preserving homeomorphisms of the sphere
15:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.1
Hao Shen (Wisconsin Madison)
Stochastic quantization and large N abstract
Abstract:
In quantum field theory, large N problem refers to a class of important questions regarding the asymptotic behavior of a model with N field components when N goes to infinity. Through stochastic quantization, one relates the large N problem with singular stochastic PDE and mean field limit theory. By combining ideas from these fields one can prove interesting results regarding the dynamic, the quantum fields, the observables, and so on. In this talk we will focus on the linear sigma model, which is an N-vector Phi4 type quantum field theory. In particular we prove some predictions by physicists such as Wilson, and we discover some new probabilistic descriptions in the large N limit. Based on joint works with Scott Smith, Rongchan Zhu and Xiangchan Zhu.
16:00 • EPF Lausanne, CM 1 517
Prof. Dr. Christiane Helzel (Mathematisches Institut, Heinrich-Heine-Universität Düsseldorf)
Active Flux Methods for Hyperbolic Conservation Laws
16:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.2