Adam Kanigowski (University of Maryland)
Sparse Equidistribution Problems in Dynamics
10:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Farrell Brumley (IUF & Sorbonne Université)
Quantum ergodicity in higher rank for Benjamini-Schramm sequences of lattices abstract
Abstract:
The quantum ergodicity theorem of Schnirelman, Colin de Verdière, andZelditch states that on a compact Riemannian manifold with ergodicgeodesic flow, most eigenfunctions of high frequency distribute theirL2 mass according to the uniform measure. More recently, there hasbeen increasing interest in the delocalization properties ofeigenfunctions of bounded frequency on spaces of increasing volume. Aparticularly well-behaved setting is that of locally symmetric spaces,attached to cocompact lattices having uniform spectral gap in a fixednon-compact semisimple Lie group, which Benjamini-Schramm converge totheir commun universal cover.In rank one, this problem has seen tremendous progress. A discreteversion of this problem was solved in the breakthrough work ofAnantharaman-Le Masson for large regular graphs. Shortly thereafter analternative approach was given by Brooks-Le Masson-Lindenstrauss whichrelied critically on the construction of a wave propagator having goodspectral and geometric properties. The latter approach wassubsequently adapted to the setting of large hyperbolic surfaces by LeMasson-Sahlsten and then to higher dimensional hyperbolic manifolds byAbert-Bergeron-Le Masson. The kernels of these propagators aresupported on spheres or annuli, and (among other things) the argumentrequires good estimates on the intersection volumes of theirtranslates.In this talk, we shall present a higher rank construction of a wavepropagator, which generalizes the one given for PGL(3,\\Q_p) by CarstenPeterson in his thesis, and show how it can be used to prove quantumergodicity for locally symmetric spaces associated with classical realLie groups in the Benjamini-Schramm limit. In doing so, we repair anerror in our previous work on this topic for quotients of SL(n,\\R)with Jasmin Matz. Our approach to controlling intersection volumes isdue to Simon Marshall, and reduces to establishing deep estimates onthe Harish-Chandra spherical function. This is joint work with SimonMarshall, Jasmin Matz, and Carsten Peterson.
13:00 • EPF Lausanne, CE 1 100
Prof. Dr. Chris Judge (Indiana University)
Shrinking targets for affine self-diffeomorphisms of translation surfaces abstract
Abstract:
The affine self-diffeomorphism group of a translation surface can be rather large. For example, the affine diffeos of a 2-torus contain a lattice. In the case of a torus $T$, Ghosh, Gorodnik, and Nevo proved that for any $\\eta > 0$, for almost every $y \\in T$ and for every $x \\in T$, there exist infinitely many $\\gamma \\in SL_2(Z)$ so that $\\| \\gamma x- y \\|\\leq \\|\\gamma\\|^{-1-\\eta}$. We show that a similar result holds for translation surfaces with the lattice property. This is joint work with Josh Southerland.
13:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room E 33.1
Dr. Johannes Schmitt (ETH Zürich)
Complex abelian varieties and their moduli X abstract
Abstract:
Piecewise polynomials and Chow rings
13:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Prof. Dr. Philippe Ciarlet (Institut für Mathematik, Universität Zürich)
A two-dimensional nonlinear shell model of Koiter\'s type abstract
Abstract:
As is well-known, Koiter\'s model is often used in numerical simulations, because it is a two-dimensional model that captures well the "membrane-dominated" and "flexural-dominated" effects that arise in a nonlinearly elastic shell subjected to applied forces and specific boundary conditions. Finding a satisfactory existence theory for this nonlinear shell model has stood as an open problem for a very long time. The present work, which is a joint work with Cristinel Mardare, provides a two-dimensional model that preserves all the virtues of Koiter\'s model, while being in addition amenable to a satisfactory existence theory. More precisely, our new two-dimensional mathematical model for a nonlinearly elastic shell takes the form of a minimization problem with a stored energy function that is polyconvex and orientation-preserving, and more generally satisfies all the other assumptions of John Ball\'s existence theorem. In addition, the most noteworthy feature of this model is that it is "of Koiter\'s type", in the sense that for a specific class of deformations that are "to within the first order" identical to those introduced by W.T. Koiter for defining his model, the "lowest order part" of its stored energy function coincides with the stored energy function of Koiter\'s model.
16:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.2
Dr. Titus Lupu (LPSM, Sorbonne Université)
Relation between the geometry of sign clusters of the 2D GFF and its Wick powers abstract
Abstract:
In 1990 Le Gall showed an asymptotic expansion of the epsilon-neighborhood of a planar Brownian trajectory (Wiener sausage) into powers of 1/|log eps|, that involves the renormalized self-intersection local times. In my talk I will present an analogue of this in the case of the 2D GFF. In the latter case, there is an asymptotic expansion of the epsilon-neighborhood of a sign cluster of the 2D GFF into half-integer powers of 1/|log eps|, with the coefficients of the expansion being related to the renormalized (Wick) powers of the GFF.
17:15 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H12