D-MATH Weekly BulletinNews and Events (in particular 'Research Seminars') at D-MATH, ETH Zurichen-us
http://www.fim.math.ethz.ch/bulletin
Tue, 13 Oct 2015 10:53:43 +020060Various speakers - Statistics meets Optimization: Randomization and approximation for high-dimensional problems<h2 color="grey">Nachdiplomvorlesung</h2><h1>Statistics meets Optimization: Randomization and approximation for high-dimensional problems</h1><br /><font color="grey">Speaker:</font> various speakers<br /><font color="grey">Location:</font> HG G 43 (ETH Zentrum)<br /><font color="grey">Start Date/Time:</font> 13 October 2015 @ 10:00<br /><br /><strong>Abstract:</strong><br />In the modern era of high-dimensional data, the interface between mathematical statistics and optimization has<br />become an increasingly vibrant area of research. In this course, we provide some vignettes into this interface,including the following topics:<br />(A) Dimensionality reduction via random projection. The naive idea of projecting high-dimensional data to a randomly chosen low-dimensional space is remarkably effective. We discuss the classical Johnson-Lindenstrauss<br />lemma, as well as various modern variants that provide computationally-efficient embeddings with strong guarantees.<br />(B) When is it possible to quickly obtain approximate solutions of large-scale convex programs? In practice,methods based on randomized projection can work very well, and arguments based on convex analysis and concentration of measure provide a rigorous underpinning to these observations.<br />(C) Optimization problems with some form of nonconvexity arise frequently in statistical settings - for instance,in problems with latent variables, combinatorial constraints, or rank constraints. Nonconvex programs are known to be intractable in a complexity-theoretic sense, but the random ensembles arising in statistics are not adversarially constructed. Under what conditions is it possible to make rigorous guarantees about the behavior of simple iterative algorithms for such problems? We develop some general theory for addressing these questions,exploiting tools from both optimization theory and empirical process theory.http://www.math.ethz.ch/screen/info?guid=7409?13 October 2015Tue, 13 Oct 2015 10:11:53 +0200Jean-Baptiste Teyssier - On irregular singularities of algebraic connections<h2 color="grey">FIM Minicourse</h2><h1>On irregular singularities of algebraic connections</h1><br /><font color="grey">Speaker:</font> Dr. Jean-Baptiste Teyssier, The Hebrew University of Jerusalem<br /><font color="grey">Location:</font> HG G 19.1 (ETH Zentrum)<br /><font color="grey">Start Date/Time:</font> 13 October 2015 @ 10:15<br /><br /><strong>Abstract:</strong><br />Let E be an algebraic flat connection on a smooth complex algebraic variety X, let<br />X be a smooth compactification of X such that D :“ XzX is a normal crossing divisor.<br />Levelt-Turrittin theorem asserts that the pull-back of E to the formal neighbourhood of a codimension 1 point in D decomposes (after ramification) into elementary factors<br />easy to work with.<br />This decomposition may not hold at some other points of D, but when it does, we say that E has good formal decomposition along D. A conjecture of Sabbah, recently<br />proved by Kedlaya and Mochizuki independently, asserts the existence of a chain <br />p : Y ÝŃ X of blow-ups above D such that E has good formal decomposition along p´1pDq.<br />In a sense, this result is to flat connections what Hironaka desingularization is to<br />varieties, and has recently allowed ground-breaking progresses in our understanding<br />of D-modules. The goal of this course is to introduce the concepts at stake in the<br />statement of Kedlaya-Mochizuki theorem, and to give an application to the existence<br />of periods for arbitrary algebraic flat connections.<br />No prerequisite on D-modules is necessary to follow this course.http://www.math.ethz.ch/screen/info?guid=7727Tue, 29 Sep 2015 09:43:02 +0200Alessandro Carlotto - The finiteness problem for minimal surfaces of bounded index in a 3-manifold<h2 color="grey">Analysis Seminar</h2><h1>The finiteness problem for minimal surfaces of bounded index in a 3-manifold</h1><br /><font color="grey">Speaker:</font> Dr. Alessandro Carlotto, ETH-ITS<br /><font color="grey">Location:</font> HG G 43 (ETH Zentrum)<br /><font color="grey">Start Date/Time:</font> 13 October 2015 @ 15:15<br /><br /><strong>Abstract:</strong><br />Given a closed, Riemannian 3-manifold (N,g) without symmetries (more precisely: generic) and a non-negative integer p, can we say something about the number of minimal surfaces it contains whose Morse index is bounded by p? More realistically, can we prove that such number is necessarily finite? This is the classical "generic finiteness" problem, which has a rich history and exhibits interesting subtleties even in its basic counterpart concerning closed geodesics on surfaces.<br />We settle such question when g is a bumpy metric of positive scalar curvature by proving that either finiteness holds or N does contain a copy of RP^3 in its prime decomposition and we discuss the obstructions to any further generalisation of such result. When g is assumed to be strongly bumpy (meaning that all closed, immersed minimal surfaces do not have Jacobi fields, a notion recently proved to be generic by White) then the finiteness conclusion is true for any compact 3-manifold without boundary. http://www.math.ethz.ch/screen/info?guid=7554Tue, 29 Sep 2015 14:43:33 +0200Nalini Anatharaman - Quantum ergodicity<h2 color="grey">Zurich Colloquium in Mathematics</h2><h1>Quantum ergodicity</h1><br /><font color="grey">Speaker:</font> Prof. Dr. Nalini Anatharaman, Université de Strasbourg<br /><font color="grey">Location:</font> KO2 F 150 (ETH Zentrum)<br /><font color="grey">Start Date/Time:</font> 13 October 2015 @ 17:15<br /><br /><strong>Abstract:</strong><br />"Quantum ergodicity'' usually deals with delocalization properties of eigenfunctions of the Laplacian on compact manifolds. After a review of the subject, I will discuss some recent work with Etienne Le Masson where we prove a "quantum ergodicity" result for eigenfunctions of the discrete Laplacian on large regular graphs. This means that, for most eigenfunctions $\psi_j$, the probability measure $|\psi_j(x)|^2$ on the vertices of the graph is close to uniform. I will also discuss possible extensions to other models.http://www.math.ethz.ch/screen/info?guid=7355Mon, 12 Oct 2015 11:22:56 +0200Ruodu Wang - Risk aggregation and Fréchet problems<h2 color="grey">FIM Minicourse</h2><h1>Risk aggregation and Fréchet problems</h1><br /><font color="grey">Speaker:</font> Prof. Dr. Ruodu Wang, University of Waterloo<br /><font color="grey">Location:</font> HG G 19.1 (ETH Zentrum)<br /><font color="grey">Start Date/Time:</font> 14 October 2015 @ 13:15<br /><br /><strong>Abstract:</strong><br />Fréchet problems refer to questions related to an aggregation (sum, typically) of several random variables,<br />where the marginal distribution of each individual random variable is known and the joint distribution (copula) is unspecific. Unfortunately (in fact, fortunately), a large number of questions in this field are still mathematically open.<br />In the modeling of risk aggregation, individual risks and their dependence structure are often modeled separately,<br />leading to uncertainty arising at the level of a joint model. As the dependence structure is typically uncertain, the study on quantitative characteristics (e.g. risk measures) of risk aggregation under model uncertainty leads to a variety of Fréchet problems. This course covers various topics in this quickly expanding field. The content is mainly based on recent research of the instructor and his collaborators.http://www.math.ethz.ch/screen/info?guid=7505Tue, 06 Oct 2015 08:33:43 +0200Paul Johnson - Topology of Hilbert schemes and combinatorics of partitions I<h2 color="grey">Algebraic Geometry and Moduli Seminar</h2><h1>Topology of Hilbert schemes and combinatorics of partitions I</h1><br /><font color="grey">Speaker:</font> Dr. Paul Johnson, University of Sheffield<br /><font color="grey">Location:</font> HG G 43 (ETH Zentrum)<br /><font color="grey">Start Date/Time:</font> 14 October 2015 @ 13:30<br /><br /><strong>Abstract:</strong><br />The Hilbert scheme of n points on a complex surface is a smooth manifold of dimension 2n. Their topology has beautiful structure related to physics, representation theory, and combinatorics. For instance, Göttsche's formula gives a product formula for generating functions for their Betti numbers.<br /><br />Hilbert schemes of points on C^2/G, for G a finite group, are also smooth, and when G is abelian their topology is encoded in the combinatorics of partitions. When G is a subgroup of SL_2, the topology is well understood and in terms of cores and quotients of partitions. Following Gusein-Zade, Luengo and Melle-Hernández we study general abelian G, stating a conjectural product formula, and proving a homological stability result using a generalization of cores and quotients.<br />http://www.math.ethz.ch/screen/info?guid=7359Tue, 06 Oct 2015 10:44:08 +0200FIM TEA<h2 color="grey">FIM Announcements</h2><h1>FIM TEA</h1><br /><font color="grey">Location:</font> HG G 69 (ETH Zentrum)<br /><font color="grey">Start Date/Time:</font> 14 October 2015 @ 15:00http://www.math.ethz.ch/screen/info?guid=7260?14 October 2015Tue, 30 Nov 1999 00:00:00 +0100Jean-Claude Latché - Staggered schemes for all Mach flows<h2 color="grey">Zurich Colloquium in Applied and Computational Mathematics</h2><h1>Staggered schemes for all Mach flows</h1><br /><font color="grey">Speaker:</font> Prof. Dr. Jean-Claude Latché, CEA-IRNS<br /><font color="grey">Location:</font> Y27 H 25 (UZH Irchel)<br /><font color="grey">Start Date/Time:</font> 14 October 2015 @ 16:15<br /><br /><strong>Abstract:</strong><br />Finite volume schemes using a staggered arrangement of the unknowns are widely used for the computation of incompressible flows. This talk will present extensions of theses algorithms to compressible flows. Space discretization is based either on the classical Marker And Cell (MAC) scheme or on the low-order finite elements of Rannacher&Turek or Crouzeix&Raviart. Time discretization may be implicit or realized by a fractional step algorithm inspired from pressure-correction techniques. The barotropic Euler equations will first be addressed : the schemes will be described, and the asymptotic preserving property for vanishing Mach numbers will be proved ; more precisely speaking, we will show that, for a given mesh and when the Mach number tends to zero, the discrete density converges to a constant, and the pressure and velocity fields converge to a solution of a standard (inf-sup stable) scheme for incompressible flows. Then the approach will be extended to cope with full (i.e. non-barotropic) Euler equations.http://www.math.ethz.ch/screen/info?guid=7244Tue, 06 Oct 2015 10:45:01 +0200Christophe Sabot - A random Schrödinger operator associated with the edge reinforced random walk and the vertex reinforced Jump process<h2 color="grey">Seminar on Stochastic Processes</h2><h1>A random Schrödinger operator associated with the edge reinforced random walk and the vertex reinforced Jump process</h1><br /><font color="grey">Speaker:</font> Christophe Sabot, Université de Lyon 1<br /><font color="grey">Location:</font> HG G 43 (ETH Zentrum)<br /><font color="grey">Start Date/Time:</font> 14 October 2015 @ 17:15<br /><br /><strong>Abstract:</strong><br />The ERRW and the VRJP are self-interacting processes that<br />have been shown to be related to a supersymetric sigma field<br />investigated by Disertori, Spencer and Zirnbauer.<br />In this talk we construct a random Schrödinger operator, with a<br />1-dependent potential, and show that some of its spectral properties at<br />ground state are related to the behavior of the VRJP and ERRW.<br />We deduce from this a functional central limit theorem for the ERRW and<br />the VRJP in dimension d>2 at weak disorder, and recurrence of the ERRW<br />in dimension d=2 for any choice of initial constant weights.<br />Based on joint works with P. Tarrčs and X. Zeng.http://www.math.ethz.ch/screen/info?guid=7469Thu, 17 Sep 2015 09:34:40 +0200