D-MATH Weekly BulletinNews and Events (in particular 'Research Seminars') at D-MATH, ETH Zurichen-us
http://www.fim.math.ethz.ch/bulletin
Tue, 24 May 2016 15:37:06 +020060Benjamin Sharp - Morse index and Betti numbers of minimal hypersurfaces<h2 color="grey">Analysis Seminar</h2><h1> Morse index and Betti numbers of minimal hypersurfaces</h1><br /><font color="grey">Speaker:</font> Prof. Dr. Benjamin Sharp, Imperial College London<br /><font color="grey">Location:</font> HG G 43 (ETH Zentrum)<br /><font color="grey">Start Date/Time:</font> 24 May 2016 @ 15:15<br /><br /><strong>Abstract:</strong><br />Abstract: As critical points of the area functional, minimal hypersurfaces of Riemannian manifolds have a well-defined Morse index. In general, a minimal hypersurface with bounded index and area is also qualitatively controlled in terms of both geometry and topology (Buzano - Sharp 2016 preprint). However, in the case where the ambient manifold has positive curvature it is expected that control on the index alone is enough to conclude quantitative linear bounds on the first Betti number of the minimal hypersurface - a conjecture of Schoen and Marques-Neves. In this talk, we will show that under certain conditions on the ambient manifold, the index of a minimal hypersurfaces grows linearly with their first Betti numbers. The hypotheses on the ambient manifold are flexible enough to include all compact symmetric spaces of rank one and small graphical perturbations of the round sphere, for example. Thus we verify the Schoen, Marques-Neves conjecture in these cases. This is a joint work with L. Ambrozio and A. Carlotto.http://www.math.ethz.ch/screen/info?guid=8324Tue, 17 May 2016 16:57:42 +0200Oleg Pikhurko - Combinatorics behind circle squaring<h2 color="grey">Conference: Probabilistic and Extremal Combinatorics</h2><h1>Combinatorics behind circle squaring</h1><br /><font color="grey">Speaker:</font> Prof. Dr. Oleg Pikhurko, University of Warwick<br /><font color="grey">Location:</font> HG G 19.1 (ETH Zentrum)<br /><font color="grey">Start Date/Time:</font> 24 May 2016 @ 15:30<br /><br /><strong>Abstract:</strong><br />I will discuss combinatorial aspects of the proof of Laczkovich that a square can be cut into finitely many parts which can be rearranged using translations to form a disk and our recent strengthening (with L.Grabowski and A.Mathe) that the parts can be additionally required to be both Baire and Lebesgue measurable.http://www.math.ethz.ch/screen/info?guid=8957Tue, 17 May 2016 16:07:58 +0200Deryk Osthus - On the decomposition threshold of a graph<h2 color="grey">Conference: Probabilistic and Extremal Combinatorics</h2><h1>On the decomposition threshold of a graph</h1><br /><font color="grey">Speaker:</font> Prof. Dr. Deryk Osthus, University of Birmingham<br /><font color="grey">Location:</font> HG G 19.1 (ETH Zentrum)<br /><font color="grey">Start Date/Time:</font> 24 May 2016 @ 16:45<br /><br /><strong>Abstract:</strong><br />A fundamental theorem of Wilson states that, for every graph F, every sufficiently large F-divisible clique has an F-decomposition. Here a graph G has an F-decomposition if the edges of G can be covered by edge-disjoint copies of F and F-divisibility is a trivial necessary condition for this. We extend Wilson’s theorem to graphs which are allowed to be far from complete. In particular, we determine the `decomposition threshold' for arbitrary bipartite graphs F. For general graphs F we reduce the decomposition threshold to at most 3 possible values.<br />Our main contribution is a general "iterative absorption" method which turns an approximate or fractional decomposition into an exact one. Our results are also connected to the question of when a partially completed Latin square can be extended to a full one. (This covers joint work with Ben Barber, Stefan Glock, Allan Lo, Richard Montgomery, Deryk Osthus and Amelia Taylor.)<br />http://www.math.ethz.ch/screen/info?guid=8958Tue, 17 May 2016 16:08:04 +0200Lorenz Halbeisen - Über die Existenz mathematischer Objekte<h2 color="grey">Inaugural Lectures</h2><h1>Über die Existenz mathematischer Objekte</h1><br /><font color="grey">Speaker:</font> Dr. Lorenz Halbeisen, ETH Zurich, Switzerland<br /><font color="grey">Location:</font> HG G 5 (ETH Zentrum)<br /><font color="grey">Start Date/Time:</font> 24 May 2016 @ 17:15http://www.math.ethz.ch/screen/info?guid=8608Fri, 20 May 2016 14:56:48 +0200Anne Thomas - Geometric and topological aspects of Coxeter groups and buildings<h2 color="grey">Nachdiplomvorlesung</h2><h1>Geometric and topological aspects of Coxeter groups and buildings</h1><br /><font color="grey">Speaker:</font> Dr. Anne Thomas, University of Sydney<br /><font color="grey">Location:</font> HG G 43 (ETH Zentrum)<br /><font color="grey">Start Date/Time:</font> 25 May 2016 @ 10:00<br /><br /><strong>Abstract:</strong><br />We will begin by reviewing the basic theory of Coxeter and reflection groups. We will then study the Davis complex, a cell complex with "good" geometric and topological properties on which the associated Coxeter group acts "nicely". We will prove Moussong's Theorem, which characterises the Coxeter groups which are hyperbolic in the sense of Gromov, and discuss the use of the Davis complex to determine cohomology of Coxeter groups.<br /><br />In the second part of the course we will study buildings. Using the theory of Coxeter groups and the Davis complex already discussed, we will establish the equivalence of the main definitions of a building, and describe the main geometric realisations of a building. We then discuss the use of buildings to study groups which act on them, including algebraic groups over local fields, arithmetic groups, and other lattices. If time permits we will consider the theory of twin buildings, which appears in the study of Kac-Moody groups.http://www.math.ethz.ch/screen/info?guid=8406Wed, 03 Feb 2016 14:21:54 +0100Christoph Schwab - Numerische Mathemaik<h2 color="grey">Wahlfachvorstellungen der Mathematik</h2><h1>Numerische Mathemaik</h1><br /><font color="grey">Speaker:</font> Prof. Dr. Christoph Schwab, ETH Zurich, Switzerland<br /><font color="grey">Location:</font> HG G 5 (ETH Zentrum)<br /><font color="grey">Start Date/Time:</font> 25 May 2016 @ 12:05http://www.math.ethz.ch/screen/info?guid=8549Thu, 24 Mar 2016 16:31:32 +0100Péter Frankl - Toward a complete solution of a problem of Erdos and Kleitman from 1966<h2 color="grey">Conference: Probabilistic and Extremal Combinatorics</h2><h1>Toward a complete solution of a problem of Erdos and Kleitman from 1966</h1><br /><font color="grey">Speaker:</font> Prof. Dr. Péter Frankl, Alfréd Rényi Institute of Mathematics<br /><font color="grey">Location:</font> HG G 19.1 (ETH Zentrum)<br /><font color="grey">Start Date/Time:</font> 25 May 2016 @ 14:30http://www.math.ethz.ch/screen/info?guid=8959Tue, 17 May 2016 16:08:09 +0200Michele Elia - Tridiagonal matrices over finite fields<h2 color="grey">Arbeitsgemeinschaft in Codierungstheorie und Kryptographie (uzh)</h2><h1>Tridiagonal matrices over finite fields</h1><br /><font color="grey">Speaker:</font> Prof. Dr. Michele Elia, Politecnico di Torino<br /><font color="grey">Location:</font> Y27 H 28 (UZH Irchel)<br /><font color="grey">Start Date/Time:</font> 25 May 2016 @ 15:00http://www.math.ethz.ch/screen/info?guid=9004Tue, 30 Nov 1999 00:00:00 +0100Mathias Schacht - A generalisation of Mantel's theorem for hypergraphs<h2 color="grey">Conference: Probabilistic and Extremal Combinatorics</h2><h1>A generalisation of Mantel's theorem for hypergraphs</h1><br /><font color="grey">Speaker:</font> Prof. Dr. Mathias Schacht, Universität Hamburg<br /><font color="grey">Location:</font> HG G 19.1 (ETH Zentrum)<br /><font color="grey">Start Date/Time:</font> 25 May 2016 @ 15:30<br /><br /><strong>Abstract:</strong><br />We consider the extremal problem for three hyperedges on $k+1$-vertices in $k$-uniform hypergraphs. For $k=2$ this reduces to the classical result of Mantel in extremal graph theory, which implies that any graph with density more than $1/2$ contains a triangle, i.e. three edges on three vertices.<br />For $k>2$ this problem is widely open and we investigate a variation, where the considered large hypergraph satisfies an additional hereditary density assumption with respect to $(k-2)$-tuples.<br />In that direction it was shown by Glebov, Kral', and Volec that for $k=3$ the corresponding extremal density is $1/4$. We generalise these results by showing that for arbitrary $k$ the extremal density<br />for this problem is $2^{1-k}$. This presents joint work with Christian Reiher and Vojtech Rodl.<br />http://www.math.ethz.ch/screen/info?guid=8961Tue, 17 May 2016 16:08:16 +0200Aditi Kar - Ping Pong in CAT(0) cube complexes<h2 color="grey">Geometry Seminar</h2><h1>Ping Pong in CAT(0) cube complexes</h1><br /><font color="grey">Speaker:</font> Aditi Kar, University of Southampton<br /><font color="grey">Location:</font> HG G 43 (ETH Zentrum)<br /><font color="grey">Start Date/Time:</font> 25 May 2016 @ 15:45<br /><br /><strong>Abstract:</strong><br />Groups acting on CAT(0) cube complexes have played a seminal role in contemporary mathematics. I am interested in properties of CAT(0) cubical groups like property P_naive and uniform exponential growth. Property P_naive is a very strong form of the Tits Alternative and was introduced by de la Harpe to study the analytic property of a group being C*-simple. Variations on this theme lead to a concrete description of free sub-semigroups contained inside groups acting on CAT(0) cube complexes of a given dimension. This is joint work with Michah Sageev (Technion) and leads us to interesting variations of uniform exponential growth. http://www.math.ethz.ch/screen/info?guid=8756Mon, 23 May 2016 11:20:49 +0200Christoph Gasche - Minimal unimodular Matrix Decomposition<h2 color="grey">Arbeitsgemeinschaft in Codierungstheorie und Kryptographie (uzh)</h2><h1>Minimal unimodular Matrix Decomposition</h1><br /><font color="grey">Speaker:</font> Christoph Gasche, <br /><font color="grey">Location:</font> Y27 G 28 (UZH Irchel)<br /><font color="grey">Start Date/Time:</font> 25 May 2016 @ 16:00http://www.math.ethz.ch/screen/info?guid=9005Tue, 30 Nov 1999 00:00:00 +0100Stephanie Kovalchik - The Past, Present, and Future of Prediction in Professional Tennis<h2 color="grey">ZüKoSt Zürcher Kolloquium über Statistik</h2><h1>The Past, Present, and Future of Prediction in Professional Tennis</h1><br /><font color="grey">Speaker:</font> Stephanie Kovalchik, RAND Corporation, USA<br /><font color="grey">Location:</font> HG G 26.5 (ETH Zentrum)<br /><font color="grey">Start Date/Time:</font> 25 May 2016 @ 16:15<br /><br /><strong>Abstract:</strong><br />Sports forecasting models – beyond their interest to bettors – are important resources for sports analysts and coaches. Like the best athletes, the best forecasting models<br />should be rigorously tested and judged by how well their performance holds up against top competitors. Although a number of models have been proposed for predicting match<br />outcomes in professional tennis, their comparative performance is largely unknown. In this talk I will present results comparing the performance of 11 published forecasting models for predicting the outcomes of 2395 singles matches during the 2014 season of the Association of Tennis Professionals Tour. I’ll discuss the implications of these findings for current application of forecasting in tennis and how the advent of computer vision data will shape how prediction is used in future applications.http://www.math.ethz.ch/screen/info?guid=8181Fri, 13 May 2016 10:38:24 +0200Xavier Claeys - Analysis of Block-Jacobi Preconditioners for Local Multi-Trace Formulations<h2 color="grey">Zurich Colloquium in Applied and Computational Mathematics</h2><h1>Analysis of Block-Jacobi Preconditioners for Local Multi-Trace Formulations</h1><br /><font color="grey">Speaker:</font> Dr. Xavier Claeys, LJLL, UPMC, Paris i=Ralf Hiptmair<br /><font color="grey">Location:</font> HG E 1.2 (ETH Zentrum)<br /><font color="grey">Start Date/Time:</font> 25 May 2016 @ 16:15<br /><br /><strong>Abstract:</strong><br />Local Multi-Trace Formulations (local MTF) are block-sparse boundary integral equations adapted to elliptic PDEs with piece-wise constant coefficients (typically multi-subdomain scattering problems) only recently introduced in [Hiptmair & Jerez-Hanckes, 2012]. In these formulations, transmission conditions are enforced by means of local operators, so that only adjacent subdomains communicate. Although they provide an appealing framework for domain decomposition, present literature only offers two contributions in this direction. In [Hiptmair, Jerez-Hanckes, Lee, Peng, 2013] a new version of local MTF is proposed that involves a relaxation parameter in the enforcement of transmission conditions. In [Dolean & Gander, 2014] the authors conduct a basic explicit<br />study of this modified local MTF in a 1-D setting with 2 subdomains and determine a critical value for the relaxation parameter that minimises the spectral radius of block-Jacobi iteration operators. In the present talk, we describe new contributions extending these results to arbitrary geometrical settings in 2-D and 3-D, assuming that the subdomain partition does not involve any junction point.http://www.math.ethz.ch/screen/info?guid=8474Fri, 22 Apr 2016 10:45:02 +0200Daniela Kühn - A blow-up lemma for approximate decompositions<h2 color="grey">Conference: Probabilistic and Extremal Combinatorics</h2><h1>A blow-up lemma for approximate decompositions</h1><br /><font color="grey">Speaker:</font> Prof. Dr. Daniela Kühn, University of Birmingham<br /><font color="grey">Location:</font> HG G 19.1 (ETH Zentrum)<br /><font color="grey">Start Date/Time:</font> 25 May 2016 @ 16:45<br /><br /><strong>Abstract:</strong><br />Questions on packings and decompositions have a long history, going back to the 19th century. For instance, the existence of Steiner triple systems (proved by Kirkman in 1847) corresponds to a decomposition of the edge set of the complete graph $K_n$ on $n$ vertices into triangles (if $n$ satisfies the necessary divisibility conditions). There are several beautiful conjectures which have driven a large amount of research in this area. A prime example is the tree packing conjecture of Gyárfás and Lehel, which would guarantee a decomposition of a complete graph into a suitable given collection of trees. We develop a new tool for constructing approximate decompositions of dense quasirandom graphs into bounded degree graphs. Our result can be viewed as an extension of the classical blow-up lemma of Komlós, Sárközy and Szemerédi to the setting of approximate decompositions. I will discuss this tool and some of its applications.<br />(Joint work Jaehoon Kim, Deryk Osthus and Mykhaylo Tyomkyn)http://www.math.ethz.ch/screen/info?guid=8962Tue, 17 May 2016 16:08:23 +0200