Arkady Berenstein (University of Oregon)
Generalized electrical Lie algebras abstract
Abstract:
My talk is based on joint work with Azat Gainutdinov and Vassily Gorbounov, in which we generalize in several ways the electrical Lie algebras originally introduced by Lam and Pylyavskyy. To each semisimple or Kac-Moody Lie algebra g we associate a family of flat deformations of its nilpotent part parametrized by the points of the Cartan subalgebra of g. If g=sl_n, then the generic electrical Lie algebra is sp_{n-1}, which is simple if n is odd. Similar situation is with other classical lie algebras, for instance if g=sp_{2n}, then its generic electrical Lie algebra is sp_n\\oplus sp_{n-1}, which is never semisimple. If time permits, I will explain the "edge models" of electrical Lie algebras in semisimple and affine case, where the deformation parameters can be viewed as edge weights of the Dynkin diagram of g.
13:00 • Université de Genève, Conseil Général 7-9, Room 1-07
Andrea Ulliana (Universität Zürich)
Delocalization of Eigenfunctions for Discrete Schrödinger Operators on Graphs abstract
Abstract:
<p>Schrödinger operators and their localization phenomena play a central role in spectral theory and its connection to dynamical systems. In this talk, I will focus on discrete Schrödinger operators defined on large finite graphs and investigate their asymptotic behavior as the graph size tends to infinity. In joint work with A. Avila, we establish a general criterion showing that for any family of graphs without eigenvalues concentration, delocalization of eigenfunctions become asymptotically dense in the space of potentials. Along the way, I will emphasize the interplay with ergodic Schrödinger operators, where the potential is generated by an underlying topological dynamical system.</p>
13:30 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H 28
Dr. Olivier de Gaay Fortman (University of Utrecht)
Matroids, the integral Hodge conjecture for abelian varieties, and optimal algebraic multiples of the minimal class abstract
Abstract:
I will discuss joint work with Philip Engel and Stefan Schreieder, in which we prove that the cohomology class of any curve on a very general principally polarized abelian variety of dimension at least 4 is an even multiple of the minimal class, and that the same holds for the intermediate Jacobian of a very general cubic threefold. This disproves the integral Hodge conjecture for abelian varieties and shows that verygeneral cubic threefolds are not stably rational. I will also discuss our most recent result, which shows that on a very general principally polarized abelian 6-fold, the smallest multiple of the minimal curve class which can be represented by an algebraic cycle is exactly 6.
13:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Alina Ostafe (UNSW)
Abstract:
Title: Counting linear recurrence sequences with zeros and solvable S-unit equations Abstract: In this talk I will discuss recent joint work with Carl Pomerance and Igor Shparlinski where we obtain a tight upper bound on the number of integer linear recurrence sequences which attain a zero value. The argument is based on modular techniques combined with a classical idea of P. Erdos. Using similar ideas, we also show that only a rather small proportion of linear equations are solvable in elements of a fixed finitely generated subgroup of a multiplicative group of a number field. Alte Universität - Seminarraum -201
14:15 • Universität Basel
Jingeon An (Universität Basel)
Abstract:
Minimal surfaces and Allen-Cahn equations are central subjects in Geometric Partial Differential Equations and Geometric Measure Theory. We provide a brief overview of the research history, with a particular focus on Allen-Cahn equations. Subsequently, we introduce a promising alternative to the Allen-Cahn equation, known as the free boundary Allen-Cahn equation.
14:15 • Universität Basel, Spiegelgasse 5, Seminarraum 05.002
Antoine Pinardin (Universität Basel)
Finite simple subgroups of the real Cremona group of rank three abstract
Abstract:
Very little is known about the classification of finite subgroups of Cremona in dimension three. It is natural to start with the case of simple groups, and this step was achieved by Prokhorov in 2009 over the field of complex numbers. In the work I will present, we show that the only non-cyclic finite simple subgroups of the real Cremona group of rank three are A5 and A6. This is a joint project with I. Cheltsov and Y. Prokhorov.
15:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Chiara Ricciuti (Imperial)
Stochastic Burgers Equation from Non-Product Stationary Measures via a Generalised Second-Order Boltzmann-Gibbs Principle abstract
Abstract:
In this talk, we present a generalised second-order Boltzmann-Gibbs principle for conservative interacting particle systems on a lattice whose stationary measures are not of product type and not invariant under particle jumps. The result, which requires neither a spectral gap bound nor an equivalence of ensembles, extends the classical framework to settings with correlated invariant measures and is based on quantitative bounds for the correlation decay. As an application, we show that the equilibrium density fluctuations of the Katz-Lebowitz-Spohn model, for a suitable choice of parameters, converge under diffusive scaling to the stationary energy solution of the stochastic Burgers equation. Based on joint work with P. Gonçalves and G. M. Schütz.
15:30 • EPF Lausanne, CM 1 517
Prof. Dr. Daniel Kressner (EPFL Lausanne)
Randomized linear algebra in scientific computing abstract
Abstract:
Randomized algorithms are becoming increasingly popular in matrix computations. In fact, randomization is on the verge of replacing existing deterministic techniques for several large-scale linear algebra tasks in scientific computing. The poster child of these developments, randomized SVD, is now one of the state-of-the-art approaches for performing low-rank approximation. In this talk, we will go beyond the randomized SVD and illustrate the great potential of randomization to not only speed up existing algorithms, but to also yield novel and often simple algorithms for solving notoriously difficult problems. Examples covered in this talk include reduced order modeling, acceleration of scientific simulations, joint diagonalization, and large null space computation. A common theme of these developments is that randomization helps to transform linear algebra results that only hold generically into robust and reliable numerical algorithms.
15:45 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.2
Irit Dinur (IAS Princeton)
High dimensional expansion and locally testable codes
17:00 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room F 30
Dr. Francesco Pedrotti (ETH Zürich, Switzerland)
Cutoff for the proximal sampler via transport inequalities abstract
Abstract:
The cutoff phenomenon is a sharp transition in the convergence of high-dimensional Markov chains to equilibrium: the total variation distance remains close to 1 for a long time and then rapidly decreases to almost 0 over a much shorter time window.It was initially discovered in the context of card shuffling by Diaconis and Shahshahani, and since then observed in a variety of different models. In spite of its ubiquity, it is still largely unexplained, and most proofs are model-specific.In this talk, we discuss a high-level approach to establishing cutoff based on transport inequalities, and we illustrate it on a popular algorithm known as the proximal sampler, when the target measure on Rd is log-concave.Based on joint work with Justin Salez.
17:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43