Claudio Llosa (Karlsruhe Institute of Technology)
Finiteness properties of coabelian subgroups of hyperbolic groups abstract
Abstract:
Hyperbolic groups form an important class of finitely generated groups that has attracted much attention in Geometric Group Theory. We call a group of finiteness type $F_n$ if it has a classifying space with finitely many cells of dimension at most $n$, generalising finite generation and finite presentability, which are equivalent to types $F_1$ and $F_2$. Hyperbolic groups are of type $F_n$ for all $n$ and it is natural to ask if their subgroups inherit these strong finiteness properties. In recent work with Py, we used methods from Complex Geometry to prove that for every $n>0$ there is a hyperbolic group with a subgroup of type $F_{n-1}$ and not $F_n$. This answers an old question of Brady and produces many finitely presented non-hyperbolic subgroups of hyperbolic groups. In this talk we will explain this result and present other recent progress on constructing coabelian subgroups of hyperbolic groups with exotic finiteness properties. This talk is based on joint works with Kropholler, Martelli--Py, and Py.
10:30 • Université de Genève, Conseil Général 7-9, Room 1-05
Dr. Jean-Baptiste Teyssier (Université Sorbonne)
Cohomological boundedness for flat bundles and applications abstract
Abstract:
We will advertise some consequences of the conjectural existence of moduli spaces for flat bundles with prescribed behaviour at infinity. We will then sketch unconditional proofs in the surface case. This is joint work with Haoyu Hu.
13:15 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H 25
Davide Perego (University of Sevilla)
Finiteness properties of coabelian subgroups of hyperbolic groups abstract
Abstract:
The Gromov boundary of a hyperbolic group is a widely studied object in the field of geometric group theory. Many authors tried to provide topological approximations and recursive presentations for this boundary. After recalling some properties of hyperbolic groups and language theoretic notions, we will describe the tree of atoms. It was originally introduced by Belk, Bleak and Matucci in order to prove that hyperbolic groups embed into the rational group of asynchronous transducers and, later, to prove the Boone-Higman conjecture. Then, we will speak about its connections with the hyperbolic world and we will see some ways to approximate and recursively present the Gromov boundary via this tree.
14:00 • Université de Genève, Conseil Général 7-9, Room 6-13
Nicola Guglielmi (GSSI L\'Aquilla)
Solving numerically differential equations with distributed delays abstract
Abstract:
Sinopsis:In the early Nineties Ernst Hairer developed a famous code for the numerical approximation of stiff and differential algebraic problems, Radau5, which is based on the $3$-stage Radau IIa Runge Kutta method. The code became very popular and is nowadays one of the most important for the numerical approximation of implicit and stiff ODEs.Later, between 2000 and 2005, Ernst and I developed a code, Radar5, which extended Radau5 to delay differential equations with discrete delays (in short DDEs).Due to the increasing importance of models with distributed delays, for example in pharmacodynamics and pharmacokinetics (e.g Shuhua Hu et al., 2018), we have been recently addressed to certain kind of differential equations with distributed delays (in short DDDEs), where the dependence on the solution in the past appears through an integral term.In this talk I will explain how these problems can indeed be approximated by suitable systems of ODEs or DDEs, according to the kind of distributed term.The main ideas here are two:(i) replacing the kernels by suitable quasi-polynomial expansions, that is sums of polynomials multiplied by exponentials, and then transforming the distributed (integral) delay term into a set of ODEs (or DDEs);(ii) making the method efficient by exploiting the structure at the level of the linear algebra.Numerical evidence of the effectiveness of the proposed approach is illustrated on a few illustrative examples.
14:00 • Université de Genève, Conseil Général 7-9, Room 1-05
Prof. Dr. Christian Brennecke (University of Bonn )
Operator Norm Bounds on the Correlation Matrix of the SK Model abstract
Abstract:
In this talk I will review basic predictions for the high temperature regime, the so called replica symmetric regime, of the Sherrington-Kirkpatrick mean field spin glass. I will recall the TAP equations and their derivation in connection with the decay of the two point correlation functions. For the simplified case of vanishing external field, I will present some details on recent results that characterize the susceptibility of the model as a resolvent of the interaction matrix, which predicts in a simple way the (well-known) RS-RSB transition temperature. The talk is based on joint work with Adrien Schertzer, Changji Xu and Horng-Tzer Yau.
14:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.1
Stevan Gajovic (Charles University Prague)
Title T.B.A.
14:15 • EPF Lausanne
Giuseppe Carleo (EPFL)
Title T.B.A.
16:15 • EPF Lausanne, GA 3 21
Zohreh Ravanpak (Timisoara)
Nonassociative generalization of Lie groupoids and discrete mechanics abstract
Abstract:
Smooth Loops are a generalization of Lie groups by dropping associativity.They are well-established objects in mathematics and they found severalapplications in physics and geometry. In this talk, we extend this notion tosmooth loopoids, nonassociative analogs of Lie groupoids.Lie groupoids play an important role in the standard formulation of discreteLagrangian and Hamiltonian Mechanics. After recalling this formalism in thesecond part of the talk, we show that the associativity assumption is notessential here. This is illustrated in an example using unitary octonions as thediscrete configuration space of a mechanical system.This is based on joint work with J. Grabowski.
16:30 • Université de Genève, Section de mathématiques, 7-9 rue du Conseil-Général, Room 1-07
Peter Feller (ETHZ)
Controlled hyperbolization of 3-manifolds abstract
Abstract:
After a brief survey of the study of low-dimensional manifolds -- spaces locally modelled on the topological space R^n for n<5 -- we will discuss the idea of geometrization. The latter refers to a program, initiated by Thurston, of studying 3-dimensional manifolds by means of eight geometric model spaces, which include the Euclidean space (R^3 endowed with the ordinary Euclidean metric) and hyperbolic space.It turns out that most 3-dimensional manifolds carry a hyperbolic structure, i.e. they are locally modelled on hyperbolic space. A precise version of this statement was proven by Maher invoking topological work of Hempel and Perelman\'s celebrated analysis results on Ricci-flow. We will discuss an approach to hyperbolization of most 3-dimensional manifolds that circumvents invoking the Ricci flow. As an upshot, with this approach one can control many geometric quantities such as injectivity radius, diameter, and volume of hyperbolic structures. We will provide ``hands-on\'\' examples of 3-manifolds that can be hyperbolized with this scheme.Based on joint work in progress with A. Sisto and G. Viaggi. No knowledge of low-dimensional topology or hyperbolic geometry will be assumed.
17:00 • Université de Neuchâtel, Institut de Mathématiques, B103
Daniela M. Witten (University of Washington)
Data thinning and its applications abstract
Abstract:
We propose data thinning, a new approach for splitting an observation from a known distributional family with unknown parameter(s) into two or more independent parts that sum to yield the original observation, and that follow the samedistribution as the original observation, up to a (known) scaling of a parameter. This proposal is very general, and can be applied to a broad class of distributions within the natural exponential family, including the Gaussian, Poisson,negative binomial, Gamma, and binomial distributions, among others. Furthermore, we generalize data thinning to enable splitting an observation into two or more parts that can be combined to yield the original observation using anoperation other than addition; this enables the application of data thinning far beyond the natural exponential family.Data thinning has a number of applications to model selection, evaluation, and inference. For instance, cross-validation via data thinning provides an attractive alternative to the "usual" approach of cross-validation via sample splitting,especially in unsupervised settings in which the latter is not applicable. We will present an application of data thinning to single-cell RNA-sequencing data, in a setting where sample splitting is not applicable.This is joint work with Anna Neufeld (Fred Hutch), Ameer Dharamshi (University of Washington), Lucy Gao (University of British Columbia), and Jacob Bien (University of Southern California)
17:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room F 30
Thomas Mettler (FernUni Schweiz)
The Schwarzian derivative and the degree of a classical minimal surface abstract
Abstract:
The talk starts with a gentle introduction to minimal surfaces and basic notions from projective geometry. Using the Schwarzian derivative I will then explain how to construct a sequence of meromorphic differentials on every non-flat oriented minimal surface in Euclidean 3-space. A minimal surface is said to have degree n if its n-th differential is a polynomial expression in the differentials of lower degree. Various well-known minimal surfaces are identified as surfaces of low degree. Based on joint work with Jacob Bernstein & Lukas Poerschke.
17:15 • Université de Fribourg, room Phys 2.52