Karoly Böröczky (Alfréd Rényi Institute of Mathematics)
The Isoperimetric inequality, the Brunn-Minkowski theory, and the Lp Minkowski problem
10:15 • Zoom
Letizia Issini (Université de Genève)
Divergence of wreath products and Houghton groups abstract
Abstract:
Divergence of finitely generated groups is a quasi-isometry invariant that describes how difficult it is to connect two points in a Cayley graph of a group, avoiding a certain ball around the identity. It was defined by Gersten in 1994, when he gave the first example of a CAT(0)-group whose divergence is neither linear nor exponential. In this talk I will present the definition of divergence, mention some results about it, and focus on divergence of wreath products and Houghton groups.
10:30 • Université de Genève, Conseil Général 7-9, Room 1-05
Elena Vigna (University of Turin)
Tail optimality and preferences consistency for intertemporal optimization problems abstract
Abstract:
Given an intertemporal optimization problem over a time interval $[t_0,T]$ and a control plan associated to it, we introduce the four notions of local and global tail optimality of the control plan, and local and global preferences consistency of the agent. While the notion of tail optimality of a control plan is not new, the main innovation of this paper is the definition of preferences consistency of an agent, that is a novel concept.
We prove that, in the case of a \\emph{linear} time-consistent problem where dynamic programming can be applied, the optimal control plan is globally tail-optimal and the agent is globally preferences-consistent. Opposite, in the case of a \\emph{non-linear} problem that gives rise to time inconsistency, we find that global tail optimality and global preferences consistency do not coexist. We analyze three common ways to attack a time-inconsistent problem: (i) precommitment approach, (ii) dynamically optimal approach, (iii) consistent planning approach. We find that none of the three approaches keeps simultaneously the desirable properties of global tail optimality and global preferences consistency: the existing approaches to time inconsistency are flawed in various ways. We also prove that if the performance criterion includes a convex function of expected final wealth and a globally tail-optimal plan exists, then the three approaches coincide and the problem is linear.
The contribution of the paper is to disentangle the notion of time consistency into the two notions of tail optimality and preferences consistency. The analysis should shed light on the price to be paid in terms of tail optimality and preferences consistency with each of the three approaches currently available for time inconsistency.
11:00 • EPF Lausanne, UniL campus, Extranef 125
Julien Levallois (Science Innovation Hub, Université de Genève)
L’Innovation et l’Entrepreneuriat à l’Université abstract
Abstract:
L’Entrepreneuriat est-il compatible avec une activité de recherche ou lorsque l’on est étudiant-e en Mathématiques ? Vous avez éventuellement une idée (commerciale) innovante et vous aimeriez créer votre propre entreprise ?
Ce séminaire vise à encourager et à renforcer la culture de l’innovation, l’esprit d’entreprise et le développement de nouvelles idées auprès des étudiant-es et des chercheur-euses. Nous aborderons en particulier les différentes étapes du développement d’un projet entrepreneurial et verrons qu’il s’agit d’un processus quasi-scientifique et qui peut s’apprendre. Le plus important étant qu’il constitue une véritable opportunité de carrière et de transfert de savoir.
14:00 • Université de Genève, Conseil Général 7-9, Room 1-05
Nicolas Perkowski (Freie Universität Berlin)
Title T.B.A.
15:00 • EPF Lausanne, Salle CM 0 11
Prof. Dr. Matteo Bonforte (Universidad Autonoma Madrid)
Nonlinear and Nonlocal Diffusions. Smoothing effects, Green functions and functional inequalities abstract
Abstract:
We will consider the Cauchy problem for Nonlinear Diffusion equations of porous medium type $u_t=-\\mathcal{L} u^m$, with $m>1$ and investigate whether or not integrable data produce bounded solutions. The diffusion operator belongs to a quite general class of nonlocal operators, and we will see how different assumption on the operator imply (or not) smoothing properties. We will briefly compare the approach based on Moser iteration and the approach through Green functions. On the one hand, we show that if the linear case ($m=1$) enjoys smoothing properties, also the nonlinear will do. On the other hand, we see that in some cases the nonlinear diffusion enjoys the smoothing properties also when the linear counterpart does not, thanks to the convex nonlinearity. Following Nash\' ideas, we see how smoothing properties are often equivalent to the validity of Gagliardo-Nirenberg-Sobolev (and Nash) inequalities: we explore these implications also in the nonlinear and nonlocal context and the connection with dual inequalities (Hardy-Littlewood-Sobolev) and Green function estimates. This is a work with J. Endal (NTNU, Trondheim). Finally, I shall present smoothing and higher regularity estimates for a class of zero-order p-Laplacian evolution equations, showing another case in which the regularization is true in the nonlinear setting while it fails for the linear counterpart. This is a work in progress with A. Salort (Univ. Buenos Aires).
15:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Boaz Nadler (The Weizmann Institute of Science, Israel)
Spectral Methods for Reconstructing Trees abstract
Abstract:
Tree graphical models are common statistical models for data in a wide variety of applications. Tree models are particularly popular in phylogenetics, where an important task is to infer the evolutionary history of current species. Given observations at the leaves of the tree, a common problem is to reconstruct the tree\'s latent structure. We present two simple spectral-based methods for tree recovery:
(i) A bottom up spectral neighbor joining method (SNJ); and
(ii) STDR - a spectral based top down method.
We prove that under suitable assumptions, both methods are consistent and derive finite sample recovery guarantees. We illustrate the competitive performance of our algorithms in comparison with popular tree recovery methods.
15:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.2
Andrey Krutov (University of Prague)
Noncommutative differential geometry of the quantum Grassmannians abstract
Abstract:
Noncommutative geometry is, in general, more tractable on quantum homogeneous spaces than on quantum groups themselves. Some of the best-behaved examples are the irreducible quantum flag manifolds. We will review recent results about noncommutative (complex) differential geometry of the irreducible quantum flag manifolds. The main example here will be the quantum Grassmannians. In particular, in the talk we will discuss noncommutative generalization of the following notions from the classical complex differential geometry: complex structures, holomorphic homogeneous line bundles, Hodge structures, Fano structures, and Schubert calculus.
15:15 • Université de Genève, Conseil Général 7-9, Room 1-07
Laura Ciobanu (Heriot-Watt University, Edinburgh)
Equations in groups: between decidability and undecidability abstract
Abstract:
For a group or semigroup or ring G, solving equations where the coefficients are elements in G and the solutions take values in G can be seen as akin to solving systems of linear equations in linear algebra, Diophantine equations in number theory, or more generally, polynomial systems in algebraic geometry.
In this talk I will give a survey about solving equations in infinite groups, with emphasis on the free ones, and show how imposing certain constraints on the solutions can tilt the balance between decidability and undecidability.
16:00 • Université de Neuchâtel, Rue Emile Argand 11, Auditoire B013
Mireille Soergel (ETHZ)
What is... the Davis Complex? abstract
Abstract:
The study of abstract reflection groups is due to Tits, who defines Coxeter systems (W,S) through their presentation. There are many different combinatorial and geometric objects associated to such Coxeter systems (W,S). One of them is the Davis complex. The goal of this talk is to introduce abstract Coxeter groups and describe their associated Davis complex.
16:15 • UZH Zentrum, Building KO2, Room F 150