Sami Douba (IHES Paris)
Systoles of hyperbolic hybrids abstract
Abstract:
We exhibit in any dimension n > 2 and for any positive integer m acollection of m pairwise incommensurable closed hyperbolic n-manifoldsof the same volume each possessing a unique shortest closed geodesic ofthe same length less than 1/m.
10:20 • Université de Fribourg, room Phys 2.52
Stefan Kebekus
Differential forms on singular spaces abstract
Abstract:
This talk surveys extension theorems for differential forms on singular complex spaces and explains their use in the study of minimal varieties. We survey a number of applications, pertaining to classification and characterisation of special varieties, non-Abelian Hodge Theory in the singular setting, and quasi-étale uniformization.
13:00 • EPF Lausanne, CM 1 517
Prof. Dr. Martin Leguil (École polytechnique)
Rigidity of u-Gibbs measures for certain Anosov diffeomorphisms of the 3-torus. abstract
Abstract:
We consider Anosov diffeomorphisms of the 3-torus $\\mathbb{T}^3$ which admit a partially hyperbolic splitting $\\mathbb{T}^3 = E^s \\oplus E^c \\oplus E^u$ whose central direction $E^c$ is uniformly expanded. We may consider the 2-dimensional unstable foliation $W^{cu}$ tangent to $E^c \\oplus E^u$, but also the 1-dimensional strong unstable foliation $W^u$ tangent to $E^u$. The behavior of $W^{cu}$ is reasonably well understood; in particular, such systems have a unique invariant measure whose disintegrations along the leaves of $W^{cu}$ are absolutely continuous: the SRB measure. The behavior of $W^u$ is less understood; we can similarly consider the class of measures whose disintegrations along the leaves of $W^u$ are absolutely continuous, the so-called u-Gibbs measures. It is well-known that the SRB measure is u-Gibbs; conversely, in a joint work with S. Alvarez, D. Obata and B. Santiago, we show that in a neighborhood of conservative systems, if the strong bundles $E^s$ and $E^u$ are not jointly integrable, then there exists a unique u-Gibbs measure, which is the SRB measure.
13:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.1
Prof. Dr. Ran Tessler (Weizmann Institute)
Open FJRW theory in genus 0 and mirror symmetry abstract
Abstract:
We define the g=0 open FJRW theory for (W,G) where W is a Fermat polynomial and G is its maximal symmetry group. We calculate all disk invariants, and classify the wall crossing group. We prove mirror symmetry with Saito\'s B-model.Based on joint works with Mark Gross and Tyler Kelly.
13:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Prof. Dr. Anna Florio (Université Paris Dauphine-PSL)
Birkhoff attractor of dissipative billiards abstract
Abstract:
In a joint work with Olga Bernardi and Martin Leguil, we study the dynamics of dissipative convex billiards. In these billiards, the usual elastic reflection law is replaced with a new law where the angle bends towards the normal after each collision. For such billiard dynamics there exists a global attractor; we are interested in the topological and dynamical complexity of an invariant subset of this attractor, the so-called Birkhoff attractor, whose study goes back to Birkhoff, Charpentier, and, more recently, Le Calvez. We show that for a generic convex table, on one hand, the Birkhoff attractor is simple, i.e., a normally contracted submanifold, when the dissipation is strong; while, on the other hand, the Birkhoff attractor is topologically complicated and presents a rich dynamics when the dissipation is mild.
14:45 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.1
Mario Jung
Construction of Linear Codes using Latin squares abstract
Abstract:
In our globalised and digitalised world, fast and error-free communication is very important. To ensure this, we use error-correcting codes which should always be more efficient and have a higher error-correcting capacity. In this thesis, we investigate two types of LDPC codes which are obtained from Latin squares. The first is based on orthogonal Latin squares and the second is formed using Steiner 2-designs generated by a Latin square. For each code there is a bipartite graph in which cycles can occur. Such cycles can negatively influence the decoding efficiency. To counteract this, we will see how to locate and analyse these cycles and how to remove them.
15:15 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H 25
Laura Marino (Institut de Mathématiques de Jussieu-Paris Rive Gauche)
Gordian distance bounds from Khovanov homology abstract
Abstract:
The Gordian distance u(K,K\') between two knots K and K\' is defined asthe minimal number of crossing changes needed to relate K and K\'. Theunknotting number of a knot K, a classical yet hard to compute knotinvariant, arises as the Gordian distance between K and the trivialknot.Several lower bounds for both invariants exist. A well-known bound forthe unknotting number is given by the Rasmussen invariant, which isextracted from Khovanov homology, a bigraded chain complex associated toa knot up to chain homotopy equivalence.In this talk, I will introduce a new lower bound for the Gordiandistance, \\lambda, coming from Khovanov homology. After introducing allthe relevant ingredients I will present some results about \\lambda. Inparticular, \\lambda turns out to be sharper than the Rasmussen invariantas a lower bound for the unknotting number. This is based on joint work with Lukas Lewark and Claudius Zibrowius.
15:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Prof. Dr. Sergios Agapiou (University of Cyprus)
A new way for achieving Bayesian nonparametric adaptation abstract
Abstract:
We will consider Bayesian nonparametric settings with functional unknowns and we will be interested in evaluating the asymptotic performance of the posterior in the infinitely informative data limit, in terms of rates of contraction. We will be especially interested in priors which are adaptive to the smoothness of the unknown function.In the last decade, certain hierarchical and empirical Bayes procedures based on Gaussian process priors, have been shown to achieve adaptation to spatially homogenous smoothness. However, we have recently shown that Gaussian priors are suboptimal for spatially inhomogeneous unknowns, that is, functions which are smooth in some areas and rough or even discontinuous in other areas of their domain. In contrast, we have shown that (similar) hierarchical and empirical Bayes procedures based on Laplace (series) priors, achieve adaptation to both homogeneously and inhomogeneously smooth functions. All of these procedures involve the tuning of a hyperparameter of the Gaussian or Laplace prior.After reviewing the above results, we will present a new strategy for adaptation to smoothness based on heavy-tailed priors. We will illustrate it in a variety of nonparametric settings, showing in particular that adaptive rates of contraction in the minimax sense (up to logarithmic factors) are achieved without tuning of any hyperparameters and for both homogeneously and inhomogeneously smooth unknowns. We will also present numerical simulations corroborating the theory. This is joint work with Masoumeh Dashti, Tapio Helin, Aimilia Savva and Sven Wang (Laplace priors) and Ismaël Castillo (heavy-tailed priors)
16:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room E 1.2
Dr. Victor Rivero (CIMAT Guanajuato)
Recurrent extensions and Stochastic Differential equations abstract
Abstract:
In the 70\'s Itô settled the excursion theory of Markov processes, which is nowadays a fundamental tool for analyzing path properties of Markov processes. In his theory, Itô also introduced a method for building Markov processes using the excursion data, or by gluing excursions together, the resulting process is known as the recurrent extension of a given process. Since Itô\'s pioneering work the method of recurrent extensions has been added to the toolbox for building processes, which of course includes the martingale problem and stochastic differential equations. The latter are among the most popular tools for building and describing stochastic processes, in particular in applied models as they allow to physically describe the infinitesimal variations of the studied phenomena. In this work we answer the following natural question. Assume X is a Markov process taking values in R that dies at the first time it hits a distinguished point of the state space, say 0, which happens in a finite time a.s., that X satisfies a stochastic differential equation, and finally that X admits a recurrent extension, say Z, is a processes that behaves like Z up to the first hitting time of 0, and for which 0 is a recurrent and regular state. If any, what is the SDE satisfied by Z? Our answer to this question allows us to describe the SDE satisfied by many Feller processes. We analyze various particular examples, as for instance the so-called Feller brownian motions and diffusions, which include their sticky and skewed versions, and also continuous state branching processes and spectrally positive Levy processes.
17:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43