Prof. Dr. Shahar Mendelson
Do we really need the Rademacher complexities? abstract
Abstract:
The sample complexity of learning in a convex class and with respect to the squared loss is arguably the most important question in Statistical Learning Theory. The state-of-the-art estimates in this setting rely on Rademacher complexities, and those are generally difficult to control. I will explain why (contrary to prevailing belief) and under minimal assumptions, the Rademacher complexities are not really needed: the sample complexity is actually governed by the behaviour of the limiting gaussian process. In particular, all such learning problems that have the same L_2 structure - even those with heavy-tailed distributions - share the same sample complexity as if the problem were light-tailed. At the heart of the proof is the construction of uniform mean estimation procedures for some natural function classes. I will show how such uniform mean estimation procedures can be derived by combining optimal mean estimation techniques for real-valued random variables with Talagrand\'s generic chaining method.
10:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room F 26.1
Adam Kanigowski (University of Maryland)
Sparse Equidistribution Problems in Dynamics
10:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Andrey Gogolyev (-)
Rigidity of partially hyperbolic skew products abstract
Abstract:
This is joint work with Jon DeWitt. We study skew products over area-preserving Anosov diffeomorphisms on T^2×G, where G is a compact Lie group, given by (x,g)?(f(x),h(x)·g). We establish smooth rigidity; that is, if two such skew products are C^0 conjugate, then they are smoothly conjugate, unless h:T^2->G is cohomologous to a constant and the skew product is, in fact, a product with a translation on G. Interestingly, on twisted principal G-bundles, our approach gives exception-free rigidity.
13:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room E 33.1
Prof. Dr. Qile Chen (Boston College)
The tropical geometry of logarithmic Gauged Linear Sigma Models abstract
Abstract:
How does counting curves in a complete intersection relate to the geometry of the ambient space? In this talk, I will introduce a tropical decomposition formula as an explicit answer to this Quantum Lefschetz type problem in the Gromov-Witten setting. More precisely, the tropical decomposition formula shows that Gromov-Witten of complete intersections can be approximated using ambient data, with correction terms given by virtual counts of (generalized) special linear series. The tropical decomposition formula is derived from studying the boundary structures of logarithmic Gauged Linear Sigma Models. This is a joint work in progress with Felix Janda and Yongbin Ruan.
13:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Stefano Modena (GSSI L\'Aquila)
Abstract:
For the linear continuity equation associated to incompressible vector fields we show that the set of vector fields in $L^q_x$, $q<\\infty$, for which the continuity equation admits a unique distributional solution in $L^{q\'}_x$ (for all initial data) is generic in the Baire category sense, whereas its complement, as well as some particular subset of it, is dense. Analog results for the ODE associated to continuous vector fields will be also discussed. (Joint work with Francesco Cianfrocca).
14:15 • Universität Basel, Spiegelgasse 5, Seminarraum 05.002
Paula Truöl (MPIM Bonn)
Non-complex cobordisms between quasipositive knots abstract
Abstract:
Quasipositive knots occur in complex geometry as transverse intersections of smooth algebraic curves in the complex plane ℂ2 with the 3-sphere. A complex cobordism is a surface that arises as a transverse intersection of a smooth algebraic curve with the region bounded between two 4-balls of different radius with common center in ℂ2. The two knots bounded by a complex cobordism are necessarily quasipositive, and such a cobordism is necessarily optimal (defined in the talk). Feller asked whether these two necessary conditions for the existence of a complex cobordism between two knots are sufficient. In a joint work with Maciej Borodzik we answer this in the negative for cobordisms of any genus g ≥ 0. In the case of genus g = 0, we improve our result to strongly quasipositive knots.In the talk, we will define the relevant terms and provide some context for our results.
15:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Yves Lejan (Université Paris-Saclay)
Loops, trees and fields on complete graphs abstract
Abstract:
After introducing the relations between spanning trees, random loops and bosonic/fermionic fields on general graphs, we focus on the case of the complete graph and derive a few asymptotics as its size increases to infinity.
16:00 • EPF Lausanne, CM1 517
Dr. Allen Fang (Universität Münster)
Wave behavior in the vanishing cosmological constant limit abstract
Abstract:
Black hole stability is a central topic in mathematical relativity that has seen numerous advancements in recent years. Both the Kerr-de Sitter and the Kerr black hole spacetimes have been proven to be stable in the slowly-rotating regime. However, the methods used have been markedly different, as well as the decay rates proven. Perturbations of Kerr-de Sitter converge exponentially back to a nearby Kerr-de Sitter black hole, while perturbations of Kerr only converge polynomially back to the family. In this talk, I will speak about wave behavior that is uniform in the cosmological constant by considering solutions to the Teukolsky equations in Kerr(-de Sitter). The main point is a careful handling of the relevant estimates on the region of the spacetime far from the black hole. This provides a first step into understanding the uniform (in the cosmological constant) stability of black hole spacetimes. This is joint work with Jeremie Szeftel and Arthur Touati.
16:15 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H 46
Dr. Martin Halla (Karlsruhe Inst. of Technology)
On the redundancy of regularity splittings for wavenumber explicit hp-FEM analysis abstract
Abstract:
It is well known that finite element approximations of the Helmholtz equation suffer from thepollution effect for large wavenumbers k>0. This degeneracy can be avoided by the applicationof high order FEMs, with polynomial degree p chosen proportional to log k. The key ingredientof the respective analysis [1] is a so-called regularity splitting, which decomposes the solutionof the Helmholtz equation with a L^2 right hand-side into an analytical part and k-well behavedH^2 part. The generalization of this technique for nonconstant coefficients and other boundaryconditions is technical and nontrivial, but has received much attention lately. In this talk I showhow the classical Schatz technique can be adapted to circumvent the necessity of any regularitysplitting, which significantly simplifies the analysis. In the second part of the talk I discuss theapplication of this approach to heterogeneous media and Maxwell-impedance problems.[1] M. Melenk and S. Sauter, Convergence analysis for finite element discretizations ofthe Helmholtz equation with Dirichlet-to-Neumann boundary conditions, Math. Comp.,79(272):1871–1914, 2010.
16:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.2
Prof. Dr. Justin Salez (Université Paris-Dauphine & PSL)
An invitation to the cutoff phenomenon abstract
Abstract:
The cutoff phenomenon is an abrupt transition from out of equilibrium to equilibrium undergone by certain Markov processes in the limit where the size of the state space tends to infinity. Discovered four decades ago in the context of card shuffling, this surprising phenomenon has since then been observed in a variety of models, from random walks on groups or complex networks to interacting particle systems. It is now believed to be universal among fast-mixing high-dimensional processes. Yet, current proofs are heavily model-dependent, and identifying the general conditions that trigger a cutoff remains one of the biggest challenges in the quantitative analysis of finite Markov chains. In this talk, I will provide a self-contained introduction to this fascinating question, and then describe a recent partial answer based on entropy and curvature. Joint work with Francesco Pedrotti.
17:15 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H12