Prof. Dr. Shahar Mendelson (Australian National University)
Proof of the Majorizing Measure Theorem: Part I abstract
Abstract:
As part of a mini-course hosted by the FIM, the speaker will give a complete proof of the Majorizing Measures Theorem (roughly 4h of lecture). In the occasion of the announcement of the awarding of the Abel prize to Michel Talagrand, the organisers suggested, and the speaker kindly agreed, to isolate this part of the course as a 4h event, where the proof (and some of the motivation) will be made accessible also to audience that is not attending the course. This will take place on 10.04.24 split in two two-hour sessions, one in the morning (10:15) and another in the afternoon (14:15), both at G43. All are welcome and we hope to see many of you there!
10:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Sofia Amontova (UniGE)
Numerical invariants of representations of complex hyperbolic lattices abstract
Abstract:
Representations of fundamental groups of manifolds into PU(n, 1) havebeen studied from various viewpoints. In the context of higher Teich-müller theory, the so-called Toledo invariant in its different incarnationshas been most commonly employed to single out special classes of re-presentations of surface groups. In the extended setting of higher di-mensional non-compact complex hyperbolic manifolds of finite volume,other types of volume invariants prove to be useful. The talk aims topresent the volume invariant of representations using the machinery ofbounded cohomology and to prove an integrality result in the extendedsetting. Joint work with Michelle Bucher.
10:20 • Université de Fribourg, room Phys 2.52
Prof. Dr. Carlos Matheus Silva Santos (CNRS)
Non-conical strictly convex divisible sets are maximally anisotropic abstract
Abstract:
Let U be a non-conical strictly convex divisible set. Even though the boundary S of U is not C^2, Benoist showed that S is C^1+ and Crampon established that S has a sort of anisotropic Holder regularity -- described by a list L of real numbers -- at almost all of its points. In this talk, we discuss our joint work with P. Foulon and P. Hubert showing that S is maximally anisotropic in the sense that the list L contains no repetitions thanks to the features of the Hilbert flow.
13:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.1
Roman Shvydkoy (University of Illinois at Chicago)
Abstract:
The classical Kolmogorov-41 theory of turbulence is based on a set of pivotal assumptions on scaling and energy dissipation for solutions satisfying incompressible fluid models. In the early 80\'s experimental evidence emerged that pointed to departure from the K41 predictions, which was attributed to the phenomenon of statistical intermittency. In this talk we give an overview of the classical results in the subject, relationship of intermittency to the problem of global well-posedness of the 3D Navier-Stokes system, and discuss a new approach developed jointly with A. Cheskidov on how to measure and study intermittency from a rigorous perspective. At the center of our discussion will be a new interpretation of an intermittent signal described by volumetric properties of the filtered field. It provides, in particular, a systematic approach to the Frisch-Parisi multifractal formalism, and recasts intermittency from the point of view of information theory.
14:15 • Universität Basel, Spiegelgasse 5, Seminarraum 05.002
Prof. Dr. Shahar Mendelson (Australian National University)
Proof of the Majorizing Measure Theorem: Part II abstract
Abstract:
As part of a mini-course hosted by the FIM, the speaker will give a complete proof of the Majorizing Measures Theorem (roughly 4h of lecture). In the occasion of the announcement of the awarding of the Abel prize to Michel Talagrand, the organisers suggested, and the speaker kindly agreed, to isolate this part of the course as a 4h event, where the proof (and some of the motivation) will be made accessible also to audience that is not attending the course. This will take place on 10.04.24 split in two two-hour sessions, one in the morning (10:15) and another in the afternoon (14:15), both at G43. All are welcome and we hope to see many of you there!
14:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Jean-Dominique Deuschel (TU Berlin)
An isomorphism theorem for anharmonic fields and scaling limits abstract
Abstract:
We introduce a natural measure on bi-infinite random walk trajectories evolving in a time-dependent environment driven by the Langevin dynamics associated to a gradient Gibbs measure with convex potential. We derive an identity relating the occupation times of the Poissonian cloud induced by this measure to the square of the corresponding gradient field, which is generically not Gaussian. In the quadratic case, we recover a well-known generalization of the second Ray-Knight theorem. We further determine the scaling limits of the various objects involved in dimension 3, which are seen to exhibit homogenization. In particular, we prove that the renormalized square of the gradient field converges under appropriate rescaling to the Wick-ordered square of a Gaussian free field on R^3 with suitable diffusion matrix, thus extending a celebrated result of Naddaf and Spencer regarding the scaling limit of the field itself.
16:00 • EPF Lausanne, CM 1 517
Dr. Kaibo Hu (University of Edinburgh, UK)
Towards Finite Element Tensor Calculus abstract
Abstract:
Finite Element Exterior Calculus (FEEC) provides a cohomology framework for structure-preserving discretisation of a large class of PDEs. Differential complexes are important tools in FEEC. The de Rham complex is a basic example, with applications in curl-div related problems such as the Maxwell equations. There is a canonical finite element discretisation of the de Rham complex, which in the lowest order case coincides with discrete differential forms (Whitney forms). Different problems involve different complexes. In this talk, we provide an overview of some efforts towards Finite Element Tensor Calculus, inspired by tensor-valued problems from continuum mechanics and general relativity. On the continuous level, we systematically derive new complexes from the de Rham complexes. On the discrete level, We review the idea of distributional finite elements, and use them to obtain analogies of the Whitney forms for these new complexes. A special case is Christiansen’s finite element interpretation of Regge calculus, a discrete geometric scheme for metric and curvature.
16:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room E 1.2
Dr. Hugo Vanneuville (CNRS, Université Grenoble Alpes)
Exponential decay for Bernoulli percolation via stochastic comparison abstract
Abstract:
Bernoulli percolation of parameter p on Z^d is defined by deleting each edge of Z^d with probability 1-p, independently of the other edges. The exponential decay theorem - proven in the 80\'s by Menshikov and, independently, by Aizenman and Barsky - can be stated as follows: If the cardinality of the cluster of 0 is a.s. finite at some parameter p, then it has an exponential moment at every parameter q<p. I like to state this theorem this way because it illustrates the fact that decreasing p infinitesimally has a regularising effect on the percolation clusters. A new - shorter - proof has been proposed by Duminil-Copin and Tassion in 2016. The goal of this talk is to propose yet a new proof of this theorem, inspired by Russo\'s work from the early 80s, which relies on stochastic comparison techniques.
17:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43