Gigliola Staffilani (Massachusetts Institute of Technology)
Dispersive equations and wave turbulence theory abstract
Abstract:
In this course we will investigate questions of weak turbulence theory by using as explicit example of wave interactions the solutions to periodic and nonlinear Schrödinger equations. We will start with Strichartz estimates on periodic setting, then we will move to well-posedness.We will then present two different ways of introducing the evolution of the energy spectrum. We will first work on a method proposed by Bourgain and involving the growth of high Sobolev norms. Then, we will give some ideas of how to derive rigorously the effective dynamics of the energy spectrum itself (wave kinetic equation), when one considers weakly nonlinear dispersive equations.
10:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Ariel Yadin (Ben Gurion University of the Negev)
Big subsets in small groups abstract
Abstract:
There are many different ways groups can be considered "big" or "small". Similarly this can be said about subsets in groups. The simplest example of a big subset in an (amenable) group is a subset that has full density. It is immediate that for any subset of full density, its complement has 0 density. Moreover, one cannot find two disjoint subsets of density greater than a half each.In ongoing joint work with G. Salomon and Y. Svoray, we consider a different notion of big subsets, which is called completely syndetic (CS). It is known that in non-virtually-nilpotent groups there is "enough room" to fit two disjoint CS subsets. We prove that in virtually-Abelian groups this is not possible: the intersection of any two CS subsets is again a CS subset. Moreover, we show that it is possible to find CS subsets of arbitrarily small density.The question of what happens in nilpotent but non-Abelian groups is still open.I will explain all the notions above during the talk, as well as the connection to ideals in the Stone-Cech compactification. No prior knowledge is required.
10:30 • Université de Genève, Conseil Général 7-9, Room 1-05
Marco Inversi (Basel)
Abstract:
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12:15 • Universität Basel, Seminarraum 00.003, Spiegelgasse 1
Philippe Marchner (Université de Grenoble)
Non-overlapping optimized Schwarz method for large scale time-harmonic flow acoustics problems abstract
Abstract:
The numerical resolution of time-harmonic flow acoustic problems at high frequencies is an important tool for noise prediction of aeroengines. However, the upper frequency limit that can be computed is dictated by the available computer memory, which represents a significant bottleneck. In this talk, I will present a substructured optimized Schwarz method for exterior time-harmonic problems governed by the Pierce aeroacoustic operator. Based on developments on non-reflecting boundary conditions, I will discuss the design of efficient transmission operators that account for strong mean flow convection and spatially varying medium properties, in order to accelerate the convergence of the iterative solver. Finally, I will show the application of the method to large-scale three-dimensional problems in a distributed memory setting, highlighting the challenges and potential future improvements.
14:00 • Université de Genève, Conseil Général 7-9, Room 1-05
Lenpeng Ji (University of Leeds)
CANCELLED: Bayesian CART models for aggregate claim modeling abstract
Abstract:
In this talk, we discuss three types of Bayesian CART (or BCART) models for aggregate claim amount, namely, frequency-severity models, sequential models and joint models. We first introduce a general framework for the BCART models applicable to data with multivariate responses, which is particularly useful for the joint BCART models with a bivariate response: the number of claims and aggregate claim amount. To facilitate frequency-severity modeling, we investigate BCART models for the right-skewed and heavy-tailed claim severity data by using various distributions. We discover that the Weibull distribution is superior to gamma and lognormal distributions, due to its ability to capture different tail characteristics in tree models. Additionally, we find that sequential BCART models and joint BCART models, which incorporate dependence between the number of claims and average severity, are beneficial and thus preferable to the frequency-severity BCART models in which independence is assumed. The effectiveness of these models\' performance is illustrated by carefully designed simulations and real insurance data.
14:00 • EPF Lausanne, Extranef 125
Lucas Pesenti (Bocconi University, IT)
Understanding iterative algorithms with Fourier diagrams abstract
Abstract:
We study a broad class of nonlinear iterative algorithms applied to random matrices, including power iteration, belief propagation, approximate message passing, and various forms of gradient descent. We show that the behavior of these algorithms can be analyzed by expanding their iterates in an appropriate basis of polynomials, which we call the Fourier diagram basis. As the dimension of the input grows, this basis simplifies to the tree-shaped diagrams, that form a family of asymptotically independent Gaussian vectors. Moreover, the dynamics of the iteration restricted to the tree diagrams exhibit properties reminiscent of the assumptions of the cavity method from statistical physics. This enables us to "implement" heuristic cavity-based reasoning into rigorous arguments, including a new simple proof of the state evolution formula. Based on joint work with Chris Jones (https://arxiv.org/abs/2404.07881)
14:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.1
Adi Dickstein (Tel Aviv University)
Symplectic versus topological quasi-states abstract
Abstract:
Topological quasi-states are special functionals on the algebra of continuous functions which are linear on single-generated subalgebras. They trace their origins to the von Neumann axioms of quantum mechanics. On symplectic surfaces, every topological quasi-state is symplectic, i.e., linear on Poisson-commutative subalgebras. We discuss the failure of this phenomenon in higher dimensions based on the study of symplectic embeddings of polydiscs. Furthermore, we introduce a Wasserstein-type metric on quasi-states and use it for quantitative constraints on symplectic quasistates. The talk is based on a joint work with Frol Zapolsky.
14:30 • Université de Neuchâtel, Rue Emile-Argand 11, Room A017
Vladimir Rubtsov (LAREMA, UMR 6093 CNRS-Université d’Angers))
Kontsevich and Buchstaber polynomials, multiplication kernels, and beyond abstract
Abstract:
We discuss several partial results of ongoing work in collaboration (with I. Gaiur & D. Van Straten and with V. Buchstaber & I. Gaiur) on interesting properties of multiplication kernels, which include the famous Sonine –Gegenbauer formulas, examples of polynomials for Kontsevich discriminant locus given as addition laws for special 2-valued formal groups (Buchstaber–Novikov–Veselov) as well as a connection with generalized Kowalevska integrable systems. If I have time, I shall try to describe a link between the multiplication kernels and a (kind of) Sklyanin Separation of Variables using our old construction with B. Enriquez.
15:00 • Université de Genève, Conseil Général 7-9, Room 1-07
Dr. Laura Prat
Removable singularities for solutions of the Heat equation and the fractional Heat equation in time varying domains abstract
Abstract:
The talk will be about removable singularities for solutions of the Heat Equation and the Fractional Heat Equation in time varying domains. In order to talk about removability, some associated capacities will be introduced to study its metric and geometric properties. I will discuss onsome results obtained in joint work with X. Tolsa and J. Mateu and also mention some recent achievements with J. Hernández.
15:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Beatrice Toesca di Castellazzo (Institut für Mathematik, Universität Zürich)
What is... Network Coding? abstract
Abstract:
Suppose you want to send a message to your friend. Can errors occur during the transmission? Unfortunately yes. It is then crucial to find ways to detect errors in the received message and possibly correct it. The goal of algebraic coding theory is to design ways of encoding messages (vectors over a finite field) with an algebraic structure that guarantees that, with a limited number of errors, the meaning of the original message is not compromised. In multi-cast communication, as in the streaming of data over the Internet, one deals with sending information to multiple receivers across a network with several intermediate nodes. To improve the network throughput, a coding technique called random linear network coding was developed. In this scenario, the intermediate nodes transmit a random linear combination of the vectors received. With this technique, it is possible to asymptotically achieve the maximum capacity of the network, without relying on its topology. In this talk, we will start studying the basic notions of coding theory with only one sender and one receiver, and then switch to the case of data transmission over a network and explain how in this case giving the messages the structure of a linear subspace helps correcting errors.
16:30 • UZH Zentrum, Building KO2, Room F 150
Vladimir Fock (Université de Strasbourg)
TBK-symplectic structures abstract
Abstract:
A K-symplectic structure on an (algebraic) manifold X is a section of a certain quotient sheaf on X. The Steinberg symbol is a map of this sheaf to an Abelian group. A certain Steinberg symbol gives a symplectic structure on X. Such structures do not exist for every symplectic manifold, but once it exists (and it exists for cluster varieties) one can say much more about this manifold. In particular it gives a pre-quantum line bundle, computes hyperbolic volumes, and in addition gives certain invariants for manifolds over number fields as well as central extensions of simple and affine Lie groups.
16:30 • Université de Neuchâtel, Rue Emile-Argand 11, Room A017