Bo\'az Klartag (The Weizmann Institute of Science)
Isoperimetric inequalities in high-dimensional convex sets
10:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Prof. Dr. Marco Mondelli (ISTA)
Precise Asymptotics for Spectral Estimators: A Story of Phase Transitions, Random Matrices and Approximate Message Passing abstract
Abstract:
Spectral methods are a simple yet effective approach to extract information from data which is high-dimensional, i.e., where sample size and signal dimension grow proportionally. As a prelude, we will consider the prototypical problem of inference from a generalized linear model with an i.i.d. Gaussian design. Here, the spectral estimator is the principal eigenvector of a data-dependent matrix. We will discuss the emergence of a (BBP-like) phase transition in the spectrum of this random matrix and how such phase transition is related to signal recovery. The core of the talk will then deal with two models that capture the heterogeneous and structured nature of practical data. First, we will consider a multi-index model where the output depends on the inner product between the feature vector and a fixed number $p$ of signals, and the focus is on recovering the subspace spanned by the signals via spectral estimators. By using tools from random matrix theory, we will locate the top-$p$ eigenvalues of the spectral matrix and establish the overlaps between the corresponding eigenvectors (which give the spectral estimators) and a basis of the signal subspace. Second, we will consider a generalized linear model with a correlated design matrix. Here, the analysis of the spectral estimator relies on tools based on approximate message passing, and we will present a methodology which is broadly applicable to the study of spiked matrices. In all these settings, the precise asymptotic characterization we put forward enables the optimization of the data preprocessing, thus allowing to identify the spectral estimator that requires the minimal sample size for signal recovery.
14:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.1
Sasha Merkurjev
Inverse Galois Problem and Galois cohomology abstract
Abstract:
A central issue in modern Galois theory is the profinite inverseGalois problem, which asks how to characterize absolute Galois groups offields among all profinite groups. While an answer to this question isunknown, even conjecturally, several necessary conditions for a profinitegroup to qualify as an absolute Galois group have been established.The most classical result in this direction is due to Artin and Schreier, whoproved thatevery non-trivial finite subgroup of an absolute Galois group is cyclic oforder 2.A much deeper necessary condition is the Bloch-Kato conjecture, now a theoremdue to Voevodsky and Rost, which in particular implies that the mod pcohomology ring of an absolute Galois group of a field containing aprimitive p-th root of unity is generated in degree 1 with relations in degree2.In the lecture, we will discuss restrictions to the profinite inverse Galoisproblemcoming from the embedding problem with abelian kernel and negligible classes inGalois cohomology. In particular, the lifting problem modulo p^2 of Galoisrepresentations over Z/pZ will be discussed.This is a joint work with Federico Scavia.
14:15 • EPF Lausanne, CM 1 517
Marc Abboud (University of Neuchâtel)
Abstract:
Title: On the rigidity of periodic points for automorphisms of affine surfaces Abstract: I will discuss the following results. Let S be a complex affine surface and f,g be two automorphisms of positive entropy. If f and g have a Zariski dense set of periodic points in common then they have the same set of periodic points. The proof uses the dynamics at infinity of such automorphisms and the construction of their canonical Green functions and equilibrium measures both for archimedean places and non-archimedean ones. One of the main ingredients is the theorem of arithmetic equidistribution on adelic line bundles over quasiprojective varieties from Yuan and Zhang. I will also discuss examples of affine surfaces where I manage to show a stronger rigidity: having the same periodic points imply that the automorphisms share a common iterate. The examples are the affine plane and Markov surfaces which are related to the character variety of the punctured torus.
14:15 • Universität Basel
Alex Ferrer (CIMNE, Universitat Politècnica de Catatlunya, Barcelona)
Additive manufacturing constraints in Topology optimization abstract
Abstract:
Additive manufacturing has motivated the development of new constraints in topology optimization to ensure the manufacturability of optimized designs. This work reviews and compares several important classes of constraints, considering both density-based and level-set methods. First, the perimeter constraint and its anisotropic extension are discussed as ways to control the complexity of boundaries and the orientation of features, which is relevant for directional manufacturing processes. The overhang constraint directly addresses the need to limit unsupported regions, a key issue in layer-by-layer fabrication. Minimum length scale control ensures the elimination of excessively small features that are impractical to fabricate and helps avoid mesh dependency. Connectivity constraints play a crucial role in guaranteeing that optimized structures remain manufacturable and free of disconnected components. In this context, we propose solving an auxiliary problem that enforces connectivity by penalizing or eliminating isolated regions, thus ensuring structural integrity. Both density and level-set formulations are examined, highlighting how these constraints can be integrated and the advantages and limitations of each approach. The study emphasizes that an appropriate combination of these constraints is essential to bridge the gap between mathematically optimal designs and physically realizable additive manufacturing components.
14:45 • EPF Lausanne, CM 1 106
Léo Belzile (HEC Montréal)
Choosing the threshold in extreme value analysis abstract
Abstract:
Univariate extreme value analysis often focus on observations that are large in the sense that they exceed a large threshold, above which observations are approximately generalized Pareto distributed under mildassumptions. The choice of threshold has a large impact on inference and its uncertainty is often ignored in subsequent analysis. Starting with the statistical properties underlying the various proposals, this talkprovides an extensive review of threshold selection mechanisms, including semiparametric methods based on Hill’s estimator, visual diagnostics, goodness-of-fit tests, extended generalized Pareto models,among others. We perform an extensive simulation study under various tail regimes, with serial dependence and varying sample sizes, to identify the most promising methodologies. Methods are showcased on the Padova rainfall series and we provide critical assessment of methods strengths and weaknesses. This presentation is based on joint work withSonia Alouini (MeteoSwiss) and Anthony Davison (EPFL).
15:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Joaquín A. Hernández (CIMNE, Universitat Politècnica de Catatlunya, Barcelona)
Empirical Interscale Finite Element Method (EIFEM): a data-driven multiscale framework for nonlinear heterogeneous structures abstract
Abstract:
The Empirical Interscale Finite Element Method (EIFEM) is a data-driven multiscale approach for efficient simulation of nonlinear heterogeneous and architected materials. It integrates domain decomposition, reduced-order modeling, and hyperreduction to connect fine- and coarse-scale responses with high accuracy.Each subdomain displacement is split into interface-induced and orthogonal nonlinear “bubble” components, the latter serving as internal coarse degrees of freedom. These are parametrized by linear or nonlinear expansions (e.g., POD or neural-network-based). EIFEM uses a three-field variational formulation with Localized Lagrange Multipliers, where user-defined interface modes act as coarse-scale boundary DOFs. This formulation establishes a direct mapping between coarse displacements and fine stresses, removing the need for FE²-type nested iterations and ensuring compatibility with standard FEM codes.Computational efficiency is achieved through the Continuous Empirical Cubature Method (CECM), which builds sparse integration rules for accurate reduced integration. Applications to nonlinear beams and metamaterial lattices demonstrate over three orders-of-magnitude reduction in unknowns and integration points while preserving strain-energy errors below 1%.
15:30 • EPF Lausanne, CM 1 106
Danica Kosanovic (Universität Bern)
Knotted families from graspers abstract
Abstract:
I will introduce a geometric object called a grasper, and explain how it gives rise to families of embeddings of an arc or a circle into an arbitrary manifold of any dimension. These families are detected by Goodwillie—Weiss embedding calculus, so the question of their nontriviality is reduced to algebraic topology. In dimension 3 our discussion reduces to constructions of knots using gropes/claspers.
Susan Hermiller (University of Nebraska)
Unknotting number is not additive under connected sum
Martin Deraux (Institut Fourier, Grenoble)
Complex hyperbolic surfaces of finite volume abstract
Abstract:
I will survey the known constructions of lattices in the isometry groups of the complex hyperbolic plane (explicit generating sets and fundamental domains, arithmetic groups, uniformization), and explain how to relate some specific examples produced using these three very different constructions.
16:15 • Université de Genève, Conseil Général 7-9, Room 1-15
Dr. Vedran Sohinger (University of Warwick)
Gibbs measures as local equilibrium Kubo-Martin-Schwinger states for focusing nonlinear Schrödinger equations abstract
Abstract:
<div class="elementToProof" style="font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; text-align: left; background-color: white; margin: 0px; font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: black;">Gibbs measures for nonlinear dispersive PDEs have been used as a fundamental tool in the study of low-regularity almost sure global well-posedness of the associated Cauchy problem following the pioneering work of Bourgain in the 1990s. In the first part of the talk, we will discuss the connection of Gibbs measures with the classical Kubo-Martin-Schwinger (KMS) condition. The latter is a property characterizing equilibrium measures of the Liouville equation. In particular, we show that Gibbs measures are the unique KMS equilibrium states for a wide class of Hamiltonian PDEs, including nonlinear Schrödinger equations with defocusing interactions. Our proof is based on Malliavin calculus and Gross-Sobolev spaces. This is joint work with Zied Ammari (University of Besançon, Bourgogne-Franche-Comté). </div> <div class="elementToProof" style="font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; text-align: left; background-color: white; margin: 0px; font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: black;"> </div> <div class="elementToProof" style="font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; text-align: left; background-color: white; margin: 0px; font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: black;">In the second part of the talk, we study (local) Gibbs measures for focusing nonlinear Schrödinger equations. These measures have to be localized by a truncation in the mass in one dimension and in the Wick-ordered (renormalized) mass in dimensions two and three. We show that local Gibbs measures correspond to suitably localized KMS states. This is joint work with Andrew Rout (Politecnico di Milano) and Zied Ammari (University of Besançon, Bourgogne-Franche-Comté).</div>
17:00 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.2
Fabian Ziltener (ETH Zürich)
Variationsrechnung, Symmetrien und Erhaltungssätze abstract
17:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.1
Prof. Dr. Jonathan Ziveyi (University of New South Wales)
Efficient decumulation strategy with long-term care insurance and guaranteed minimum death benefit abstract
Abstract:
With the global shift from defined benefit to defined contribution pension systems, retirement planning is now fully borne on individuals elevating their exposure to longevity, health, and market risks. This transition has prompted more precautionary saving behaviour, as retirees become more conservative in fully consuming their wealth. This research proposes a decumulation strategy which combines long-term care insurance (LTCI) and guaranteed minimum death benefit (GMDB) purchased at retirement with a withdrawal-then-rebalance investment approach. Within this framework, the retirement fund is modelled using a regime-switching structure, while a target volatility strategy detects asset allocation to smooth wealth dynamics and reduces likelihood ofextreme losses. The LTCI covers late-life healthcare costs, whereas the GMDB secures a minimum bequest, thereby supporting both consumption confidence and legacy objectives. Numerical experiments compare consumption patterns under this strategy with default account-based pension drawdown strategies. Results reveal that the proposed strategy provides smoother long-term consumption and better resilience to adverse financial shocks. Sensitivity analyses exploringvariations in insurance allocation ratios, health state transitions, and target volatility levels are performed. Preliminary results suggest that moderate volatility targets strike an effective balance between risk and sustainability, and that the strategy remains robust across different health scenarios. Joint work with Jennifer Alonso-Garcia, Mengdie Hu and Yuxin Zhou.
17:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43