Yash Lodha (University of Hawaii at Manoa)
The space of enumerated groups and Rubin\'s theorem abstract
Abstract:
In 1989, Matatyahu Rubin proved a remarkable theorem showing that if a group admits a faithful action by homeomorphisms on a locally compact,Hausdorff space satisfying some dynamical hypothesis, then such an action is unique up to topological conjugacy (indeed even the space on which it acts in this manner is uniquely determined up to homeomorphism). In this talk we shall study this theorem and some key ideas of the proof, and investigate whether generic groups in a natural Polish topology on countable enumerated groups admit such an action.
10:30 • Université de Genève, Conseil Général 7-9, Room 1-05
Marie-Pier Côté (University of Laval, Québec)
Selection bias in insurance: why portfolio-specific fairness fails to extend market-wide abstract
Abstract:
Fairness centres on people. In insurance, the scope of fairness should be the entire insured population, not solely an insurer\'s clients. However, each insurance company’s portfolio represents a possibly skewed subsample. We examine how portfolio composition affects fair premium methodologies for mitigating direct and indirect discrimination on a protected attribute. We illustrate how unfairness mitigation based on a selection-biased portfolio does not yield a fair market from the perspective of insureds. Relying on causal inference and a portfolio composition indicator, we describe the selection mechanism and determine conditions under which each bias affects various fairness-adjusted premiums. We propose a method to recover the population-wide fairness-adjusted premiums from selection-biased data, by using a (third-party provided) unbiased estimate of the prohibited attribute distribution. We show that this approach effectively mitigates selection bias but leads to overall premiums that are not balanced.
11:00 • EPF Lausanne, Extranef 125
Peter Stevenhagen (Leiden)
Global to local obstructions for primitivity abstract
Abstract:
An integer is called a primitive root modulo a prime number p when its reduction generates the multiplicative group of the field ofp elements.Similarly, a point on an elliptic curve over Q is called a primitive point modulo p when its reduction generates the point group of the elliptic curve modulo p.Proving that a given integers is a primitive root modulo infinitely many primes can only be done under the assumption of Riemann hypotheses, and proving primitivity of a given point modulo infinitely many primes is currently beyond our technical means.Contrary to this, proving that primitivity occurs only modulo finitely many primes tends to be easy, as it is implied by global properties of a “finite" kind.I will discuss such global properties, which can be of a non-trivial group theoretical nature.This lecture is based on joint work with Francesco Campagna, Francesco Pappalardi and Nathan Jones.
14:15 • EPF Lausanne, CM 1 517
Nikolay Perry (UniGE)
Factorization Homology: an Introduction abstract
Abstract:
Factorization homology is a gadget which pairs geometric data in the form of an n-manifold (possibly with tangential structure) with appropriate algebraic data, giving an object in a symmetric monoidal (higher) category. Importantly, this gadget satisfies a local-to-global gluing principle: an appropriate notion of excision generalising the Eilenberg-Steenrod axioms. Naturally a higher-categorical theory, this framework has been used in approaches to various quantisation problems and in the construction of fully extended TFTs. The aim of this talk is to give a brief introduction to the theory of factorization homology, introducing important background concepts and examples in advance of Jan Pulmann\'s talk.
15:00 • Université de Genève, Conseil Général 7-9, Room 1-07
Ting-Han Huang (Paris XIII)
On p-adic Gross–Zagier formulae for two triple product p-adic L-functions attached to finite slope families abstract
Abstract:
In this talk, we will briefly explain the works in the thesis and a recent paper (with A. Kazi) of the speaker, which revolve around the p-adic Gross–Zagier formula for (twisted) triple product p-adic L-functions attached to finite slope families. We will skip the geometric part of the story and focus instead on the computation of the polynomial q-expansions. In the end, we will demonstrate the relation between the special values of p-adic L-functions and the syntomic Abel–Jacobi images of diagonal cycles.
Prof. Dr. Jill Pipher (Brown University)
A parabolic Regularity problem: nontangential estimates on the gradient of solutions abstract
Abstract:
In recent joint work with M. Dindos and L. Li, we show that the Regularity problem for a second order divergence form parabolic operator is solvable when the data belongs to an appropriate L^p space. The parabolic operator has coefficients that vary in both space and time, and satisfy a certain minimal smoothness assumption defined by a Carleson measure condition - one that has been well-studied for the elliptic analog of these equations. The long term goal, of which this is a step, is to bring the parabolic theory to the level of understanding that has now been achieved for elliptic boundary value problems and beyond, to free boundary problems.
15:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Dragomir Saric (CUNY)
The Fenchel-Nielsen parameters for infinite Riemann surfaces and the geodesic flow abstract
Abstract:
An infinite Riemann surface is parabolic if it does not support Green’s function. Hopf-Tsuji-Sullivan theorem states that X is parabolic iff the geodesic flow is ergodic iff the Brownian motion on X is recurrent iff the covering Fuchsian group is of divergence type. We consider the question of determining whether an explicitly given Riemann surface (in terms of Fenchel-Nielsen parameters) is parabolic. Some sufficient conditions are obtained depending on the size of the lengths and choice of relative twists. We also solve a conjecture of Kahn and Markovic by showing that lengths can be arbitrarily large while the surface remains parabolic when the twists are appropriately chosen.
15:15 • Université de Fribourg, PER23 room 0.05
Jan Pulmann (Mittag-Leffler Institute, Stockholm)
Deformation quantization of categories and moduli spaces of flat connections abstract
Abstract:
Factorization homology can be used to assign functorial invariants to surfaces, starting from a braided monoidal category. If this category is obtained by deforming a symmetric monoidal category, this deformation can be tracked through factorization homology. Applying this to the cases of the Drinfeld-Jimbo quantum groups and Drinfeld\'s quasi-triangular quasi-Hopf algebras, we obtain the Fock-Rosly and the Alekseev-Malkin-Meinrenken bivectors as well as their quantizations, in terms of fusion and skein theory. Based on joint work with Eilind Karlsson, Corina Keller and Lukas Mueller [arxiv:2410.12516].
16:10 • Université de Genève, Conseil Général 7-9, Room 1-07
Barbara Palumbo (University of Genoa)
What is... Applied Mathematics in Solar Physics? abstract
Abstract:
In this talk, I will present my research on the application of mathematical techniques to the analysis of data from STIX and HXI, two indirect imagers that measure X-rays emitted by the Sun during solar flares. The presentation will introduce the underlying physical problem, followed by a mathematical formulation that leads to an ill-posed inverse problem. I will discuss the stability of the problem and explore suitable algorithms for its solution. Finally, I will showcase preliminary reconstructions obtained by applying these methods to real observational data.
16:30 • UZH Zentrum, Building KO2, Room F 150