Leandro Arosio (University of Rome, Tor Vergata)
A Julia-Wolff-Carathaléodory theorem in convex domains of finite type abstract
Abstract:
The classical Julia-Wolff-Carathéodory shows that, if f is a holomorphic self-map of the disc, the derivative f′ admits a positive nontangential limit near any boundary regular fixed point z, and the limit equals the dilation of f at z which can be computed in terms of the Poincaré distance. This result had several generalizations to several variables, in particular by Rudin and Abate. In this talk I will show how to generalize the theorem to the context of a convex domain Ω ⊂ Cq of D’Angelo finite type, using as a main tool the fact that Ω is Gromov hyperbolic with respect to the Kobayashi distance kΩ and that holomorphic maps do not expand kΩ.This is a joint work with Matteo Fiacchi.
10:30 • Université de Genève, Conseil Général 7-9, Room 1-05
Arthur Charpentier (UQAM Montréal, Canada)
Using optimal transport to mitigate unfair predictions and quantify counterfactual fairness abstract
Abstract:
Many industries are heavily reliant on predictions of risks based on characteristics of potential customers. Although the use of said models is common, researchers have long pointed out that such practices perpetuate discrimination based on sensitive features such as gender or race. Given that such discrimination can often be attributed to historical data biases, an elimination or at least mitigation, is desirable. With the shift from more traditional models to machine-learning based predictions, calls for greater mitigation have grown anew, as simply excluding sensitive variables in the pricing process can be shown to be ineffective. In the first part of this seminar, we propose to mitigate possible discrimination (related to so call «group fairness», related to discrepancies in score distributions) through the use of Wasserstein barycenters instead of simple scaling. To demonstrate the effects and effectiveness of the approach we employ it on real data and discuss its implications. This part will be based on recent work with François Hu and Philipp Ratz (2310.20508, 2309.06627, 2306.12912 and 2306.10155). In the second part, we will focus on another aspect of discrimination usually called « counterfactual fairness », where the goal is to quantify a potential discrimination « if that person had not been Black » or « if that person had not been a woman ». The standard approach, called «ceteris paribus» (everything remains unchanged) is not sufficient to take into account indirect discrimination, and therefore, we consider a « mutates mutants » approach based on optimal transport. With multiple features, optimal transport becomes more challenging, and we suggest a sequential approach based on probabilistic graphical models. This part will be based on recent work with Agathe Fernandes Machado and Ewen Gallic (2408.03425 and 2501.15549).
11:00 • EPF Lausanne, Extranef, 126
Marco Golla (Université de Nantes, CNRS)
Alexander polynomials and symplectic curves in CP^2 abstract
Abstract:
Libgober defined the Alexander polynomial of a (complex) plane projective curve and showed that it detects some Zariski pairs ofcurves: these are curves with the same degree and the same singularities but with non-homeomorphic complements. He also proved that the Alexander polynomial of a curve divides the Alexander polynomial of its link at infinity and the product of Alexander polynomials of the links of its singularities. We extend Libgober\'s definition to the symplectic case and prove that the divisibility relations also hold in this context. This is joint work with Hanine Awada.
13:00 • Université de Neuchâtel, Rue Emile-Argand 11, Room B217
Victorita Dolean
Using Spectral Coarse Spaces of the H-Geneo Type for Efficient Solutions of the Helmholtz Equation abstract
Abstract:
The Helmholtz equation is a widely used model in wave propagation and scattering problems. However, its numerical solution can be computationally expensive in high-frequency regime due to the oscillatory solution and the potential contrasts in coefficients. Parallel domain decomposition methods have been identified as promising solvers for such problems, but they often require a suitable coarse space to achieve robust behaviour. In this talk, we present the H-GenEO coarse space, which constructs an effective coarse space using localized eigenvectors of the Helmholtz operator. Since the GenEO coarse space is designed for symmetric positive definite problems, the theory cannot be extended directly to the H-GenEO coarse space due to the indefinite nature of the underlying problem. During this talk it will be shown that the H-GenEO coarse space is capable of providing the required robust behaviour when used with a suitable domain decomposition method. Numerical experiments for increasing wave numbers demonstrate the efficiency of the method in solving complex Helmholtz problems, with potential applications in various scientific and engineering domains.
14:00 • Université de Genève, Conseil Général 7-9, Room 1-05
Conan Leung (The Chinese University of Hong Kong)
3d Mirror Symmetry is 2d Mirror Symmetry abstract
Abstract:
We introduce an approach to study 3d mirror symmetry via 2d mirror symmetry. The main observations are: (1) 3d brane transforms are given by SYZ-type transforms; (2) the exchange of symplectic and complex structures in 2d mirror symmetry induces the exchange of Kähler and equivariant parameters in 3d mirror symmetry; and (3) the functionalities of 2d mirror symmetry control the gluing of 3d mirrors.
14:30 • Université de Neuchâtel, Rue Emile-Argand 11, Room B217
Prof. Dr. Frédéric Hélein (Université Paris Diderot)
Kaluza-Klein theories without a priori fibration hypotheses abstract
Abstract:
I will present a Lagrangian action on fields, the critical points of which lead to solutions of the Einstein-Yang-Mills equations, in the spirit of Kaluza-Klein theories. The novelty is that the a priori fiber bundle structure hypothesis is not required: fields are defined on a "space-time" $Y$ of dimension $4+r$ without any a priori principal bundle structure, where $r$ is the dimension of the structure group. If the latter group is compact and simply connected, to each solution of the Euler-Lagrange equations it corresponds a 4-dimensional pseudo-Riemannian manifold $X$ (which can be interpreted as our usual space-time) in such a way that $Y$ acquires a principal bundle structure over $X$ equipped with a connection. Moreover the metric on $X$ and the connection on $Y$ are solutions of the Einstein-Yang-Mills system. If the structure group is $U(1)$ (the case which corresponds to the Einstein-Maxwell system) the situation is slightly degenerated and supplementary hypotheses are necessary.
15:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Sobhan Seyfaddini (ETH Zürich)
Closing Lemmas on Symplectic Manifolds abstract
Abstract:
Given a diffeomorphism of a manifold, can one perturb it to create a periodic orbit passing through a specified region? This question, first raised in the 1960s, is known as the Closing Lemma. While the problem was resolved positively in C^1 regularity long ago, it remains largely open at higher levels of smoothness. Recent years have seen significant progress in the C^\\infty setting, particularly for area-preserving maps on surfaces. In this talk, I will review these developments, highlighting works by Asaoka, Irie, Cristofaro-Gardiner, Edtmair, Hutchings, Prasad, and Zhang. I will also present some recent joint work with Cineli & Tanny and Mak & Smith, including partial results in higher dimensions.
16:00 • Université de Neuchâtel, Rue Emile-Argand 11, Room B217
Samuel Koovely (Universität Zürich)
What is... Free Convolution? abstract
Abstract:
We will start this talk by describing how to model heat diffusion on graphs and the relation between this model and the eigenvalues of random matrices, in particular Wigner\'s semicircle law. These considerations will lead us to discuss free probability theory at an introductory level, highlighting its similarities with standard probability theory.
16:30 • UZH Zentrum, Building KO2, Room F 150
Prof. Dr. Bastian Grossenbacher (Uni Fribourg)
Shapes, Spaces, Simplices, and Structure: Geometry, Topology, and Machine Learning abstract
Abstract:
A large driver contributing to the undeniable success of deep-learningmodels is their ability to synthesise task-specific features from data.For a long time, the predominant belief was that \'given enough data, allfeatures can be learned.\' However, as large language models are hittingdiminishing returns in output quality while requiring an ever-increasingamount of training data and compute, new approaches are required. Onepromising avenue involves focusing more on aspects of modelling, whichinvolves the development of novel *inductive biases* such as invariancesthat cannot be readily gleaned from the data. This approach isparticularly useful for data sets that model real-world phenomena, aswell as applications where data availability is scarce. Given their dualnature, geometry and topology provide a rich source of potentialinductive biases. In this talk, I will present novel advances inharnessing multi-scale geometrical-topological characteristics of data.A special focus will be given to show how geometry and topology canimprove representation learning tasks. Underscoring the generality ofa hybrid geometrical-topological perspective, I will furthermoreshowcase applications from a diverse set of data domains, includingpoint clouds, graphs, and higher-order combinatorial complexes.
17:15 • Université de Fribourg, room Phys 2.52