Elena Botti (Vrije Universiteit Brussel)
Abstract:
The classification of gait patterns is an important challenge in movement analysis, as it supports clinical assessment and decision-making by enabling diagnosis and severity stratification. In this talk, I will discuss the potential of Topological Data Analysis (TDA) for gait pattern classification. Unlike conventional approaches that rely on explicit detection of Gait Events (GEs) to compute Spatiotemporal Gait Parameters (SGPs), TDA characterises the global structure of gait signals directly, capturing relationships and patterns in the data without requiring GEs. This is particularly relevant in real-world settings, where GE detection can be diQicult due to heterogeneity in walking conditions and gait patterns, potentially biasing clinically relevant metrics and, consequently, decision-making.Within our department, preliminary results have shown that TDA-based features can achieve classification performance comparable to that of SGPs in fall-risk assessment. These findings suggest that topology oQers a competitive alternative for representing gait data, with the potential to better handle variability across subjects and pathological conditions.Building on these results, we plan to further extend the TDA framework in two directions. First, we aim to investigate time-aware topological methods to better capture the temporal structure of gait signals. Second, we will explore Topological Deep Learning (TDL) approaches to reduce reliance on handcrafted design choices and potentially improve classification performance. By combining the robustness of topology with data- driven representation learning, this work seeks to provide robust tools for the classification of typical and pathological gait patterns.
Sylvain Crovisier (Université Paris-Saclay)
Ergodic theory of surface diffeomorphisms
10:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Mohsen Shahidkalhori (Universität Basel)
Abstract:
Abstract Frequency functions provide a quantitative way to measure how fast a function vanishes. For harmonic maps, the key fact is that the frequency function is monotone, and this already has remarkable consequences: it leads to quantitative unique continuation and prevents solutions from vanishing too rapidly. In particular, touching sets of harmonic functions are necessarily small, with codimension at least two. In this talk, we use this viewpoint as a guiding principle for more geometric problems. In minimal surface theory, singularities arise from sheets touching each other, suggesting that similar ideas should apply. We first examine the linear model given by multi-valued Dirichlet minimizers, where frequency methods again yield the same dimension bounds for the singular set, and then briefly discuss why extending this approach to minimal surfaces is substantially more subtle.
12:15 • Universität Basel, Seminarraum 05.001, Spiegelgasse 5
Álvaro Del Valle (Universidad de Sevilla)
Turaev genus and arc index: a new conjecture for links abstract
Abstract:
The Turaev genus $g_T$ is a numerical invariant of knots and links that measures how far a link is from being alternating (that is, from admitting an alternating diagram). Determining whether a link is alternating is, in general, not straightforward. In this work we compare the Turaev genus with another numerical invariant, the arc index $\\alpha$. In particular, we conjecture that $c(L) + 2 - \\alpha(L) \\geq 2 g_T(L)$ for any prime, non-split link L, where $c(L)$ is the number of crossings of L. We present various techniques to verify the conjecture for relevant families of links: adequate links, closures of positive 3-braids, torus links, and Kanenobu knots. This is joint work with Adam M. Lowrance.
14:15 • Université de Genève, Conseil Général 7-9, Seminar Room, 8th floor,
Francesca Carocci
The multiple cover formula conjecture for Gromov-Witten invariants of abelian surfaces abstract
Abstract:
Abelian surfaces are complex tori whose enumerative invariants satisfy remarkable regularity properties. The computation of their (reduced) Gromov-Witten invariants for the so called primitive classes is fairly well understood and many complete computations are available. A few years ago, G. Oberdieck conjectured a multiple cover formula expressing in a very simple way the invariants for the non-primitive classes in terms of the primitive one. The proof of the conjecture would solve completely the GW theory of abelian surfaces.In this talk, we\'ll sketch a proof of multiple cover formula conjecture for many insertions. The argument relies on a reduced degeneration formula and on the computation of correlated Gromov-Witten invariants for trivial bundles on elliptic curves. This is joint work with T. Blomme
14:15 • EPF Lausanne, CM 1 517
Prof. Dr. Jelle J. Goemann
Abstract:
We present a novel necessary and sufficient principle for multiple testing methods controlling an expected loss. This principle asserts that every such multiple testing method is a special case of a general closed testing procedure based on e-values. It generalizes the Closure Principle, known to underlie all methods controlling familywise error and tail probabilities of false discovery proportions, to a large class of error rates -- in particular to the false discovery rate (FDR). By writing existing methods as special cases of this procedure, we can achieve uniform improvements, as we demonstrate for the e-Benjamini-Hochberg and the Benjamini-Yekutieli procedures, and the self-consistent method of Su (2018). We also show that methods derived using our novel e-Closure Principle generally control their error rate not just for one rejected set, but simultaneously over many, allowing post hoc flexibility for the researcher.Moreover, we show that because all multiple testing methods for all error metrics are derived from the same procedure, researchers may even choose the error metric post hoc. Under certain conditions, this flexibility even extends to post hoc choice of the nominal error rate.
16:15 • Universität Bern, Hörsaal B7, ExWi, Sidlerstrasse 5, 3012 Bern
Thomas Vidick (EPFL)
Inapproximability through undecidability abstract
Abstract:
Infinite combinatorial, algebraic or other structures, such as a graph, a group, or aprobability space, can sometimes be approximated (in a suitable sense) by finite structures, andsometimes not. In the former case, finite approximability can provide a convenient proxy for studyingthe infinite structure; in the latter, inapproximability underscores a genuinely distinct behavior fromthe finite case. While the existence of finite approximations can follow from suitable approximationtechniques, their in-existence often requires deeper conceptual observations.Recently we were able to resolve some long-standing inapproximability questions, in algebra and inergodic theory, by showing that an associated computational problem is undecidable. Associating ameasure of complexity to the infinite structure allows us to make use of methods from complexitytheory and demonstrate the in-existence of finite approximations in an unexpected way.In the talk we will discuss this "method" and show how we used it to answer the Connes EmbeddingProblem, about the existence of inapproximable classes of (type II_1) von Neumann algebras, and theAldous-Lyons conjecture, about the existence of inapproximable (unimodular) infinite graphs.Based on joint works with Ji, Natarajan, Yuen and Wright, and Bowen, Chapman and Lubotzky.
16:15 • Université de Genève, Conseil Général 7-9, Room 1-15
Prof. Dr. Eyal Neuman (Imperial College London)
Stochastic Games on Large Sparse Graphs abstract
Abstract:
We introduce a framework for stochastic games on large sparse graphs, covering continuous-time and discrete-time dynamic games as well as static games. Players are indexed by the vertices of simple, locally finite graphs, allowing both finite and countably infinite populations, with asymptotics described through local weak convergence of marked graphs. The framework allows path-dependent utility functionals that may be heterogeneous across players. Under a contraction condition, we prove existence and uniqueness of Nash equilibria and establish exponential decay of correlations with graph distance. We further show that global equilibria can be approximated by truncated local games, and can even be reconstructed exactly on subgraphs given information on their boundary. Finally, we prove convergence of Nash equilibria along locally weakly convergent graph sequences, including sequences sampled from hyperfinite unimodular random graphs. This is a joint work with Sturmius Tuschmann.
17:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43