Dylan Müller (UNIGE)
Special values and symmetries of the spectral zeta function of regular trees abstract
Abstract:
In this talk, we study the spectral zeta function of regular trees. We determine its special values at integers and relate them with combinatorics of two-coloured Dyck words. We also show that they enjoy unexpected symmetries, mostly expressed at the level of their generating functions. These symmetries ultimately lead to a functional equation of the type \\( s \\) versus \\( 1-s \\).
10:30 • Université de Genève, Conseil Général 7-9, Room 1-05
Sofian Tur-Dorvault (Université de Montpellier)
The motivic fundamental groupoid at tangential basepoints abstract
Abstract:
<p>If U is a smooth scheme over a subfield of the field of complex numbers, it is known from the work of Pierre Deligne and Alexander Goncharov that the prounipotent completion of the fundamental group of U^an based at any point has a motivic incarnation. More precisely, its coordinate ring arises as the degree-zero homology of the Betti realization of a Hopf algebra object in Voevodsky's triangulated category of motives. More generally, Deligne conjectured a similar property for the fundamental group based at a "point at infinity", i.e. the datum of a point x on a smooth compactification of U with normal crossings boundary, together with the datum of a tangent vector at x, normal to the boundary. While Deligne and Goncharov proved this conjecture in the case of the projective line minus three points, the general case remained open. In this talk, I will explain how logarithmic geometry, together with the notion of virtual morphisms between log schemes, allows one to construct the motivic fundamental group in full generality and to compute its realizations.</p>
13:15 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H 25
Xinxin Li
A Semismooth Newton-Type Method for the Nearest Doubly Stochastic Matrix Problem abstract
Abstract:
In this talk, we study a semismooth Newton-type method for the nearest doubly stochastic matrix problem where the nonsingularity of the Jacobian can fail. The optimality conditions for this problem are formulated as a system of strongly semismooth functions. We show that the nonsingularity of the Jacobian does not hold for this system. By exploiting the problem structure, we construct a modified two step semismooth Newton method that guarantees a nonsingular Jacobian matrix at each iteration, and that converges to the nearest doubly stochastic matrix quadratically.
14:00 • Université de Genève, Conseil Général 7-9, Room 1-05
Prof. Dr. Shohei Nakamura (University of Birmingham)
Inequalities for symmetric convex bodies via the Brascamp—Lieb theory abstract
Abstract:
This talk is based on joint work with Emanuel Milman (Technion) and Hiroshi Tsuji (Institution of Science Tokyo).The Brascamp–Lieb inequality (for multilinear functionals), originally introduced in 1976 as a generalization of Young’s convolution inequality, has since been found to be useful across a wide range of fields. For example, in 1991, within convex geometry, Ball showed that the Brascamp–Lieb inequality implies the reverse isoperimetric inequality. More recently, it has played a critical role in harmonic analysis, particularly in the context of the Fourier restriction conjecture and the Kakeya conjecture (e.g. Bennett—Carbery—Tao).In this talk, we focus on inequalities for symmetric convex bodies within convex geometry. Specifically, we consider the Blaschke–Santaló inequality and its multilinear version, a Talagrand-type inequality for the Wasserstein barycenter, the Gaussian correlation inequality and its strengthened version. On the analytic side, we also include a Laplace transform bound and an improvement of Borell’s reverse hypercontractivity.We will report on new developments obtained by reinterpreting this collection of inequalities from the perspective of the Brascamp–Lieb inequality.
15:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Ivan Dokmanić (Universität Basel, Switzerland)
Abstract:
We introduce Flowers, a neural architecture for learning PDE solution operators built entirely from multihead warps. Aside from pointwise channel mixing and a multiscale scaffold, Flowers use no Fourier multipliers, no dot-product attention, and no convolutional mixing. Each head predicts a displacement field and warps the mixed input features. Motivated by physics and computational efficiency, displacements are predicted pointwise, without any spatial aggregation, and nonlocality enters only through sparse sampling at source coordinates, one per head. Stacking warps in multiscale residual blocks yields Flowers, which implement adaptive, global interactions at linear cost. We theoretically motivate this design through three complementary lenses: flow maps for conservation laws, waves in inhomogeneous media, and a kinetic-theoretic continuum limit. Flowers achieve excellent performance on a broad suite of 2D and 3D time-dependent PDE benchmarks, particularly flows and waves. A compact 17M-parameter model consistently outperforms Fourier, convolution, and attention-based baselines of similar size, while a 150M-parameter variant improves over recent transformer-based foundation models with much more parameters, data, and training compute.
Dr. Kaloyan Slavov (ETHZ)
What is ... the packing problem (over finite fields)? abstract
Abstract:
<div style="font-size: 12pt; font-family: Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;" data-olk-copy-source="MessageBody">The classical Kakeya problem in Euclidean space asks how "small" a set can be if it contains a unit line segment in every direction. More generally, packing sets contain all images of a given set under a collection of transformations. Finite field analogues offer a combinatorial and algebraic perspective and motivate our work. </div> <div style="font-size: 12pt; font-family: Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;"> </div> <div style="font-size: 12pt; font-family: Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;">We study sets E in the affine plane over a finite field that are invariant under a large subgroup R of SL_2. We prove that if |R|>c|E|^{3/2}, then E must be contained in a line. The exponent 3/2 is sharp. We also state a conjecture in the Euclidean setting. This is joint work with Thang Pham and Le Quang-Hung.</div>
16:30 • UZH Zentrum, Building KO2, Room F 150