Dr. Yuriy Tumarkin (CY Cergy Paris Université)
Invariant sets in the wind-tree model
13:30 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H 28
Allen Knutson (Cornell University)
The mathematics of juggling, old and new abstract
Abstract:
I\'ll explain how to associate a juggling pattern to a matrix (and in the process, give a mathematical definition of juggling pattern, familiar to jugglers since the mid-\'80s). This defines the "positroid" stratification of the space of k x n matrices, with many great geometric features (e.g. the strata are smooth and their closures are normal). Much of this has been understood since 2013 downon the Grassmannian (matrices up to row operations) but there are new features when working upstairs on matrices. The 2013 work is joint with Thomas Lam and David Speyer, the new with Paul Zinn-Justin.
14:15 • EPF Lausanne, GR A3 32
Julia Elena Würsch
An Analysis of the Number of Reduction Steps for Special Two-Dimensional Lattices abstract
Abstract:
<p><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: #000000;" data-olk-copy-source="MessageBody">This talk analyzes the reduction-step behavior of the Gaussian lattice-reduction algorithm on lattices arising from ideals in imaginary quadratic fields, which appear in isogeny-based cryptography. We focus on the probability that the algorithm requires more than a fixed number of reduction steps and model how these lattices are distributed geometrically. Using these geometric insights, we propose a line-intersection model that predicts the distribution of number of reduction steps and compare it with experimental data.</span></p>
15:15 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H 28
Segev Gonen Cohen (ETH Zürich, Switzerland)
Actions of lattices on manifolds abstract
Abstract:
In this talk we describe recent progress on the Zimmer Programme, the study of actions of lattices in Lie groups on manifolds by diffeomorphisms. We begin by recalling motivations and some important examples, explain the general strategy introduced by Brown-Fisher-Hurtado when the manifold is of low enough dimension, and discuss modifications that allow us to prove results in more general semisimple and S-arithmetic groups. Time willing, we will also describe some recent progress on actions of dense subgroups of Lie groups on manifolds.
15:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Prof. Dr. Ivan Dokmanić (Universität Basel, Switzerland)
On learning operators with pullbacks and pushforwards abstract
Abstract:
This talk discusses the theory and practice of operator learning, motivated by inverse problems and PDE solution maps. We start with function graph transformers which represent functions by measures supported on their graphs and operators by graph-preserving pushforwards. This viewpoint connects discrete data with continuum operators and yields constructive approximation results. Turning from approximation to sample complexity, we show how compressibility in phase space makes a class of double fibration transforms, including Radon and geodesic ray transforms, learnable from few input–output examples, even when their geometry is unknown. Finally, we use the method of characteristics to motivate Flowers, neural PDE surrogates built from state-dependent pullbacks. Despite their simplicity, Flowers outperform Fourier-, convolution-, and attention-based models of comparable size across a broad range of two- and three-dimensional PDE benchmarks.
16:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.2
Mike Ineichen
Decoding Algorithms for Moderate-Density Parity-Check Codes abstract
Abstract:
<p>In this presentation we introduce a wide variety of decoding methods for MDPC codes, collected from many different authors. These include BIKE-Flip, the decoder used in the most sophisticated MDPC-based application to date named BIKE. We test the decoding performance of these decoders on QC-MDPC codes by measuring how many errors each method can correct, and we extrapolate the theoretical DFR at BIKE Level 1 parameters using the decoders that are strong enough to reach their waterfall region before the block size r = 12323. We then introduce different methods for generating MDPC codes and conclude that, unless a catastrophic attack exploiting the quasi-cyclic structure of QC-MDPC codes is found, there is no benefit in using other generation methods for MDPC codes. Finally, we inspect the row weight of parity-check-induced MDPC codes and examine how the performance differs.</p>
16:30 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H 28
Prof. Dr. Fredrik Viklund (KTH Royal Institute of Technology)
Confined planar Coulomb gases abstract
Abstract:
I will discuss probabilistic and analytic aspects of two-dimensional Coulomb gases confined to Jordan domains, curves, and arcs. In particular, I will describe the asymptotic behavior of particle distributions as the number of particles tends to infinity. I will also explain how the Loewner energy and related quantities arise in the asymptotic expansion of the free energy. A key analytical tool throughout is the Grunsky operator. The talk is based on joint work with Kurt Johansson and Klara Courteaut.
17:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43