Rares Buhai
Finding Colorings in One-Sided Expanders abstract
Abstract:
Finding a 3-coloring in a 3-colorable graph is NP-hard. Given this worst-case hardness, the problem has been studied extensively in average-case and pseudo-random settings. Recently, Bafna, Hsieh, and Kothari [STOC\'25] initiated the study of 3-colorable one-sided expander graphs, for which they gave an algorithm that finds an independent set of size 0.01n -- far from a 3-coloring. In this talk, I will present recent work [FOCS\'25] in which we give an algorithm that finds a 3-coloring on all but o(1)n of the vertices of a 3-colorable one-sided expander graph with balanced color class sizes. On the other hand, if the graph has imbalanced color class sizes, our algorithm finds an independent set of size (1/2-o(1))n, and we give a matching hardness result. We also extend our results to k-colorable one-sided expanders with k > 3. Joint work with Yiding Hua, David Steurer, and Andor Vári-Kakas.
11:00 • EPF Lausanne, INJ114
Eugenia Malinnikova (Stanford University)
Carleman estimates, unique continuation, and Landis conjecture
13:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Ezra Getzler (Northwestern University)
Cyclic L-infinity algebras and shifted symplectic forms abstract
Abstract:
A cyclic L-infinity algebra is a shifted symplectic formal derived stack. Using a new geometric approach to homological perturbation theory, we construct a shifted symplectic form on the associated derived stack. (This is a derived analogue of the correspondence between Lie algehroids and Lie groupoids.)
13:30 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H 25
Nikita Gladkov (UNIGE)
Exploration in Bernoulli percolation abstract
Abstract:
Consider Bernoulli percolation on a graph, where edges are kept open independently with some probability. By revealing edges one at a time, one can analyze the structure of connected clusters and establish correlation inequalities for connectivity events. I will present several of these inequalities and outline the exploration-based arguments behind them.
14:15 • Université de Genève, Conseil Général 7-9, Room 1-15
Zhen-Qing Chen (University of Seattle)
Boundary trace of symmetric reflected diffusions abstract
Abstract:
Starting with a transient irreducible diffusion process $X^0$ on a locally compact separable metric space $(D, d)$ (for example, absorbing Brownian motion in a snowflake domain), one can construct a canonical symmetric reflected diffusion process $\\bar X$ on a completion $D^*$ of $(D, d)$ through the theory of reflected Dirichlet spaces. The boundary trace process $\\check X$ of $X$ on the boundary $\\partial D:=D^*\\setminus D$ is the reflected diffusion process $\\bar X$ time-changed by a smooth measure $\\nu$ having full quasi-support on $\\partial D$, which is unique up to a time change. The Dirichlet form of the trace process $\\check X$ is called the trace Dirichlet form. In this talk, I will address the following two fundamental questions:1) How to characterize the boundary trace Dirichlet space in a concrete way?2) How does the boundary trace process behave? Based on a joint work with Shiping Cao.
15:00 • EPF Lausanne, Bernoulli Center
Kyler Siegel (University of Southern California)
Symplectic ellipsoid embeddings, singular plane curves, and scattering diagrams abstract
Abstract:
A fundamental problem in quantitative symplectic geometry is to understand in which ways a Hamtilonian flow can "squeeze" phase space. The special case of ellipsoids has been a great source of motivation for the last several decades, in many ways mirroring various important developments in the field (e.g. Gromov-Witten theory, Floer homology, symplectic field theory, embedded contact homology, and more). In this talk, I will survey some new developments in the study of high dimensional symplectic embeddings, and in particular the recent resolution of the so-called stabilized ellipsoid conjecture. Our framework sets up a bridge between quantitative symplectic geometry and the classical study of singular algebraic curves, studying the latter using tools from log Calabi-Yau mirror symmetry. I will not assume familiarity with any of this background.
15:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Leonid Polterovich (Tel-Aviv University)
Contact topology meets thermodynamics abstract
Abstract:
I discuss the appearance of certain notions and results from contact topology in both equilibrium and non-equilibrium thermodynamics. These include non-smooth Legendrian submanifolds, Reeb chords, and the partial order on the space of Legendrians. Based on joint work with Michael Entov and Lenya Ryzhik.
16:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43