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Autumn Semester 2024

Date / Time Speaker Title Location
* 17 September 2024
15:30-16:30 		Anshul Adve
Princeton University
Details

Analysis Seminar

Title Algebraic equations characterizing hyperbolic surface spectra
Speaker, Affiliation Anshul Adve, Princeton University
Date, Time 17 September 2024, 15:30-16:30
Location HG G 19.2
Abstract Given a compact hyperbolic surface together with a suitable choice of orthonormal basis of Laplace eigenforms, one can consider two natural spectral invariants: 1) the Laplace spectrum Lambda, and 2) the 3-tensor C_{ijk} representing pointwise multiplication (as a densely defined map L^2 x L^2 -> L^2) in the given basis. Which pairs (Lambda,C) arise this way? Both Lambda and C are highly transcendental objects. Nevertheless, we will give a concrete and almost completely algebraic answer to this question, by writing down necessary and sufficient conditions in the form of equations satisfied by the Laplace eigenvalues and the C_{ijk}. This answer was conjectured by physicists, who introduced these equations (in an equivalent form) as a rigorous model for the crossing equations in conformal field theory.
Algebraic equations characterizing hyperbolic surface spectraread_more
HG G 19.2
24 September 2024
15:15-16:15 		Dr. Jaume De Dios Pont
ETH Zurich, Switzerland
Details

Analysis Seminar

Title Log-concave measures can have interior hot spots
Speaker, Affiliation Dr. Jaume De Dios Pont, ETH Zurich, Switzerland
Date, Time 24 September 2024, 15:15-16:15
Location HG G 19.2
Abstract Let u(x,t) be the temperature distribution of a d-dimensional convex domain at time t with given initial temperature u(x,0) and insulating boundary. The hot-spots conjecture of Rauch asserts that for large times, the maximum of the function x -> u(x,t) is taken near the boundary of the domain. Equivalently, the conjecture asserts that the first nontrivial Neumann Laplace eigenfunction of a convex domain takes its maximum (and minimum) in the boundary. A general philosophy in convex analysis is that dimension free statements about convex sets imply an analogous, dimension-free statement about log-concave measures. In this talk I will construct the log-concave analogue to the hot spots conjecture, and construct a counterexample for it in high dimensions.
Log-concave measures can have interior hot spotsread_more
HG G 19.2
* 1 October 2024
15:30-16:30 		Prof. Dr. Guy David
Université de Paris Sud (Orsay)
Details

Analysis Seminar

Title Absolute continuity of the Robin harmonic measure on irregular domains
Speaker, Affiliation Prof. Dr. Guy David, Université de Paris Sud (Orsay)
Date, Time 1 October 2024, 15:30-16:30
Location HG G 19.1
Abstract This will describe joint work with Decio, Engelstein, Mayboroda, Michetti, with help of Filoche. The main question is the boundary behavior of harmonic functions on a domain in Euclidean space, subject to a Robin condition on the boundary $\frac{\partial u}{\partial n} + a u = f$, where $a > 0$ is a positive parameter and $f$ is the data, and measured by the Robin analogue of the harmonic measure on the boundary. For the Dirichlet condition $u = f$ on the boundary, we get the usual harmonic measure and it is known that its absolute continuity with respect to surface measure is a subtle issue. For the Robin condition, it turns out that the situation is much simpler, even on domains with a fractal boundary.
Absolute continuity of the Robin harmonic measure on irregular domainsread_more
HG G 19.1
8 October 2024
15:15-16:15 		Dr. William Cooperman
ETH Zurich, Switzerland
Details

Analysis Seminar

Title Exponential scalar mixing for 2D Navier–Stokes with degenerate stochastic forcing
Speaker, Affiliation Dr. William Cooperman, ETH Zurich, Switzerland
Date, Time 8 October 2024, 15:15-16:15
Location HG G 43
Abstract I will discuss a joint work with Keefer Rowan (Courant Institute, NYU) in which we show exponential mixing of passive scalars advected by a solution to the stochastic Navier–Stokes equations with finitely many (e.g. four) forced modes satisfying a hypoellipticity condition. Our proof combines the asymptotic strong Feller framework of Hairer and Mattingly with the mixing theory of Bedrossian, Blumenthal, and Punshon-Smith.
Exponential scalar mixing for 2D Navier–Stokes with degenerate stochastic forcingread_more
HG G 43
15 October 2024
15:15-16:15 		Dr. Stefano Decio
ETH Zurich, Switzerland
Details

Analysis Seminar

Title A unique continuation result for area minimizing currents
Speaker, Affiliation Dr. Stefano Decio, ETH Zurich, Switzerland
Date, Time 15 October 2024, 15:15-16:15
Location HG G 43
Abstract Can two minimal surfaces touch each other to infinite order at a point without coinciding in a neighborhood of the point? Intuition from the theory of unique continuation for elliptic PDEs suggests this should not happen. Of course, part of the game here is to specify the notion of minimal surface. In joint work with Camillo Brena we give an answer to an instance of the question above: if an m-dimensional area minimizing integral current has infinite order of contact at a point with an m-dimensional surface with zero mean curvature then the current coincides with the surface in a neighborhood of the point.
A unique continuation result for area minimizing currentsread_more
HG G 43
22 October 2024
15:15-16:15 		Dr. Zineb Hassainia
NYU Abu Dhabi
Details

Analysis Seminar

Title On the desingularization of time-periodic vortex motion for the 2D Euler equations
Speaker, Affiliation Dr. Zineb Hassainia , NYU Abu Dhabi
Date, Time 22 October 2024, 15:15-16:15
Location HG G 43
Abstract In this talk, I will discuss vortex dynamics in the planar Euler equations, focusing on two key aspects. First, I will present a rigorous derivation of leapfrogging quartets of concentrated vortex patches near singular time-periodic relative equilibria of the point vortex system, using KAM theory. In the second part, I will show how to extend these techniques to desingularize time-periodic vortex orbits when the Euler equation is set in a generic bounded simply-connected domain. Specifically, we can prove that for a single point vortex, under certain non-degeneracy conditions, it is possible to desingularize most of these trajectories into time-periodic concentrated vortex patches.
On the desingularization of time-periodic vortex motion for the 2D Euler equationsread_more
HG G 43
29 October 2024
15:15-16:15 		Dr. Laura Prat
Details

Analysis Seminar

Title Title T.B.A.
Speaker, Affiliation Dr. Laura Prat,
Date, Time 29 October 2024, 15:15-16:15
Location HG G 43
Title T.B.A.
HG G 43
5 November 2024
15:15-16:15 		Dr. Luis Martinez Zoroa
Universität Basel
Details

Analysis Seminar

Title Title T.B.A.
Speaker, Affiliation Dr. Luis Martinez Zoroa, Universität Basel
Date, Time 5 November 2024, 15:15-16:15
Location HG G 43
Title T.B.A.
HG G 43
12 November 2024
15:15-16:15 		Dr. Francisco Mengual
Max Planck Institute Leipzig
Details

Analysis Seminar

Title Title T.B.A.
Speaker, Affiliation Dr. Francisco Mengual, Max Planck Institute Leipzig
Date, Time 12 November 2024, 15:15-16:15
Location HG G 43
Title T.B.A.
HG G 43
19 November 2024
15:15-16:15 		Prof. Dr. Gigliola Staffilani
Massachusetts Institute of Technology
Details

Analysis Seminar

Title Title T.B.A.
Speaker, Affiliation Prof. Dr. Gigliola Staffilani, Massachusetts Institute of Technology
Date, Time 19 November 2024, 15:15-16:15
Location HG G 43
Title T.B.A.
HG G 43
26 November 2024
15:15-16:15 		Dr. Dorian Martino
ETH Zurich, Switzerland
Details

Analysis Seminar

Title Title T.B.A.
Speaker, Affiliation Dr. Dorian Martino, ETH Zurich, Switzerland
Date, Time 26 November 2024, 15:15-16:15
Location HG G 43
Title T.B.A.
HG G 43
3 December 2024
15:15-16:15 		Michele Caselli
Scuola Normale Superiore Pisa
Details

Analysis Seminar

Title Title T.B.A.
Speaker, Affiliation Michele Caselli, Scuola Normale Superiore Pisa
Date, Time 3 December 2024, 15:15-16:15
Location HG G 43
Title T.B.A.
HG G 43
10 December 2024
15:15-16:15 		Gerard Orriols Gimenez
ETH Zurich, Switzerland
Details

Analysis Seminar

Title Title T.B.A.
Speaker, Affiliation Gerard Orriols Gimenez, ETH Zurich, Switzerland
Date, Time 10 December 2024, 15:15-16:15
Location HG G 43
Title T.B.A.
HG G 43

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