Departement Mathematik

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For Zoom URL please contact Laura Keller

Herbstsemester 2024

Datum / Zeit Referent:in Titel Ort
* 17. September 2024
15:30-16:30 		Anshul Adve
Princeton University
Details

Analysis Seminar

Titel Algebraic equations characterizing hyperbolic surface spectra
Referent:in, Affiliation Anshul Adve, Princeton University
Datum, Zeit 17. September 2024, 15:30-16:30
Ort 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

Titel Log-concave measures can have interior hot spots
Referent:in, Affiliation Dr. Jaume De Dios Pont, ETH Zurich, Switzerland
Datum, Zeit 24. September 2024, 15:15-16:15
Ort 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. Oktober 2024
15:30-16:30 		Prof. Dr. Guy David
Université de Paris Sud (Orsay)
Details

Analysis Seminar

Titel Absolute continuity of the Robin harmonic measure on irregular domains
Referent:in, Affiliation Prof. Dr. Guy David, Université de Paris Sud (Orsay)
Datum, Zeit 1. Oktober 2024, 15:30-16:30
Ort 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. Oktober 2024
15:15-16:15 		Dr. William Cooperman
ETH Zurich, Switzerland
Details

Analysis Seminar

Titel Exponential scalar mixing for 2D Navier–Stokes with degenerate stochastic forcing
Referent:in, Affiliation Dr. William Cooperman, ETH Zurich, Switzerland
Datum, Zeit 8. Oktober 2024, 15:15-16:15
Ort 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. Oktober 2024
15:15-16:15 		Dr. Stefano Decio
ETH Zurich, Switzerland
Details

Analysis Seminar

Titel A unique continuation result for area minimizing currents
Referent:in, Affiliation Dr. Stefano Decio, ETH Zurich, Switzerland
Datum, Zeit 15. Oktober 2024, 15:15-16:15
Ort 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. Oktober 2024
15:15-16:15 		Dr. Zineb Hassainia
NYU Abu Dhabi
Details

Analysis Seminar

Titel On the desingularization of time-periodic vortex motion for the 2D Euler equations
Referent:in, Affiliation Dr. Zineb Hassainia , NYU Abu Dhabi
Datum, Zeit 22. Oktober 2024, 15:15-16:15
Ort Online via Zoom (for the Zoom credentials please send an email to Laura Kobel)
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
Online via Zoom (for the Zoom credentials please send an email to Laura Kobel)
29. Oktober 2024
15:15-16:15 		Dr. Laura Prat
Details

Analysis Seminar

Titel Removable singularities for solutions of the Heat equation and the fractional Heat equation in time varying domains
Referent:in, Affiliation Dr. Laura Prat,
Datum, Zeit 29. Oktober 2024, 15:15-16:15
Ort HG G 43
Abstract The talk will be about removable singularities for solutions of the Heat Equation and the Fractional Heat Equation in time varying domains. In order to talk about removability, some associated capacities will be introduced to study its metric and geometric properties. I will discuss onsome results obtained in joint work with X. Tolsa and J. Mateu and also mention some recent achievements with J. Hernández.
Removable singularities for solutions of the Heat equation and the fractional Heat equation in time varying domainsread_more
HG G 43
5. November 2024
15:15-16:15 		Dr. Luis Martinez Zoroa
Universität Basel
Details

Analysis Seminar

Titel Singularity formation in incompressible fluids
Referent:in, Affiliation Dr. Luis Martinez Zoroa, Universität Basel
Datum, Zeit 5. November 2024, 15:15-16:15
Ort HG G 43
Abstract The question of whether solutions exist globally in time or if they develop singularities in finite time is a question of great importance in the study of incompressible fluids. In this talk, I will discuss some of the recent results of the field, with a special emphasis on the 3D incompressible Euler equations.
Singularity formation in incompressible fluidsread_more
HG G 43
12. November 2024
15:15-16:15 		Dr. Francisco Mengual
Max Planck Institute Leipzig
Details

Analysis Seminar

Titel Unstable vortices and sharp non-uniqueness for the forced SQG equation
Referent:in, Affiliation Dr. Francisco Mengual, Max Planck Institute Leipzig
Datum, Zeit 12. November 2024, 15:15-16:15
Ort HG G 43
Abstract In the groundbreaking works [2,3], Vishik proved non-uniqueness for the 2D Euler equation with forcing, below the Yudovich well-posedness class. A nice exposition of this result can be found in [1]. In this talk, we present a simpler proof and show how to extend the result to the Surface Quasi-Geostrophic (SQG) equation. Specifically, we prove non-uniqueness for the forced $\alpha$-SQG equation in $H^s$ for any $s<1+\alpha$ and $0\leq\alpha\leq 1$. This family of active scalar equations interpolates between the 2D Euler equation ($\alpha=0$) and the SQG equation ($\alpha=1$). This is a joint work with Castro, Faraco and Solera. [1] D. Albritton, E. Brué, M. Colombo, C. De Lellis, V. Giri, M. Janisch, and H. Kwon. Instability and non-uniqueness for the 2D Euler equations, after M. Vishik. Annals of Mathematics Studies. Princeton University Press, Princeton, 2024. [2] M. Vishik. Instability and non-uniqueness in the Cauchy problem for the Euler equations of an ideal incompressible fluid. Part I. arXiv:1805.09426, 2018. [3] M. Vishik. Instability and non-uniqueness in the Cauchy problem for the Euler equations of an ideal incompressible fluid. Part II. arXiv:1805.09440, 2018.
Unstable vortices and sharp non-uniqueness for the forced SQG equationread_more
HG G 43
19. November 2024
15:15-16:15 		Prof. Dr. Gigliola Staffilani
Massachusetts Institute of Technology
Details

Analysis Seminar

Titel Nonlinear blow up for supercritical defocusing NLS
Referent:in, Affiliation Prof. Dr. Gigliola Staffilani, Massachusetts Institute of Technology
Datum, Zeit 19. November 2024, 15:15-16:15
Ort HG G 43
Abstract In this talk I will present some recent results concerning non-radial implosions for compressible Euler and Navier-Stokes equation and non radial blow up for certain defocusing supercritical nonlinear Schrodinger equations. This work is a non radial generalization of the breakthrough results of Merle-Raphael-Rodnianski-Szeftel. The work presented is in collaboration with Gonzalo Cao-Laboratories, Javi Gomez-Serrano and Jia Shi.
Nonlinear blow up for supercritical defocusing NLSread_more
HG G 43
26. November 2024
15:15-16:15 		Dr. Dorian Martino
ETH Zurich, Switzerland
Details

Analysis Seminar

Titel Title T.B.A.
Referent:in, Affiliation Dr. Dorian Martino, ETH Zurich, Switzerland
Datum, Zeit 26. November 2024, 15:15-16:15
Ort HG G 43
Title T.B.A.
HG G 43
3. Dezember 2024
15:15-16:15 		Michele Caselli
Scuola Normale Superiore Pisa
Details

Analysis Seminar

Titel Title T.B.A.
Referent:in, Affiliation Michele Caselli, Scuola Normale Superiore Pisa
Datum, Zeit 3. Dezember 2024, 15:15-16:15
Ort HG G 43
Title T.B.A.
HG G 43
10. Dezember 2024
15:15-16:15 		Gerard Orriols Gimenez
ETH Zurich, Switzerland
Details

Analysis Seminar

Titel Title T.B.A.
Referent:in, Affiliation Gerard Orriols Gimenez, ETH Zurich, Switzerland
Datum, Zeit 10. Dezember 2024, 15:15-16:15
Ort HG G 43
Title T.B.A.
HG G 43

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