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Autumn Semester 2024

Date / Time Speaker Title Location
* 17 September 2024
15:30-16:30 		Anshul Adve
Princeton University
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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
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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)
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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
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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
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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 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 October 2024
15:15-16:15 		Dr. Laura Prat
Details

Analysis Seminar

Title Removable singularities for solutions of the Heat equation and the fractional Heat equation in time varying domains
Speaker, Affiliation Dr. Laura Prat,
Date, Time 29 October 2024, 15:15-16:15
Location 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

Title Singularity formation in incompressible fluids
Speaker, Affiliation Dr. Luis Martinez Zoroa, Universität Basel
Date, Time 5 November 2024, 15:15-16:15
Location 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

Title Unstable vortices and sharp non-uniqueness for the forced SQG equation
Speaker, Affiliation Dr. Francisco Mengual, Max Planck Institute Leipzig
Date, Time 12 November 2024, 15:15-16:15
Location 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

Title Nonlinear blow up for supercritical defocusing NLS
Speaker, Affiliation Prof. Dr. Gigliola Staffilani, Massachusetts Institute of Technology
Date, Time 19 November 2024, 15:15-16:15
Location 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

Title Recent progress on the regularity of n-harmonic maps
Speaker, Affiliation Dr. Dorian Martino, ETH Zurich, Switzerland
Date, Time 26 November 2024, 15:15-16:15
Location HG G 43
Abstract The full regularity of harmonic maps from a given surface into an arbitrary Riemannian manifold has been proved by Hélein in 1991. This is not true anymore when the domain has dimension strictly greater than 2, Rivière constructed an example of harmonic map from a 3-dimensional domain which is everywhere discontinuous in 1995. There are many possible generalizations of these maps to the higher dimensional case in order to recover the regularity of some "optimal" maps. For most of these generalizations, the full regularity in the general case is still open. In this talk, we will discuss some recent progress obtained for n-harmonic maps. This is a joint work with Armin Schikorra.
Recent progress on the regularity of n-harmonic mapsread_more
HG G 43
3 December 2024
15:15-16:15 		Michele Caselli
Scuola Normale Superiore Pisa
Details

Analysis Seminar

Title Nonlocal approximation of area in codimension two
Speaker, Affiliation Michele Caselli, Scuola Normale Superiore Pisa
Date, Time 3 December 2024, 15:15-16:15
Location HG G 43
Abstract In this talk, I will present a geometric (to say that it also works in the case of ambient Riemannian manifolds) notion of codimension-two fractional mass that Gamma-converges to the (n-2)-dimensional Hausdorff measure. I will also discuss possible extensions to higher codimension and applications to the construction of minimal surfaces in codimension two. The talk is based on a joint work with Mattia Freguglia and Nicola Picenni.
Nonlocal approximation of area in codimension tworead_more
HG G 43
10 December 2024
15:15-16:15 		Gerard Orriols Gimenez
ETH Zurich, Switzerland
Details

Analysis Seminar

Title Area minimization among Lagrangian and Legendrian submanifolds
Speaker, Affiliation Gerard Orriols Gimenez, ETH Zurich, Switzerland
Date, Time 10 December 2024, 15:15-16:15
Location HG G 43
Abstract I will introduce the problem of minimizing area among Lagrangian submanifolds in a Riemannian symplectic manifold, and the related problem for Legendrian submanifolds in a contact manifold. This constrained variational problem was introduced by Schoen and Wolfson with the aim of constructing Lagrangian minimal surfaces and Special Lagrangians. I will explain the connection between the Lagrangian and Legendrian problem, what is known in two dimensions, what goes wrong in higher dimension and some new progress in this direction.
Area minimization among Lagrangian and Legendrian submanifoldsread_more
HG G 43

Notes: events marked with an asterisk (*) indicate that the time and/or location are different from the usual time and/or location and if you want you can subscribe to the iCal/ics Calender.

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