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Autumn Semester 2025

Date / Time Speaker Title Location
16 September 2025
15:15-16:15 		Prof. Dr. Yannick Sire
Johns Hopkins University
Details

Analysis Seminar

Title Regularity vs singularity formation for harmonic map heat flows with free boundaries
Speaker, Affiliation Prof. Dr. Yannick Sire, Johns Hopkins University
Date, Time 16 September 2025, 15:15-16:15
Location HG G 43
Abstract I will report on recent results on geometric flows associated to harmonic mappings with free boundary. Those maps are instrumental in several geometric problems, such as extremal metrics for the Steklov spectrum for instance and one can formulate several possible parabolic equations whose stationnary solutions are such maps. I will describe these formulations, each of which offering interesting applications and analytic problems. In various cases, one can derive partial regularity results for weak solutions and describe the structure of the singular set. I will try to give an overview of such results. However, a formulation, related to the Plateau flow, poses more challenging issues and I will formulate some conjectures about its singularity formation. The construction of solutions blowing up in finite or infinite time uses a new gluing technique, which has been successfully used recently to investigate singularity formations in other flows, such as Fast Diffusion equations or Yang-Mills heat flow.
Regularity vs singularity formation for harmonic map heat flows with free boundariesread_more
HG G 43
23 September 2025
15:15-16:15 		Dr. Benedikt Gräßle
Universität Zürich, Switzerland
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Analysis Seminar

Title Stable skeleton integral equations for general-coefficient Helmholtz transmission problems
Speaker, Affiliation Dr. Benedikt Gräßle , Universität Zürich, Switzerland
Date, Time 23 September 2025, 15:15-16:15
Location HG G 43
Abstract Variational formulations of layer potentials and boundary integral operators generalize their classical construction based on Green's functions. Unlike classical approaches, our method applies even when Green's functions are not explicitly available, such as for Helmholtz problems with rough (e.g., piecewise Lipschitz) coefficients. Wave-number explicit estimates and properties like jump conditions are obtained directly from variational principles. From this, we obtain a generalised Calderón identity and derive nonlocal (integral) formulation of acoustic transmission problems in heterogeneous media. The well-posedness of the resulting boundary integral equations is directly inherited from the underlying partial differential equation. Our analytical framework treats general spatial dimensions and complex wave numbers simultaneously by imposing an artificial boundary and employing recent insights into the associated Dirichlet-to-Neumann map.
Stable skeleton integral equations for general-coefficient Helmholtz transmission problemsread_more
HG G 43
30 September 2025
15:15-16:15 		Prof. Dr. Xavier Cabré
Universitat Politècnica de Catalunya
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Analysis Seminar

Title Boundary reaction problems: from solutions in convex domains to the half-Laplacian
Speaker, Affiliation Prof. Dr. Xavier Cabré, Universitat Politècnica de Catalunya
Date, Time 30 September 2025, 15:15-16:15
Location HG G 43
Abstract We will start reviewing the Casten-Holland and Matano theorem for interior reactions. It establishes the nonexistence of nonconstant stable solutions in convex domains. We will then present a forthcoming result stating that the analogue result for boundary reactions is not true. This will require the development of a new Ginzburg-Landau theory for real valued functions, as well as the study of the half-Laplacian on the real line ---for which some open problems will be presented.
Boundary reaction problems: from solutions in convex domains to the half-Laplacianread_more
HG G 43
* 3 October 2025
12:15-13:15 		Prof. Dr. Gang Tian
Peking University
Details

Analysis Seminar

Title Special Geometric Analysis Seminar : “Ricci flow on Fano manifolds”.
Speaker, Affiliation Prof. Dr. Gang Tian, Peking University
Date, Time 3 October 2025, 12:15-13:15
Location HG G 43
Abstract Fano manifolds are complex manifolds with positive first Chern class. In this talk, I will discuss long-time behavior of Ricci flow on those particular complex manifolds. I will report some recent progress and related Laplacian comparison estimates which also hold for Riemannian manifolds with certain integral curvature conditions.
Special Geometric Analysis Seminar : “Ricci flow on Fano manifolds”.read_more
HG G 43
7 October 2025
15:15-16:15 		Prof. Dr. Alessandro Pigati
Università Bocconi
Details

Analysis Seminar

Title Anisotropic Allen-Cahn and convergence to anisotropic integrands
Speaker, Affiliation Prof. Dr. Alessandro Pigati, Università Bocconi
Date, Time 7 October 2025, 15:15-16:15
Location HG G 43
Abstract In this talk we will introduce a new PDE way to construct hypersurfaces which are critical for anisotropic integrands. Namely, we study energy concentration for rescalings of an anisotropic version of Allen-Cahn. Besides a Gamma-convergence result, we will sketch a proof of the fact that energy of stable critical points (of the rescaled Allen-Cahn) concentrates along an integer rectifiable varifold, a weak notion of hypersurface, using stability (or finite Morse index) to compensate for the lack of monotonicity formulas. Among the new technical ingredients, we will see a generalization of Modica's bound and a diffuse version of the stability inequality for hypersurfaces. This is joint work with Antonio De Rosa (Bocconi University)
Anisotropic Allen-Cahn and convergence to anisotropic integrandsread_more
HG G 43
14 October 2025
15:15-16:15 		Dr. Gonzalo Cao-Labora
EPFL
Details

Analysis Seminar

Title Unstable singularities in fluids via neural networks and computer-assisted proofs
Speaker, Affiliation Dr. Gonzalo Cao-Labora , EPFL
Date, Time 14 October 2025, 15:15-16:15
Location HG G 43
Abstract We will start talking about how to use neural networks to find unstable self-similar profiles in fluids PDE. These profiles are numerical, but are accurate up to machine precision We will then spend most of our time explaining how to use computer-assisted proofs (CAP) to rigorously prove singularity formation around those unstable solutions. The main ingredients are CAP operator norm bounds to reduce the linear problem to a finite-dimensional one, and CAP bounds on the linear propagator applied to the remaining finitely many modes. Lastly, we will briefly talk about recent work constructing the first counterexample of the Schiffer problem on the half-sphere, which is also the first contractible counterexample in any geometry Joint works with Google Deepmind, Yongji Wang, Ching-Yao Lai, Javier Gómez-Serrano, Tristan Buckmaster and Antonio J. Fernández
Unstable singularities in fluids via neural networks and computer-assisted proofsread_more
HG G 43
* 17 October 2025
12:15-13:15 		Prof. Dr. Michael Novack
Louisiana State University,
Details

Analysis Seminar

Title Special Analysis Seminar: Plateau's problem for soap films with positive volume: new directions
Speaker, Affiliation Prof. Dr. Michael Novack, Louisiana State University,
Date, Time 17 October 2025, 12:15-13:15
Location HG G 43
Abstract We discuss a Plateau problem based on capillarity theory in which soap films are described as sets with small volume v that satisfy a spanning condition. Existence and interior regularity are understood for fixed v>0 and for the limiting Plateau problem, and so several questions arise regarding boundary regularity and the nature of the convergence to minimal surfaces as v approaches zero. We present ongoing joint work in these directions with Francesco Maggi (UT Austin) and Daniel Restrepo (Johns Hopkins).
Special Analysis Seminar: Plateau's problem for soap films with positive volume: new directionsread_more
HG G 43
21 October 2025
15:15-15:15 		Prof. Dr. Nicolaos Kapouleas
Brown University
Details

Analysis Seminar

Title Minimal surface and hypersurface doublings
Speaker, Affiliation Prof. Dr. Nicolaos Kapouleas, Brown University
Date, Time 21 October 2025, 15:15-15:15
Location HG G 43
Abstract After a brief historical review I will concentrate on recent and ongoing work on constructions of hypersurface doublings (with J. Zou), results on the index and nullity of minimal surface doublings in the round three-sphere (with Zou), results on some Yau questions for minimal surfaces in the round three-sphere (with Mcgrath), on general doubling constructions in the case the base surface has nontrivial kernel for the Jacobi operator (with Zou), and finally various open questions.
Minimal surface and hypersurface doublingsread_more
HG G 43
28 October 2025
15:15-16:15 		Prof. Dr. Kelei Wang
School of Mathematics and Statistics Wuhan University
Details

Analysis Seminar

Title A Liouville theorem for supercritical Fujita equation
Speaker, Affiliation Prof. Dr. Kelei Wang, School of Mathematics and Statistics Wuhan University
Date, Time 28 October 2025, 15:15-16:15
Location HG G 43
Abstract In this talk, I’ll discuss a Liouville theorem for ancient solutions to supercritical Fujita equations, which says if the solution is close to the ODE solution at large scales, then it must be the ODE solution. Then I’ll discuss some application of this Liouville theorem to the analysis of first time singularity in this problem. This is based on a joint work with Juncheng Wei and Ke Wu.
A Liouville theorem for supercritical Fujita equationread_more
HG G 43
4 November 2025
15:15-16:15 		Dr. Christian Scharrer
Universität Bonn
Details

Analysis Seminar

Title Relating diameter and mean curvature for submanifolds
Speaker, Affiliation Dr. Christian Scharrer, Universität Bonn
Date, Time 4 November 2025, 15:15-16:15
Location HG G 43
Abstract Consider a connected surface of finite area without boundary, properly embedded in Euclidean space. By an inequality of Leon Simon from 1993, such a surface must be compact, provided its mean curvature has bounded Lebesgue 2-norm. In 2008, Simon’s inequality was improved by Peter Topping who showed that the diameter of such a surface is in fact cotrolled by the Lebesgue 1-norm of its mean curvature. Over the past decade, Topping’s diameter bound has inspired various generalizations in differential geometry and geometric measure theory. In this talk, I will give an overview of these developments and present an application to Plateau’s problem.
Relating diameter and mean curvature for submanifoldsread_more
HG G 43
* 4 November 2025
16:30-17:30 		Prof. Dr. Hector Chang
CIMAT
Details

Analysis Seminar

Title Regularity Estimates for Zeroth Order Operators
Speaker, Affiliation Prof. Dr. Hector Chang, CIMAT
Date, Time 4 November 2025, 16:30-17:30
Location HG G 43
Abstract A very interesting limit case of the fractional Laplacian in Rd is given by \(Lu(x) := \int_{B1 (x)} \frac{u(x)−u(y)}{|y−x|^d} dy \) which serves as a principal example of a zeroth-order integro-differential op- erator. This operator arises naturally as the leading term of the logarithmic Laplacian which has been studied in recent years. In contrast with the frac- tional Laplacian, the scaling properties in this scenario are very delicate; in particular, the dilation of the kernel leads to a non-integrable tail, which rep- resents a challenge for the regularity theory of solutions of equations governed by L. In this talk, I will present interior continuity estimates for solutions to a family of operators comparable to the one above, obtained in collaboration with Alberto Saldaña and Sven Jarosh.
Regularity Estimates for Zeroth Order Operatorsread_more
HG G 43
18 November 2025
15:15-16:15 		Cristina Trombetti
University of Naple (Italy)
Details

Analysis Seminar

Title Symmetrization Techniques for Elliptic Problems with Robin Boundary Conditions
Speaker, Affiliation Cristina Trombetti, University of Naple (Italy)
Date, Time 18 November 2025, 15:15-16:15
Location HG G 43
Abstract We discuss recent developments in the theory of symmetrization for elliptic partial differential equations subject to Robin-type boundary conditions. While classical symmetrization arguments are well understood in the Dirichlet and Neumann settings, the Robin case presents several new challenges. In this talk I will present sharp comparison results for solutions of elliptic problems with Robin boundary conditions. Applications to spectral inequalities will also be discussed.
Symmetrization Techniques for Elliptic Problems with Robin Boundary Conditionsread_more
HG G 43
25 November 2025
15:15-16:15 		Dr. Antoine Detaille
ETH Zurich, Switzerland
Details

Analysis Seminar

Title About some approximation problems for Sobolev maps to manifolds
Speaker, Affiliation Dr. Antoine Detaille, ETH Zurich, Switzerland
Date, Time 25 November 2025, 15:15-16:15
Location HG G 43
Abstract In a striking contrast with the classical case of real-valued Sobolev functions, a Sobolev map with values into a given compact manifold N need not be approximable with smooth N-valued maps. This observation, initially due to Schoen and Uhlenbeck (1983), gave rise to a whole area of research concerned with questions related to approximability properties of Sobolev mappings with values into a compact manifold. In this talk, I will give a broad overview of this research direction, its history, the main problems it is concerned with, important known results, as well as some recent contributions.
About some approximation problems for Sobolev maps to manifoldsread_more
HG G 43
16 December 2025
15:15-16:15 		Tian Lan
ETH Zurich, Switzerland
Details

Analysis Seminar

Title The regularity of scale-invariant Lagrangians depending on the first and second fundamental forms.
Speaker, Affiliation Tian Lan, ETH Zurich, Switzerland
Date, Time 16 December 2025, 15:15-16:15
Location HG G 43
Abstract In this talk, I will discuss some scale-invariant curvature energies depending on the first and second fundamental forms, with an emphasis on the regularity theory. We focus on the Dirichlet energy of the mean curvature for four-dimensional hypersurfaces and present a regularity theorem for weak critical points. The proof uses Noether-type conservation laws to rewrite the Euler–Lagrange equation as a lower-order elliptic system, where tools from integrability by compensation and interpolation theory apply; I will also highlight the additional difficulties compared with the two-dimensional Willmore setting. This is based on a joint work with Yann Bernard, Dorian Martino, and Tristan Rivière.
The regularity of scale-invariant Lagrangians depending on the first and second fundamental forms.read_more
HG G 43

Notes: red marked events are important, 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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