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For Zoom URL please contact Laura Keller

Autumn Semester 2021

Date / Time Speaker Title Location
21 September 2021
15:15-16:15 		Dr. Felipe Gonçalves
Universität Bonn
Event Details

Analysis Seminar

Title General Collatz Maps with Almost Bounded Orbits
Speaker, Affiliation Dr. Felipe Gonçalves, Universität Bonn
Date, Time 21 September 2021, 15:15-16:15
Location HG G 43
Streaming
Abstract We will discuss the infamous Collatz conjecture, its generalizations and connections with random walks and computation theory.
General Collatz Maps with Almost Bounded Orbitsread_more
HG G 43
Streaming
28 September 2021
15:15-16:15 		Prof. Dr. Xavier Ros-Oton
Universitat de Barcelona
Event Details

Analysis Seminar

Title Optimal regularity for the fully nonlinear thin obstacle problem
Speaker, Affiliation Prof. Dr. Xavier Ros-Oton, Universitat de Barcelona
Date, Time 28 September 2021, 15:15-16:15
Location HG G 43
Streaming
Abstract We will present some new results for the fully nonlinear version of the thin obstacle problem. More precisely, our main result establishes the uniqueness of blow-ups at regular points, and the optimal regularity of solutions. This is a joint work with Maria Colombo and Xavier Fernandez-Real.
Optimal regularity for the fully nonlinear thin obstacle problemread_more
HG G 43
Streaming
5 October 2021
15:15-16:15 		Riccardo Caniato
ETH Zurich, Switzerland
Event Details

Analysis Seminar

Title The Unique Tangent Cone Property for Pseudo-Holomorphic Maps into Projective Algebraic Varieties
Speaker, Affiliation Riccardo Caniato, ETH Zurich, Switzerland
Date, Time 5 October 2021, 15:15-16:15
Location HG G 43
Streaming
Abstract We will present some new results about uniqueness of tangent maps for general pseudo-holomorphic and locally approximable maps from an arbitrary almost complex manifold into projective algebraic varieties. As a byproduct of the approach and the techniques developed we also obtain the unique tangent cone property for a special class of non-rectifiable positive pseudo-holomorphic cycles.
The Unique Tangent Cone Property for Pseudo-Holomorphic Maps into Projective Algebraic Varietiesread_more
HG G 43
Streaming
12 October 2021
15:15-16:15 		Prof. Dr. María Medina
Universidad Autónoma in Madrid
Event Details

Analysis Seminar

Title From sign-changing solutions to the Yamabe equation to critical competitive systems
Speaker, Affiliation Prof. Dr. María Medina, Universidad Autónoma in Madrid
Date, Time 12 October 2021, 15:15-16:15
Location HG G 43
Streaming
Abstract In this talk we will analyze the existence and the structure of different sign-changing solutions to the Yamabe equation in the whole space. Later on, we will use these constructions to find positive solutions to critical competitive systems in dimension 4.
From sign-changing solutions to the Yamabe equation to critical competitive systemsread_more
HG G 43
Streaming
2 November 2021
15:15-16:15 		Prof. Dr. Otis Chodosh
Stanford University
Event Details

Analysis Seminar

Title Stable minimal hypersurfaces in R^4
Speaker, Affiliation Prof. Dr. Otis Chodosh, Stanford University
Date, Time 2 November 2021, 15:15-16:15
Location Online via Zoom
Abstract I will explain why a complete two-sided stable minimal hypersurface in R^4 is flat. This is joint work with Chao Li.
Stable minimal hypersurfaces in R^4read_more
Online via Zoom
9 November 2021
15:15-16:15 		Dr. Giorgio Tortone
Università di Pisa
Event Details

Analysis Seminar

Title Epsilon-regularity for the solutions of free boundary systems
Speaker, Affiliation Dr. Giorgio Tortone, Università di Pisa
Date, Time 9 November 2021, 15:15-16:15
Location HG G 43
Streaming
Abstract We will present some new results for a class of free boundary systems associated to shape optimization problems (spectral and integral functionals). The new main point of these results is the analysis of the regular part of the free boundary based on a linearization argument that takes care of the vectorial attitude of the problem. This is based on joint works with D. De Silva and with F.P. Maiale and B. Velichkov.
Epsilon-regularity for the solutions of free boundary systemsread_more
HG G 43
Streaming
16 November 2021
15:15-16:15 		Prof. Dr. Tomás Sanz‑Perela
Universidad Autónoma de Madrid
Event Details

Analysis Seminar

Title A universal Hölder estimate up to dimension 4 for stable solutions to half-Laplacian semilinear equations
Speaker, Affiliation Prof. Dr. Tomás Sanz‑Perela, Universidad Autónoma de Madrid
Date, Time 16 November 2021, 15:15-16:15
Location HG G 43
Streaming
Abstract The regularity of minimizers and, more generally, stable solutions to reaction-diffusion equa- tions has been a central problem in Calculus of Variations and PDEs in the last century. A phenomenon that is recurrent in these type of problems is that in low dimensions stable solutions are regular, while singularities may appear in high dimensions. We are interested in fractional semilinear equations such as (−∆)s u = f (u) with s ∈ (0, 1). A main open problem is to find the precise threshold dimension (depending on the parameter s) up to which stable solutions are bounded. Despite the problem for s = 1 involving the classical Laplacian is, nowadays, fully solved, there are quite few results in the case of the fractional Laplacian and the problem is still largely open, even in the radial case. In this talk we will present some recent developments towards the answer of the previous question on the boundedness of stable solutions (focusing on the case s = 1/2), and we will discuss some open questions and the main challenges of the fractional case.
A universal Hölder estimate up to dimension 4 for stable solutions to half-Laplacian semilinear equationsread_more
HG G 43
Streaming
23 November 2021
15:15-16:15 		Dr. Mario Schulz
Universität Münster
Event Details

Analysis Seminar

Title Noncompact self-shrinkers for mean curvature flow
Speaker, Affiliation Dr. Mario Schulz, Universität Münster
Date, Time 23 November 2021, 15:15-16:15
Location HG G 43
Streaming
Abstract In his lecture notes on mean curvature flow, Tom Ilmanen conjectured the existence of noncompact self-shrinkers with arbitrary genus. We employ min-max techniques to give a rigorous existence proof for these surfaces. Conjecturally, the self-shrinkers that we obtain have precisely one (asymptotically conical) end. We confirm this for large genus via a precise analysis of the limiting object of sequences of such self-shrinkers for which the genus tends to infinity. (joint work with Reto Buzano and Huy The Nguyen)
Noncompact self-shrinkers for mean curvature flowread_more
HG G 43
Streaming
7 December 2021
15:15-16:15 		Prof. Dr. Nicos Kapouleas
Brown University
Event Details

Analysis Seminar

Title Existence, index, and characterizations of minimal surfaces
Speaker, Affiliation Prof. Dr. Nicos Kapouleas, Brown University
Date, Time 7 December 2021, 15:15-16:15
Location HG G 43
Streaming
Abstract I will discuss some recent results and (depending on time) ongoing work and related open questions on constructions, index, nullity, characterizations, and classification of minimal surfaces In particular I will discuss recent results in the article by P. McGrath and myself, "Generalizing the Linearized Doubling approach, I: General theory and new minimal surfaces and self-shrinkers", arXiv:2001.04240v2; results on the Lawson surfaces in the articles by D. Wiygul and myself "The index and nullity of the Lawson surfaces $\xi_{g,1}$"’, Camb. J. Math. 8 (2020), 363-405 and "The Lawson surfaces are determined by their symmetries and topology", arXiv:2010.09371; existence results by D. Wiygul and myself in "Free boundary minimal surfaces with connected boundary in the 3-ball by tripling the equatorial disc", to appear in J. Differential Geometry,and ``Minimal surfaces in the three-sphere by desingularizing intersecting Clifford tori’’, Mathematische Annalen (electronic at the moment); existence results by M. Li and myself in "Free boundary minimal surfaces in the unit three-ball via desingularization of the critical catenoid and the equatorial disc", J. Reine Angew. Math. 776 (2021); and existence results by J. Zou and myself in "`Free Boundary Minimal surfaces in the Euclidean Three-Ball close to the boundary".
Existence, index, and characterizations of minimal surfacesread_more (CANCELLED)
HG G 43
Streaming
14 December 2021
15:15-16:15 		Prof. Dr. Lucas Ambrozio
IMPA
Event Details

Analysis Seminar

Title Riemannian spheres with Zoll families of minimal hyperspheres
Speaker, Affiliation Prof. Dr. Lucas Ambrozio, IMPA
Date, Time 14 December 2021, 15:15-16:15
Location HG G 43
Online via Zoom
Abstract In the beginning of the twentieth century, Otto Zoll described a large family of rotationally symmetric two-dimensional spheres whose geodesics are all closed and have the same period. Since then, a very rich (but yet incomplete) theory developed in order to construct and understand these geometries. Motivated by certain questions about minimal two-dimensional spheres in three-dimensional spheres, we were led to consider, more generally, higher dimensional Riemannian spheres that contain a family of embedded minimal hypersurfaces with the following property: a unique member of the family passes tangentially to a given tangent hyperplane of the tangent space of the ambient sphere at a given point. In this talk, we will discuss some of the results we proved about these objects. This is a joint project with F. C. Marques (Princeton) and A. Neves (UChicago).
Riemannian spheres with Zoll families of minimal hyperspheresread_more
HG G 43
Online via Zoom

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