# Analysis seminar

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## Spring Semester 2022

Date / Time Speaker Title Location
22 February 2022
15:15-16:15
Dr. Daniele Castorina
Università degli Studi di Napoli
Event Details

#### Analysis Seminar

Title Li and Yau estimates for some semilinear heat equations and applications Dr. Daniele Castorina, Università degli Studi di Napoli 22 February 2022, 15:15-16:15 HG G 43 Streamingcall_made We will show some Li and Yau–type gradient estimates for positive solutions of the semilinear heat equations $u_t = \Delta u + u^p$ with $p>$1, on a complete–dimensional Riemannian manifold (M,g) with nonnegative Ricci tensor. We then discuss some applications to ancient and eternal solutions. Joint work with Giacomo Ascione (SSM Napoli), Giovanni Catino (PoliMi) and Carlo Mantegazza (Napoli Federico II).
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1 March 2022
15:15-16:15
Università di Roma La Sapienza
Event Details

#### Analysis Seminar

Title Derivation of surface tension of grain boundaries in polycystals Prof. Dr. Adriana Garroni , Università di Roma La Sapienza 1 March 2022, 15:15-16:15 HG G 43 Streamingcall_made Inspired by a recent result of Lauteri and Luckhaus, with derive, via Gamma convergence, a surface tension model for polycrystals in dimension two. The starting point is a semi-discrete model accounting for the possibility of having crystal defects. The presence of defects is modelled by incompatible strain fields with quantised curl. In the limit as the lattice spacing tends to zero we obtain an energy for grain boundaries that depends on the relative angle of the orientations of the two neighbouring grains. The energy density is defined through an asymptotic cell problem formula. By means of the bounds obtained by Lauteri and Luckhaus we also show that the energy density exhibits a logarithmic behaviour for small angle grain boundaries in agreement with the classical Shockley Read formula. The talk is based on a paper in preparation in collaboration with Emanuele Spadaro.
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15 March 2022
15:15-16:15
Jaume de Dios Pont
UCLA
Event Details

#### Analysis Seminar

Title Uniform boundedness in operators parametrized by polynomial curves Jaume de Dios Pont, UCLA 15 March 2022, 15:15-16:15 HG G 43 Streamingcall_made Multiple results in harmonic analysis involving integrals of functions over curves (such as restriction theorems, convolution estimates, maximal function estimates or decoupling estimates) depend strongly on the non-vanishing of the torsion of the associated curve. Over the past years there has been considerable interest in extending these results to a degenerate case where the torsion vanishes at a finite number of points by using the affine arc-length as an alternative integration measure. As a model case, multiple results have been proven in which the coordinate functions of the curve are polynomials. In this case one expects the bounds of the operators to depend only on the degree of the polynomial. In this talk I will introduce and motivate the concept of affine arclength measure, provide new decomposition theorems for polynomial curves over characteristic zero local fields, and provide some applications to uniformity results in harmonic analysis.
HG G 43
Streaming
29 March 2022
15:15-16:15
Prof. Dr. Benedetta Pellacci
Università degli studi della Campania
Event Details

#### Analysis Seminar

Title Singular analysis of the optimizers of the principal eigenvalue in indefinite weighted Neumann problems Prof. Dr. Benedetta Pellacci, Università degli studi della Campania 29 March 2022, 15:15-16:15 Online via Zoom The optimization of the principal eigenvalue of indefinite weighted problems settled in bounded domains arises as a natural task in the study of the survival threshold for a species in population dynamics. We study the minimization of such eigenvalue, associated with Neumann boundary conditions, performing the analysis of the singular limit in case of arbitrarily small favourable region. We show that, in this regime, the favourable region is connected and it concentrates on the boundary of the domain. Though widely expected, these properties are still unknown in the general case. This is a joint research with Dario Mazzoleni and Gianmaria Verzini.
Online via Zoom
5 April 2022
15:15-16:15
Prof. Dr. Matteo Bonforte
Event Details

#### Analysis Seminar

Title Stability in Gagliardo-Nirenberg-Sobolev inequalities: nonlinear flows, regularity and the entropy method Prof. Dr. Matteo Bonforte, Universidad Autónoma de Madrid and ICMAT 5 April 2022, 15:15-16:15 HG G 43 Streamingcall_made We discuss stability results in Gagliardo-Nirenberg-Sobolev inequalities, a joint project with J. Dolbeault, B. Nazaret and N. Simonov. We have developped a new quantitative and costructive "flow method", based on entropy methods and sharp regularity estimates for solutions to the fast diffusion equation (FDE). This allows to study refined versions of the Gagliardo-Nirenberg-Sobolev inequalities that are nothing but explicit stability estimates. Using the quantitative regularity estimates, we go beyond the variational results and provide fully constructive estimates, to the price of a small restriction of the functional space which is inherent to the method.
HG G 43
Streaming
3 May 2022
15:15-16:15
Enric Florit
Universitat Politecnica de Catalunya
Event Details

#### Analysis Seminar

Title The Yau conjecture for nonlocal minimal surfaces Enric Florit , Universitat Politecnica de Catalunya 3 May 2022, 15:15-16:15 HG G 43 Streamingcall_made In this talk we will explain the existence of infinitely many nonlocal minimal surfaces, which are the critical points of a canonical definition of nonlocal perimeter, on any closed Riemannian manifold of dimension three. The result is a consequence of very strong compactness properties for these objects that also lead to Bernstein and De Giorgi theorems with some surprises. The talk is based on work with Michele Caselli and Joaquim Serra.
HG G 43
Streaming
10 May 2022
15:15-16:15
Dr. Georgios Dosidis
Charles University, Prague
Event Details

#### Analysis Seminar

Title The uncentered spherical maximal function and Nikodym sets Dr. Georgios Dosidis, Charles University, Prague 10 May 2022, 15:15-16:15 HG G 43 Streamingcall_made In this talk we consider the uncentered spherical maximal function, which is an analogue of the operator introduced by Stein, that also includes translations. The existence of Nikodym sets for spheres indicates that maximal operators given by translations of spherical averages are unbounded on Lp for all finite p. We study the Nikodym operator associated to this set, obtaining a control on the Lp norm. Moreover, for lower-dimensional sets of translations, we obtain Lp boundedness for the maximally translated-dillated spherical averages for a certain range of p that depends on the Minkowski dimension of the set of translations. This is joint work with A. Chang and J. Kim.
HG G 43
Streaming
17 May 2022
15:15-16:15
Dr. Fabiana Leoni
University of La Sapienza di Roma
Event Details

#### Analysis Seminar

Title New concentrations phenomena for radial solutions of fully nonlinear equations Dr. Fabiana Leoni, University of La Sapienza di Roma 17 May 2022, 15:15-16:15 HG G 43 (Streaming)call_made
New concentrations phenomena for radial solutions of fully nonlinear equations
HG G 43
(Streaming)
* 24 May 2022
15:45-16:45
Prof. Dr. Nicos Kapouleas
Brown University
Event Details

#### Analysis Seminar

Title Doubling constructions for minimal surfaces and other recent results Prof. Dr. Nicos Kapouleas, Brown University 24 May 2022, 15:45-16:45 HG G 43 Streaming I will discuss doubling constructions for minimal surfaces and (depending on time) other recent results, 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; including a new general area estimate for doublings. I will then discuss ongoing work and open questions related to this and in comparison to recent 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''.
HG G 43
Streaming

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