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Spring Semester 2023

Date / Time Speaker Title Location
21 February 2023
15:15-16:15 		Prof. Dr. Yoshihiro Tonegawa
Tokyo Institute of Technology
Event Details

Analysis Seminar

Title Some existence and uniqueness questions for mean curvature flow
Speaker, Affiliation Prof. Dr. Yoshihiro Tonegawa, Tokyo Institute of Technology
Date, Time 21 February 2023, 15:15-16:15
Location HG G 43
Abstract Given a non-smooth vector field in a Sobolev space and a smooth hypersurface in the Euclidean space, we can show that there exists a one-parameter family of hypersurfaces whose velocity is equal to the mean curvature plus the given vector field in a strong PDE sense for a short time, and more generalized sense time-globally. In some sense, there is a competition between the surface tension (regularizing effect) and non-smooth flow field (roughening effect), and apparently, there cannot be uniqueness in the usual sense for the solution despite the availability of a good regularity theorem. I plan to describe what I know about the problem, rough idea of the proof as well as some possible way to look into the uniqueness question suggested from the construction.
Some existence and uniqueness questions for mean curvature flowread_more
HG G 43
21 March 2023
15:15-16:15 		Prof. Dr. Zoltan Balogh
Universität Bern
Event Details

Analysis Seminar

Title Sharp isoperimetric and Sobolev inequalities in CD(0,N) spaces via OMT
Speaker, Affiliation Prof. Dr. Zoltan Balogh, Universität Bern
Date, Time 21 March 2023, 15:15-16:15
Location HG G 43
Abstract Optimal mass transportation is a versatile tool to prove sharp geometric inequalities in Euclidean spaces. This method works also in the case of more general metric-measure spaces satisfying a curvature condition. In this talk I will present some recent results in the setting of CD(0,N) spaces satisfying a volume growth condition at infinity. This is a joint work with Alexandru Kristaly and Francesca Tripaldi.
Sharp isoperimetric and Sobolev inequalities in CD(0,N) spaces via OMTread_more
HG G 43
4 April 2023
15:15-16:15 		Prof. Dr. Matteo Bonforte
Universidad Autonoma Madrid
Event Details

Analysis Seminar

Title Nonlinear and Nonlocal Diffusions. Smoothing effects, Green functions and functional inequalities
Speaker, Affiliation Prof. Dr. Matteo Bonforte, Universidad Autonoma Madrid
Date, Time 4 April 2023, 15:15-16:15
Location HG G 43
Abstract We will consider the Cauchy problem for Nonlinear Diffusion equations of porous medium type $u_t=-\mathcal{L} u^m$, with $m>1$ and investigate whether or not integrable data produce bounded solutions. The diffusion operator belongs to a quite general class of nonlocal operators, and we will see how different assumption on the operator imply (or not) smoothing properties. We will briefly compare the approach based on Moser iteration and the approach through Green functions. On the one hand, we show that if the linear case ($m=1$) enjoys smoothing properties, also the nonlinear will do. On the other hand, we see that in some cases the nonlinear diffusion enjoys the smoothing properties also when the linear counterpart does not, thanks to the convex nonlinearity. Following Nash' ideas, we see how smoothing properties are often equivalent to the validity of Gagliardo-Nirenberg-Sobolev (and Nash) inequalities: we explore these implications also in the nonlinear and nonlocal context and the connection with dual inequalities (Hardy-Littlewood-Sobolev) and Green function estimates. This is a work with J. Endal (NTNU, Trondheim). Finally, I shall present smoothing and higher regularity estimates for a class of zero-order p-Laplacian evolution equations, showing another case in which the regularization is true in the nonlinear setting while it fails for the linear counterpart. This is a work in progress with A. Salort (Univ. Buenos Aires).
Nonlinear and Nonlocal Diffusions. Smoothing effects, Green functions and functional inequalitiesread_more
HG G 43
18 April 2023
15:15-16:15 		Dr. Mateus Sousa
BCAM
Event Details

Analysis Seminar

Title Sharp embeddings between weighted Paley–Wiener spaces
Speaker, Affiliation Dr. Mateus Sousa, BCAM
Date, Time 18 April 2023, 15:15-16:15
Location HG G 43
Abstract In this talk we will discuss some extremal problems related to embeddings between weighted Paley–Wiener spaces. We will present some asymptotic results for sharp constants in terms of the parameters involved, deduce existence results for extremal functions as well as radial symmetry of those. For certain cases, these extremal problems can be reformulated in terms of sharp Poincaré inequalities, and for those cases we will present a characterisation of extremizers and sharp constants that recover several classical results.
Sharp embeddings between weighted Paley–Wiener spaces read_more
HG G 43
25 April 2023
15:15-16:15 		Dr. Yi Zhang
Chinese Academy of Science
Event Details

Analysis Seminar

Title Stability of geometric inequality: Old and new
Speaker, Affiliation Dr. Yi Zhang , Chinese Academy of Science
Date, Time 25 April 2023, 15:15-16:15
Location HG G 43
Abstract In 2008, Fusco, Maggi, and Pratelli proved the sharp stability of the isoperimetric inequality, an open problem originally raised by Hall in 1992. This inequality states that for any set of finite perimeter $E\subset \mathbb R^n$ with $|E|=|B|$ and a barycenter at the origin, one has $ P(E)-P(B)\ge c(n) |E\Delta B|^2.$ Here, the power $2$ on the right-hand side is optimal. During my talk, I will review some earlier results on improving their proof and share some of my recent joint work with A. Figalli in this direction.
Stability of geometric inequality: Old and newread_more
HG G 43
2 May 2023
15:15-16:15 		Dr. Francesco Palmurella
Scuola Normale Superiore Pisa
Event Details

Analysis Seminar

Title Title T.B.A.
Speaker, Affiliation Dr. Francesco Palmurella, Scuola Normale Superiore Pisa
Date, Time 2 May 2023, 15:15-16:15
Location HG G 43
Title T.B.A. (CANCELLED)
HG G 43
9 May 2023
15:15-16:16 		Prof. Dr. Costante Bellettini
University College London
Event Details

Analysis Seminar

Title Hypersurfaces with mean curvature prescribed by an ambient function
Speaker, Affiliation Prof. Dr. Costante Bellettini, University College London
Date, Time 9 May 2023, 15:15-16:16
Location HG G 43
Abstract Let N be a compact Riemannian manifold of dimension 3 or higher, and g a Lipschitz non-negative (or non-positive) function on N. In joint works with Neshan Wickramasekera we prove that there exists a two-sided (well-defined global unit normal) closed hypersurface M whose mean curvature attains the values prescribed by g. Except possibly for a small singular set (of codimension 7 or higher), the hypersurface M is C^2 immersed; more precisely, the immersion is a quasi-embedding, namely the only non-embedded points are caused by tangential self-intersections (around such a non-embedded point, the local structure is given by two disks, lying on one side of each other, and intersecting tangentially, as in the case of two spherical caps touching at a point). A special case of PMC (prescribed-mean-curvature) hypersurfaces is obtained when g is a constant, in which case the above result gives a CMC (constant-mean-curvature) hypersurface for any prescribed value of the mean curvature. The proof employs an Allen--Cahn approximation scheme, classical minmax, and gradient flow arguments. A key issue in the construction (and, more generally, in related compactness questions) is the possible formation of "hidden boundaries".
Hypersurfaces with mean curvature prescribed by an ambient functionread_more
HG G 43
16 May 2023
14:00-15:00 		Prof. Dr. Armin Schikorra
University of Pittsburgh
Event Details

Analysis Seminar

Title Regularity results for n-Laplace systems with antisymmetric potential
Speaker, Affiliation Prof. Dr. Armin Schikorra, University of Pittsburgh
Date, Time 16 May 2023, 14:00-15:00
Location HG G 43
Abstract n-Laplace systems with antisymmetric potential are known to govern geometric equations such as n-harmonic maps between manifolds and generalized prescribed H-surface equations. Due to the nonlinearity of the leading order n-Laplace and the criticality of the equation they are very difficult to treat. I will discuss some progress we obtained, combining stability methods by Iwaniec and nonlinear potential theory for vectorial equations by Kuusi-Mingione. Joint work with Dorian Martino
Regularity results for n-Laplace systems with antisymmetric potentialread_more
HG G 43
16 May 2023
15:15-16:15 		Prof. Dr. Stefan Czimek
Universität Leipzig
Event Details

Analysis Seminar

Title Obstruction-free gluing for the Einstein equations
Speaker, Affiliation Prof. Dr. Stefan Czimek, Universität Leipzig
Date, Time 16 May 2023, 15:15-16:15
Location HG G 43
Abstract We present a new approach to the gluing problem in General Relativity, that is, the problem of matching two solutions of the Einstein equations along a spacelike or characteristic (null) hypersurface. In contrast to previous constructions, the new perspective actively utilizes the nonlinearity of the constraint equations. As a result, we are able to remove the 10-dimensional spaces of obstructions to gluing present in the literature. As application, we show that any asymptotically flat spacelike initial data set can be glued to Schwarzschild initial data of sufficiently large mass. This is joint work with I. Rodnianski.
Obstruction-free gluing for the Einstein equationsread_more
HG G 43
* 23 May 2023
16:15-17:15 		Prof. Dr. Didier Smets
Laboratoire Jacques-Louis Lions Sorbonne Université
Event Details

Analysis Seminar

Title On the applicability of Doeblin Harris type methods to PDE models with partial diffusion
Speaker, Affiliation Prof. Dr. Didier Smets, Laboratoire Jacques-Louis Lions Sorbonne Université
Date, Time 23 May 2023, 16:15-17:15
Location HG G 43
On the applicability of Doeblin Harris type methods to PDE models with partial diffusion
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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