Ghent Geometric Analysis Seminar

The Ghent Geometric Analysis seminar is dedicated to studying the modern techniques of elliptic and subelliptic partial differential equations (PDEs) that are used to establish new results in differential geometry and differential topology. We are planning to invite several of the leaders in the fields of microlocal analysis, geometric analysis, and harmonic analysis abroad. The use of linear elliptic PDE dates at least as far back as Hodge theory. These techniques can be applied to the problem of computing the index of operators that have shown to have relevant geometric information for different applications in mathematical physics and other problems of classification. 

On the other hand, geometric and topological properties of spaces, such as submanifolds of the Euclidean space, Riemannian manifolds, symplectic manifolds, and vector bundles can be computed using these techniques. This approach dates back to the work by Tibor Radó and Jesse Douglas on minimal surfaces, John Nash Jr. on isometric embeddings of Riemannian manifolds into the Euclidean space, Louis Nirenberg on the Minkowski problem and the Weyl problem, Aleksandr Danilovich Aleksandrov and Aleksei Pogorelov on convex hypersurfaces. In particular, the fundamental contributions by Uhlenbeck, Shing-Tung Yau, Richard Schoen, and Richard Hamilton launched a particularly exciting and productive era of geometric analysis that continues to this day. A celebrated achievement was the solution to the Poincaré conjecture by Grigori Perelman, completing a program initiated and largely carried out by Richard Hamilton. 

Going to the recent developments on the field, the Seminar of Geometric Analysis at the Ghent Analysis and PDE center will present the aforementioned works as well as the fundamental works on Index theory, K-theory and their applications to non-commutative geometry, and K-theory, in view of the Atiyah and Singer solution of the Gelfand conjecture (their celebrated Atiyah-Singer Index theorem).

In view of the recent activities and investigations undertaken by the members of the Ghent Analysis and PDE center and the works in the interplay of geometric analysis and harmonic analysis of our group, our seminar also will be a scenario for presenting the recent developments in the field and their applications to other branches in mathematics.

Ghent Geometric Analysis Seminar Schedule

2023

Invited SpeakerResearch Topic & AffiliationTitle of the talkTime
Claire DebordGeometry and Topology, Institut de Mathématiques de Jussieu, FranceIndex theory via Lie groupoids30 January 2023,
11:00 am (CET)
Camil MuscaluHarmonic Analysis and PDE, Cornell University, USMixed norm estimates via the helicoidal method13 February 2023,
4:00 pm (CET)
David Cruz-UribeHarmonic Analysis and PDE, The University of Alabama, USBounded weak solutions to elliptic PDE with data in Orlicz spaces20 February 2023,
4:00 pm (CET)
Julio DelgadoHarmonic Analysis and Spectral Theory, Universidad del Valle, ColombiaMetrics on the phase space and well-posedness for degenerate Schrödinger equations13 March 2023, 2:00 pm (CET)
Loukas GrafakosHarmonic Analysis and PDE, University of Missouri, USMaximal averages with respect to balls and spheres02 May 2023,
4:00 pm (CEST)
Sundaram ThangaveluHarmonic Analysis and PDE, Indian Institute of Science, IndiaJoint session with the Ghent Methusalem ColloquiumMay 9, 11, 16 (Info here).
Eckhard MeinrenkenDifferential Geometry, Lie Theory and Mathematical Physics, University of Toronto, Canada(TBA)May
Gerald FollandHarmonic Analysis and PDE, University of Washington, US(TBA)June
Elmar SchroheAnalysis on Manifolds, Noncommutative Geometry and Index Theory, Leibniz Universität Hannover, Germany(TBA)September

2022

Invited SpeakerResearch Topic & AffiliationTitle of the talkTime
Andreas SeegerHarmonic Analysis, University of Wisconsin-Madison, USLp-improving bounds for maximal and variational operators associated with spherical means18 April 2022 ,
11:00 am (CEST)
Victor NistorGeometric Analysis, Institut Élie Cartan de Lorraine, FranceAnalysis on non-compact manifolds and index theory13 June 2022,
11:00 am (CEST)
Johannes SjostrandGeometric Analysis, IMB, Université de Bourgogne, FranceAnalytic microlocal analysis with exponential weights and some applications20 June 2022,
11:00 am (CEST)
Jonathan RohlederGeometric Analysis, Stockholms Universitet, SwedenA new approach to the hot spots conjecture12 September 2022,
11:00 am (CEST)
Durvudkhan SuraganAnalysis and PDE, Nazarbayev University, KazakhstanAnalysis of PDE on Nilpotent Lie groups8 August
11:30 am (CEST)
Uwe KählerPartial Differential Equations, University of Aveiro, PortugalRuzhansky-Turunen-Wirth calculus in the case of Spin groups24 October 2022, 11:00 am (CEST)
Gerd GrubbPartial Differential Equations and Harmonic Analysis, University of CopenhagenSpectral results for Dirichlet problems for fractional-order elliptic operators14 November 2022, 4:00 pm (CET)

Organisers:

Information about the sessions:
(TBA)

Our organisers:

Duvan
Santiago



Intensive sessions about advanced topics about geometric analysis:

TimeSpeakerTitle of the minicourse
25 April 2022Santiago Gómez CóbosThe Atiyah-Singer Index theorem revisited
2 May 2022Arne HendrickxAn Introduction to the Fredholm theory. Advanced Topics I.
9 May 2022Arne HendrickxAn Introduction to the Fredholm theory. Advanced Topics. II
16 May 2022Arne HendrickxAn Introduction to the Fredholm theory. Advanced Topics. III
23 May 2022Duván Cardona An introduction to vector bundles. Advanced Topics I.
27 June 2022Brian GrajalesAn introduction to vector bundles. Advanced Topics II.
10 October 2022Gihyun LeeThe integral in Noncommutative Geometry I
17 October 2022Gihyun LeeThe integral in Noncommutative Geometry II
31 October 2022Duván CardonaEstimates for eigenfunctions of elliptic operators on compact manifolds and applications to control theory
7 NovemberDuván CardonaEstimates for eigenfunctions of elliptic operators on compact manifolds and applications to control theory