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

2024

Invited Speaker	Research Topic & Affiliation	Title of the talk	Time
Xuwen Zhu	Geometric Analysis, Microlocal Analysis, PDE and Mathematical Physics, Northeastern University, US	Spectral gaps for large genus hyperbolic surfaces	29 April 2024, 3:00 pm (CEST)
Robert Yuncken	Noncommutative Geometry, Representation Theory and Pseudodifferential Operators, Université de Lorraine, France	The Helffer-Nourrigat conjecture: hypoellipticity of polynomials of vector fields	6 May 2024, 4:00 pm (CEST)

2023

Invited Speaker	Research Topic & Affiliation	Title of the talk	Time
Claire Debord	Geometry and Topology, Institut de Mathématiques de Jussieu, France	Index theory via Lie groupoids	30 January 2023, 11:00 am (CET)
Camil Muscalu	Harmonic Analysis and PDE, Cornell University, US	Mixed norm estimates via the helicoidal method	13 February 2023, 4:00 pm (CET)
David Cruz-Uribe	Harmonic Analysis and PDE, The University of Alabama, US	Bounded weak solutions to elliptic PDE with data in Orlicz spaces	20 February 2023, 4:00 pm (CET)
Julio Delgado	Harmonic Analysis and Spectral Theory, Universidad del Valle, Colombia	Metrics on the phase space and well-posedness for degenerate Schrödinger equations	13 March 2023, 2:00 pm (CET)
Loukas Grafakos	Harmonic Analysis and PDE, University of Missouri, US	Maximal averages with respect to balls and spheres	02 May 2023, 4:00 pm (CEST)
Sundaram Thangavelu	Harmonic Analysis and PDE, Indian Institute of Science, India	Joint session with the Ghent Methusalem Colloquium	May 9, 11, 16 (Info here).
Eckhard Meinrenken	Differential Geometry, Lie Theory and Mathematical Physics, University of Toronto, Canada	Euler-like vector fields and weightings	22 May 2023, 4:00 pm (CEST)
Gerald Folland	Harmonic Analysis and PDE, University of Washington, US	Compact homogeneous spaces of the Heisenberg group and their relation to Abelian varieties and their line bundles	26 June 2023, 5:00 pm (CEST)
Elmar Schrohe	Analysis on Manifolds, Noncommutative Geometry and Index Theory, Leibniz Universität Hannover, Germany	Asymptotics of the porous medium equation on manifolds with conical singularities	11 September 2023, 11:00 am (CEST)
Charles Fefferman	Geometric Analysis and PDE, Princeton University	Equations for unknown 𝑪^𝒎 functions	11 October 2023. 2:00 pm (CEST) Organised in Collaboration with ICMAM Latin America
Laurent Bessières	Riemannian Geometry, Ricci Flow, 3-manifolds and Differentiable Rigidity Phenomena, Université de Bordeaux	Deforming 3-manifolds of bounded geometry and uniformly positive scalar curvature	13 November 2023, 2:30 pm (CET)
Jörg Seiler	Pseudodifferential Operators, PDE and Global Analysis, Università degli Studi di Torino	Parametric pseudodifferential operators with point-singularity in the covariable	11 December 2023, 11:30 am (CET)

2022

Invited Speaker	Research Topic & Affiliation	Title of the talk	Time
Andreas Seeger	Harmonic Analysis, University of Wisconsin-Madison, US	Lp-improving bounds for maximal and variational operators associated with spherical means	18 April 2022 , 11:00 am (CEST)
Victor Nistor	Geometric Analysis, Institut Élie Cartan de Lorraine, France	Analysis on non-compact manifolds and index theory	13 June 2022, 11:00 am (CEST)
Johannes Sjostrand	Geometric Analysis, IMB, Université de Bourgogne, France	Analytic microlocal analysis with exponential weights and some applications	20 June 2022, 11:00 am (CEST)
Jonathan Rohleder	Geometric Analysis, Stockholms Universitet, Sweden	A new approach to the hot spots conjecture	12 September 2022, 11:00 am (CEST)
Durvudkhan Suragan	Analysis and PDE, Nazarbayev University, Kazakhstan	Analysis of PDE on Nilpotent Lie groups	8 August 11:30 am (CEST)
Uwe Kähler	Partial Differential Equations, University of Aveiro, Portugal	Ruzhansky-Turunen-Wirth calculus in the case of Spin groups	24 October 2022, 11:00 am (CEST)
Gerd Grubb	Partial Differential Equations and Harmonic Analysis, University of Copenhagen	Spectral results for Dirichlet problems for fractional-order elliptic operators	14 November 2022, 4:00 pm (CET)

Organisers:

• Duván Cardona Sanchez, Ghent University, (duvan.cardonasanchez@ugent.be).
• Gihyun Lee, Ghent University,(gihyun.lee@ghent.ac.kr).
• David Santiago Gómez Cóbos Ghent University, (davidsantiago.gomezcobos@ugent.be).
• Website for the seminar compatible with Google sites.

Information about the sessions:
(TBA)

Our organisers:

Intensive sessions about advanced topics about geometric analysis:

Time	Speaker	Title of the minicourse
25 April 2022	Santiago Gómez Cóbos	The Atiyah-Singer Index theorem revisited
2 May 2022	Arne Hendrickx	An Introduction to the Fredholm theory. Advanced Topics I.
9 May 2022	Arne Hendrickx	An Introduction to the Fredholm theory. Advanced Topics. II
16 May 2022	Arne Hendrickx	An Introduction to the Fredholm theory. Advanced Topics. III
23 May 2022	Duván Cardona	An introduction to vector bundles. Advanced Topics I.
27 June 2022	Brian Grajales	An introduction to vector bundles. Advanced Topics II.
10 October 2022	Gihyun Lee	The integral in Noncommutative Geometry I
17 October 2022	Gihyun Lee	The integral in Noncommutative Geometry II
31 October 2022	Duván Cardona	Estimates for eigenfunctions of elliptic operators on compact manifolds and applications to control theory
7 November	Duván Cardona	Estimates for eigenfunctions of elliptic operators on compact manifolds and applications to control theory