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 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 | (TBA) | May |
Gerald Folland | Harmonic Analysis and PDE, University of Washington, US | (TBA) | June |
Elmar Schrohe | Analysis on Manifolds, Noncommutative Geometry and Index Theory, Leibniz Universität Hannover, Germany | (TBA) | September |
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).
- Andrea Hurtado (Former organiser).
- 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 |