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

Invited Speaker	Research Topic & Affiliation	Time
Andreas Seeger	Harmonic Analysis, University of Wisconsin-Madison, US	18 April 2022
Jonathan Rohleder	Geometric Analysis, Stockholms Universitet, Sweden	30 May 2022
Victor Nistor	Geometric Analysis, Institut Élie Cartan de Lorraine, France	13 June 2022
Johannes Sjostrand	Geometric Analysis, IMB, Université de Bourgogne, France	20 June 2022
Durvudkhan Suragan	Analysis and PDE, Nazarbayev University, Kazakhstan	8 August 2022

Organisers:

• Duván Cardona Sanchez, Ghent University, (duvan.cardonasanchez@ugent.be).
• David Santiago Gómez Cóbos Ghent University, (davidsantiago.gomezcobos@ugent.be).
• Andrea Vanessa Hurtado Quiceno Ghent University, (andreavanessa.hurtadoquiceno@ugent.be).
• Website for the seminar compatible with Googlesites.

Information about the sessions

Our organisers:

Intensive sessions about advanced topics of the 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.