Thematic program "Geometric and Mathematical Analysis, and Weak Geometric Structures"
March 23 – December 23, 2021
This thematic program will be focused upon several areas of current mathematics research very closely interrelated between each other and having deep common roots in geometric measure theory (GMT):
- Shape optimization problems and geometric analysis: minimal surfaces (with respect to various notions of surface area/perimeter including nonlocal ones) and related problems, clusters of soap bubbles, problems with prescribed curvature, the Steiner problem and transportation networks, as well as applications of shape optimization in image analysis (e.g. Mumford-Shah problem and similar) and mechanics (e.g. eigenvalue or compliance optimization or ground states of Schrödinger equation).
- Weak geometric structures related to GMT, such as currents, as well as those arising in optimal mass transportation and the study of geometry of highly irregular metric measure spaces, in particular those without any differentiable structure, with applications to the analysis of PDEs with very low regularity (e.g. weak and/or or probabilistic notions of flows, or “differential equations” with “purely nondifferentiable”, for instance just Hölder continuous unknowns, like those in Rough paths theory) and to some modern harmonic analysis problems.
- Purely geometric problems involving weak geometric structures, like extensions of Frobenius theorem either to irregular differential forms or distributions of planes or to weaker notions of surfaces like De Rham currents; extensions of Chow-Rachevsky theorem to irregular vector fields or flows; applications to sub-Riemannian geometry, geometric control theory and dynamical systems.
The idea is to explore the deep connections between the above mentioned areas of research and to make them more comprehensible and attractive to both international and local mathematical
If you plan to attend minicourses please register here.
- "Geometric flows of networks" by Matteo Novaga (Università di Pisa) and Alessandra Pluda (Università di Pisa), March 23 – April 1, 2021
- "Loops and Bubbles" by Roberta Musina (Università di Udine), April 13 – April 21, 2021
- "Gabor analysis for rational functions" by Yurii S. Belov (St. Petersburg State University), April 14 – May 26, 2021
- "One-dimensional optimization problems" by Emanuele Paolini (Università di Pisa), May 11 – May 19, 2021
- "Mathematics and applications of manifold learning: reconstructing hidden geometric structures in the data" by Serguei Barannikov (Skoltech and CNRS), Sergey Nechaev (CNRS), Vladimir Spokoiny (WIAS) and Dario Trevisan (Università di Pisa), dates TBA
- "Sobolev vector fields and their flows" by Elia Brué (IAS) and Dario Trevisan (Università di Pisa), dates TBA
30th St.Petersburg Summer Meeting in Mathematical Analysis, July 1 – 6, 2021
- Roberta Musina, Università di Udine
- Matteo Novaga, Università di Pisa
- Eugene Stepanov, PDMI RAS
- Dario Trevisan, Università di Pisa
Institutions participating in the organization of the event
- Leonhard Euler International Mathematical Institute in Saint Petersburg
- Saint-Petersburg State University
- St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
The program is supported by a grant from the Government of the Russian Federation, agreements 075-15-2019-1619 and 075-15-2019-1620, and by a grant from Simons Foundation.