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Algèbre, Analyse, Géométrie et Physique

English title Algebra, Analysis, Geometry and Physics
Applicant Smirnov Stanislav
Number 178828
Funding scheme Project funding (Div. I-III)
Research institution Section de Mathématiques Université de Genève
Institution of higher education University of Geneva - GE
Main discipline Mathematics
Start/End 01.10.2018 - 30.09.2021
Approved amount 900'000.00
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All Disciplines (2)

Discipline
Mathematics
Theoretical Physics

Keywords (7)

statistical mechanics; geometry; algebra; topology; analysis; algebraic geometry; probability

Lay Summary (French)

Lead
Cet important projet interdisciplinaire finance les activités de recherche du département de mathématiques de l'université de Genève ainsi que ses collaborations avec les universités suisses environnantes.
Lay summary

Cet important projet interdisciplinaire finance les activités de recherche du département de mathématiques de l'université de Genève ainsi que ses collaborations avec les universités suisses environnantes.

Le projet s'articule autour de quatre grands axes de recherche et leurs interactions. Le premier s'intéresse aux différents aspects des problèmes de modules et leurs interactions avec les autres sujets tels que la théorie de Lie et la cohomologie équivariante. La deuxième partie se concentre sur les connections entre différents champs aussi bien classiques qu'émergents en géométrie et en topologie. La troisième partie étudie les modèles probabilistes dans les espaces euclidiens et sur les groupes. La quatrième partie étudie la théorie géométrique des groupes et les problèmes reliés aux théories ergodique et des systèmes dynamiques.

Le projet est basé sur un programme important de visites de courte et de longue durée, et finance plusieurs groupes de recherche interagissant entre eux, ainsi que plusieurs séminaires réguliers. Il contribue également à l'organisation de conférences, de workshops et d'écoles destinées aux étudiants en doctorat ainsi qu'aux chercheurs des universités de Genève et de la région. Finalement, le projet permet de financer certains trajets des membres du groupe.

Direct link to Lay Summary Last update: 12.09.2018

Responsible applicant and co-applicants

Project partner

Associated projects

Number Title Start Funding scheme
182111 Topics in real algebraic geometry 01.10.2018 Project funding (Div. I-III)
182767 Star-products, Drinfeld twists and Rankin-Cohen brackets 01.01.2019 Project funding (Div. I-III)
159581 Algèbre, Analyse, Géométrie et Physique 01.10.2015 Project funding (Div. I-III)
141869 NCCR SwissMAP: The Mathematics of Physics (phase I) 01.07.2014 National Centres of Competence in Research (NCCRs)

Abstract

This large multidisciplinary project supports the research activities at the Department of Mathematics of the University of Geneva during three academic years 2018-2021. It covers several research groups interacting among themselves, as well as with EPFL, ETHZ, CERN and Swiss universities. The project centers around an extensive visitor program, and supports a number of other activities. Compared with the previous application, the project becomes bigger, as the department has grown. This is a continuation of a long series of FNS grants. While it might look unusual and different from most FNS projects in size and scope, this difference is well justified by its prior success and careful planning. This series of projects runs continuously for over 40 years and is instrumental in Geneva being a top-level mathematical center. It creates a vibrant atmosphere at the Geneva mathematics department by inviting leading researchers for collaboration, running active seminars, holding workshops and conferences on topics of current interest, organizing schools on modern subjects to involve students in cutting-edge research. Many of the activities are cross-disciplinary, uniting mathematicians from different areas, which often leads to spectacular developments. Such strategy allowed the mathematics department of the University of Geneva to achieve remarkable success for a department of such a small size and made it into an important center of mathematics. Cumulatively this project led to hundreds of important results and papers in leading journals, including several fundamental contributions. Associated researchers received many prestigious prizes, including Fields medals.We expect to follow the track record of the last forty years, producing important results in several areas of mathematics, and publishing them in established peer-review journals. All the results will be made freely available on the arXiv.org server, as is customary in mathematics.The project will support about 55 months of longer visits per year for three years, as well as a number of short-term visitors to present talks at our seminars and colloquium. It will contribute to organizing several conferences, workshops and schools in 2018-2021, and to travel of our team members to conferences and other universities. We also plan to partially support a few distinguished visiting professors on sabbatical, who will give advanced courses, actively participate in our seminars, and actively pursue joint research projects.The proposed research covers several areas of modern mathematics, and we structure it around four main directions. All the permanent pure mathematics faculty will be active partners, assigned to one of the directions, with significant interaction among those:(1) Moduli spaces, Poisson structures and positivity (A. Alekseev and A. Szenes), (2) Geometry and topology (R. Kashaev, M. Marinno and G. Mikhalkin),(3) Probability, complex analysis and statistical mechanics (D. Cimasoni, H. Duminil-Copin, A. Knowles, S. Smirnov and Y. Velenik),(4) Groups, geometry and dynamics (M. Bucher, A. Karlsson and T. Smirnova-Nagnibeda).Part (1) of this project is devoted to Poisson, algebraic and topological aspects of moduli problems, to positivity phenomena in algebra and their relation to tropical correspondences, and to the theory of free Lie algebras and their applications to moduli spaces and to low-dimensional topology. In this part we expect about 11 months of longer visits per year.Part (2) is about mathematical aspects of quantum Chern-Simons theory; geometrical understanding of 3-manifold invariants; topological recursion and spectral theory; the relations of the classical theory of real algebraic curves to symplectic geometry and dynamical systems; topological classification of real algebraic curves on K3-surfaces. We expect about 13 months of longer visits per year.Part (3) focuses on non-bipartite dimers on tori; Bootstrap percolation and Kinetically Constraint Models; probability on groups; Spectra of random graphs; Harmonic measure and growth phenomena; Infinite system of mutually avoiding Ferrari-Spohn diffusions. We expect about 18 months of longer visits per year.Part (4) addresses some topics in geometric group theory and related subjects: geometry of affine manifolds and their fundamental groups; amenability; spectral theory of graphs, groups and metric spaces; subgroup structure of branch groups. We expect about 13 months of longer visits per year.
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