Geometry and Topology

The research group in Geometry and Topology focuses on the investigation of modern structures in differential geometry and their applications in theoretical physics. The connection is a generalisation of the parallel transport of tangent vectors on surfaces, and the theory of connections is applied in theoretical physics in so-called gauge field theories. Noncommutative geometry emerged in the context of the quantization problem of gravitational theory. Our research group explores the concept of connection in noncommutative geometry. The mathematical aspects of the quark model play a significant role in particle physics. Our research group delves into the mathematical aspects of the quark model. Lie groups and algebras have a crucial role in modern differential geometry. We study contemporary generalisations of Lie algebras, including ternary Lie algebras, Poisson algebras, Hom-Lie algebras, and Lie superalgebras.

Research Group Members

Viktor Abramov (Professor, MSI, research group leader)
Stefan Groote (Associate Professor, Institute of Physics)
Olga Liivapuu (Associate Professor, Estonian University of Life Sciences)
Priit Lätt (PhD in Mathematics, MSI)
Alexander Stolin (Professor Emeritus, University of Gothenburg)
Randal Annus (student, MSI)
Aleksander Beditski (student, MSI)
Nikolai Sovetnikov (student, MSI)

Research Questions

Investigation of super Riemann surfaces
Connections in bundles, gauge field theories, and noncommutative geometry
Exploration of ternary Lie algebras and superalgebras
Quark model and algebras associated with representations of rotation groups
Poisson algebra, transposed Poisson algebra, and transposed Poisson superalgebra
Poisson algebras and geometric structures in theoretical mechanics

Research Projects

Estonia-France cooperation program "G. F. Parrot," project title "Differential graded algebras and shifted curved Lie algebras," 2021-2022
COST project "Cartan Geometry, Lie, Integrable Systems, Quantum Groups and Applications," 2023-2028
ETAG program Mobilitas Pluss, project "Cohomologies of ternary self-distributive structures and invariants of framed links."

Geometry and Topology Seminar

In this seminar, we introduce students to a range of research topics. Each student is then offered a research topic. At the end of the semester, the student submits a written report and gives a presentation on the topic of the report. These reports are intermediate steps towards a bachelor or master thesis.