Seminar on Geometry and Topology
About the Seminar
The aim of the seminar is to introduce students to fascinating ideas in modern geometry and to encourage them to undertake independent research in this field.
The seminar features talks by colleagues from our institute, the Institute of Physics, and other universities. The talks cover not only modern geometry but also its applications to theoretical physics. Doctoral and master's students specializing in geometry also present their research topics and results at the seminar.
Students may choose one of the proposed topics, prepare a written report, and give a presentation at the seminar. In this case, they receive credit for the course. If a student decides to continue research on the chosen topic, the report may be developed into part of a future bachelor's thesis.
Topics for Student Presentations and Bachelor's Theses
- Fibre bundles, theory of connections, and gauge theories
- Noncommutative geometry and quantum gravity
- Lie groups, Lie algebras, their representations, and quantum field theory
- Rotation group, Riemannian geometry, and optimal trajectories of unmanned aerial vehicles
- Symplectic geometry, mechanics, and Poisson algebras
Seminar Talk Archive
Autumn Semester 2026/2027
3 September 2026
Transposed Poisson Algebras and Superalgebras
Speaker: Viktor Abramov
Time: 16:15–17:30
Room: 1026, Delta building
Abstract. The main structure considered in the talk is the transposed Poisson superalgebra and its relation to 3-Lie superalgebras. The speaker first recalled the definitions of such important structures as Poisson algebras, transposed Poisson algebras, and 3-Lie algebras and superalgebras. The talk presented an overview of recent research on transposed Poisson algebras. In particular, a classification of three-dimensional transposed Poisson algebras was presented.
10 September 2026
Ternary Structures
Ternary Lie Algebras at Cube Root of Unity
Speaker: Viktor Abramov
Time: 16:15-17.30
Room: 1026, Delta building
Abstract. The talk gives a brief overview of the main ideas of noncommutative geometry. It begins with the Gelfand–Naimark theorem for commutative C*-algebras, which can be interpreted as the possibility of reconstructing a topological space of points from an algebra of functions on that space. The transition to noncommutative geometry consists in replacing the commutative algebra by a noncommutative one.
As an example, the Manin quantum plane and the Wess–Zumino differential calculus on this plane are presented. Within the framework of noncommutative geometry, generalizations of algebraic structures involving a primitive N-th root of unity have been developed. The talk concludes with a ternary analogue of a Lie algebra in which a primitive cube root of unity plays a fundamental role.
17 September 2026
Koszul Duality
Speaker: Ülo Reimaa
Affiliation: Institute of Mathematics and Statistics, University of Tartu
Time: 16:15–17:45
Room: 1026, Delta building
Abstract. We give an introduction to linear operads and their Koszul duality. For illustration, we consider structures that appeared in earlier seminars, such as Poisson algebras or ternary Lie algebras, from this point of view.
1 October 2026
A brief Introduction to Chaotic Strings
Speaker: Stefan Groote
Affiliation: Institute of Physics, University of Tartu
Time: 16:15–17:45
Room: 1026, Delta building
Abstract. Coupled map lattices, known better under the name of Chaotic Strings, are nonlinear dynamical systems, relating a continuous state variable between discrete points in discrete steps via Chebychev maps and exhibiting a quite involved and interesting spatio-temporal chaotic behaviour. In principle, they can be derived by a stochastic quantisation of field theory. However, taken as a mathematical model be itself, chaotic strings serve as a mathematical paradigm, allowing to explain to some extend parameters of elementary particle physics. In this talk, I will give an introduction on what my colleague Christian Beck from the Queen Mary University of London has initiated and in the following investigated together with me and a couple of other colleagues.
8 October 2026
Transposed Poisson 3-Lie Superalgebras
Speaker: Nikolai Sovetnikov
Affiliation: Institute of Mathematics and Statistics, University of Tartu
Time: 16:15–17:15
Room: 1026, Delta building
Abstract. The talk is devoted to generalizations of Lie and Poisson algebras in the framework of superalgebras. We introduce transposed Poisson superalgebras and discuss their relationship with 3-Lie superalgebras. The central object of the talk is a transposed Poisson 3-Lie superalgebra. We present a method for constructing transposed Poisson 3-Lie superalgebras using even derivations of transposed Poisson superalgebras. This construction yields a broad class of examples arising from commutative superalgebras equipped with two commuting even derivations.