Mathematics, Physics & Computer Science Seminar Series

Seminář se koná 20.3.2024 od 16:30 v zasedací místnosti 300, Komenského náměstí 220/2

Bojan Mohar

Random embeddings of graphs in surfaces

Bojan Mohar is a Slovenian and Canadian mathematician whose results in topological and structural graph theory made lasting impact not only in combinatorics but also in theoretical computer science and other fields. Professor Mohar obtained his PhD in 1986 from the University of Ljubljana, and he joined Simon Fraser University as a Canada Research Chair in graph theory in 2005. Professor Mohar has been appointed to be a  member of the Slovenian Academy of Engineering in 1999, a SIAM Fellow in 2018, and a Fellow of the American Mathematical Society in 2020. In 2020, he was elected as a Royal Society of Canada Fellow.

Abstrakt:

Homeomorphism classes of 2-cell embeddings of a graph in orientable surfaces are in bijective correspondence with rotation systems around each vertex of the graph. If we want to include nonorientable surfaces, we also add a signature $\sigma:E(G)\to \{+1,-1\}$. By taking random local rotations (and a random signature), we can speak about random 2-cell embeddings. The speaker will start with a brief survey of results in the corresponding ``Random Topological Graph Theory'' and will continue with a discussion on some recent developments.

Pozvánka na veřejnou profesorskou přednášku Antona S. Galaeva, která se bude konat ve středu 6. března 2024 v 16.00 v posluchárně M1.

Přednášející: doc. A.S. Galaev, Dr. rer. nat.

Název: Holonomy groups in Differential Geometry

Abstract:

The object of study of differential geometry are smooth manifolds endowed with additional geometric structures. Probably the most significant geometric structures are pseudo-Riemannian metrics. The holonomy group is an important invariant of a metric since it gives information about the curvature and parallel objects on the manifold. After an introduction to the subject, I will explain results about the holonomy groups of the Levi-Civita connection on pseudo-Riemannian manifolds with the stress to the case of Lorentzian manifolds. I will discuss some applications, e.g., applications to the Einstein equation. Then I will speak about a generalization to the case of superconnections on supermanifolds. I will also discuss recent results of my PhD students about holonomy of Weyl connections and metric connections with torsion on Lorentzian manifolds. There is also another notion of holonomy in differential geometry: the holonomy pseudogroup of a  foliation on a smooth manifold. At the end of the talk I will explain results about characteristic classes of these pseudogroups.

Nahrávka dostupná ZDE.