Mathematics, Physics & Computer Science Seminar Series

17 April 2024, 4:30PM, Meeting room nr. 300, Komenského náměstí 220/2

Kathryn Hess

Topological perspectives on networks

Kathryn Hess Bellwald is an American mathematician who is world-known for her work in algebraic topology, category theory and homotopy theory, and on applications of algebraic topology in neuroscience, cancer research and materials science. Professor Hess received her PhD in 1989 from the Massachusetts Institute of Technology, and she has been a professor at École Polytechnique Fédérale de Lausanne since 1999. Professor Hess was appointed to be a full member of the Swiss Academy of Engineering Sciences in 2016 and a Fellow of the American Mathematical Society in 2017. In addition to her outstanding research, Professor Hess is also known for her excellent expository skills: she was awarded the Credit Suisse teaching prize at EPFL in 2012, voted by EPFL students to receive the Polysphere d'Or Prize in 2013, and invited to deliver a public lecture at the European Congress of Mathematicians in 2021.

Abstract:

Over the past decade or so, tools from algebraic topology have been shown to be very useful in the analysis and characterization of networks, in particular for exploring the relation of structure to function. I will describe some of these tools and illustrate their utility in neuroscience.

More info HERE.

Dear friends of hikes and mathematics,

you are cordially invited to the 45th mathematical hike planned on Saturday Saturday, April 13. Meet at 9:30 in front of St. Barbara's Church in Adamov.

We recommend arriving at the meeting place by train, which leaves at 9:00 a.m. from the Brno Main station and at 9:05 from Židenice (zones 100 + 2 outside Brno). Also, there are plenty of parking spaces in the area.

Planned route (length 25 km +-delta, elevation 1100 m +-epsilon) goes largely on less frequented roads and will lead us back to the train stop in Adamov. There are many places to disconnect from the route, with frequent connections to Brno.

Recommended equipment: headlamp.

Not recommended equipment: that you don't want to get dirty (some paths are not maintained).

Looking forward to see you,

Pavel Francírek and Jonatan Kolegar, organizers

If you have questions, send them to This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Mathematics, Physics & Computer Science Seminar Series

20 March 2024, 4:30PM, Meeting room nr. 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.

Abstract:

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.g

Invitation to a public professor's lecture of Anton S. Galaev, which will be held on Wednesday, March 6, 2024 at 4:00 p.m. in the auditorium M1.

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

Title: 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.

Record of the lecture is available HERE.