Research Seminar at MMF: Lecture by Visiting Professor Serge A. Lawrence

On February 16, 2026, from 16:00 to 18:00, a research seminar was held at MMF (CISI), Room 305. The invited speaker was Visiting Professor Serge A. Lawrence.

The title of the lecture was:
“What does tell us the action of the automorphism group of a graph on the set of triangulations of a given surface with this graph?”

The talk focused on the action of the automorphism group of a graph on the set of triangulations of a given surface realized with that graph. By applying Pólya's Enumeration Theorem (also known as the Pólya–Redfield Theorem), the speaker demonstrated that one can derive not only the exact number of such triangulations from the associated group action, but also explicitly list all of them with labeled vertices.

Particular attention was devoted to the complete 4-partite graph K_{2,2,2,2}. The lecture presented an explicit construction of all twelve triangulations of the torus with this graph. It was emphasized that this graph is the 1-skeleton of the four-dimensional hyperoctahedron and admits a natural algebraic interpretation as the Cayley graph of the quaternion group Q_8.

Although the primary emphasis was placed on algebraic and combinatorial methods, the geometric component of the problem was illustrated through concrete embeddings into the torus. The presentation stimulated substantial discussion among faculty members, graduate students, and doctoral researchers.