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Submitted by sutanu on 14 September, 2018 - 14:45

Date/Time:

Friday, October 5, 2018 - 14:00 to 15:00

Venue:

Seminar Room, School of Mathematical Sciences

Speaker:

Bidyut Sanki

Affiliation:

IMSc, Chennai

Title:

Graphs of systoles on hyperbolic surfaces

In this talk, we study the configuration of systoles (minimum length geodesics) on closed hyperbolic surfaces. The set of all systoles forms a graph on the surface, in fact a so-called fat graph, which we call the systolic graph. We study which fat graphs are systolic graphs for some surfaces, we call these admissible. There is a natural necessary condition on such graphs, which we call combinatorial admissibility. Our first result characterizes admissibility. It follows that a sub-graph of an admissible graph is admissible. Our second major result is that there are infinitely many minimal non-admissible fat graphs (in contrast, to the classical result that there are only two minimal non-planar graphs).

**School of Mathematical Sciences**

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