Combinatorics Seminar

Date/Day: 7th August, Wednesday.

Venue/Time: Ramanujan Hall, 11:30 am

Speaker: Dhruv Mubayi, University of Illinois at Chicago

Title: New results on the Erdos Rogers function

Abstract: Given integers 1 < s < t, what is the maximum size of a K_s-free
subgraph that every n vertex K_t-free graph is guaranteed to contain? This
problem was posed by Hajnal,  Erdos and Rogers in the 1960s as a way to
generalize classical graph Ramsey numbers (which corresponds to the case
s=2). We prove almost optimal results in the case t=s+1 using recent
constructions in Ramsey theory. We also consider the problem where we
replace K_s and  K_t by arbitrary graphs H and G and discover several
interesting new phenomena.  This is joint work with Jacques Verstraete.

Colloquium talk

Title : Billiards in Rational Prisms

Speaker : Jayadev Athreya, University of Washington

Time, Date and day : 7th August (Wed) at 4:00 pm

Venue : Ramanujan Hall

Host: Ravi Raghunathan

Abstract : This talk describes joint work-in-progress with Bedaride, Hooper,
and Hubert. Motivated by the study of billiards in polyhedra, we study
linear flows in a family of singular flat 3-manifolds which we call
translation prisms. Using ideas of Furstenberg and Veech, we connect
results about weak mixing properties of flows on translation surfaces to
ergodic properties of linear flows on translation prisms, and use this to
obtain several results about unique ergodicity of these prism flows.
Furthermore, we construct explicit eigenfunctions for translation flows in
psuedo-Anosov directions with Pisot expansion factors, and use this
construction to build explicit examples of non-ergodic prism flows, and
for
non-ergodic billiard flows in a right prism over a regular 7-gon.