The PIMS Postdoctoral Fellow Seminar: Venkata Pantangi

Let \(G\) be a finite group acting transitively on \(X\). We say \(g,h \in G\) are intersecting if \(gh^{-1}\) fixes a point in \(X\). A subset \(S\) of \(G\) is said to be an intersecting set if every pair of elements in \(S\) intersect. Cosets of point stabilizers are canonical examples of intersecting sets. The group action version of the classical Erdos-Ko-Rado problem asks about the size and characterization of intersecting sets of maximum possible size. A group action is said to satisfy the EKR property if the size of every intersecting set is bounded above by the size of a point stabilizer. A group action is said to satisfy the strict-EKR property if every maximum intersecting set is a coset of a point stabilizer. It is an active line of research to find group actions satisfying these properties. It was shown that all \(2\)-transitive satisfy the EKR property. While some \(2\)-transitive groups satisfy the strict-EKR property, not all of them do. However a recent result shows that all \(2\)-transitive groups satisfy the slightly weaker "EKR-module property"(EKRM), that is, the characteristic vector of a maximum intersecting set is a linear span of characteristic vectors of cosets of point stabilizers. We will discuss about a few more infinite classes of group actions that satisfy the EKRM property. I will also provide a few non-examples and a characterization of the EKRM property using characters of \(G\) .

Speaker Biography: Venkata Pantangi obtained a BS-MS dual degree from IISER Pune in 2012. In 2019 he obtained a doctorate from the University of Florida, under the supervision of Professor Peter Sin. From 2019-2021, he worked as a postdoc at the Southern University of Science and Technology in China, under the mentorship of Professor Cai-Heng Li. Currently, he is a PIMS CRG postdoc at the University of Lethbridge, under the supervision of Professor Joy Morris, and is a member of the CRG on Movement and Symmetry in Graphs.

Read more about Venkata on our Medium segment here.  

This event is part of the Emergent Research: The PIMS Postdoctoral Fellow Colloquium Series