## The PIMS Postdoctoral Fellow Seminar: Venkata Pantangi

• Date: 01/26/2022
• Time: 09:30
Lecturer(s):
Venkata Pantangi, ULethbridge/ URegina
Location:

Online

Topic:

EKR-Module Property [video]

Description:

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

Other Information:

This seminar takes places across multiple time zones: 9:30 AM Pacific/ 10:30 AM Mountain / 11:30 AM Central

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