Title of the talk: Graphs for circle actions (periodic flows) on 4-dimensional (almost) complex/oriented manifolds

Speaker: Donghoon Jang (Pusan National University, South Korea)

Abstract: I will explain how one can use a combinatorial object, graph, to study geometry/topology. The focus will be on actions of the circle group on manifolds with fixed points, which we can roughly regard as rotations (or periodic flows) of geometric objects. When a manifold admits an (almost) complex structure, there exists a graph that
contains data on the fixed point set. In dimension four, I will discuss a classification of such graphs. I will then turn to oriented 4-manifolds and present a classification of the corresponding graphs via equivariant connected sum and splitting, based on joint work with Oleg Musin. This talk will be expository and aimed at a broad audience. I will start from
basic concepts and illustrate the ideas with concrete examples.

Short Bio: Dr. Donghoon Jang is an Associate Professor of Mathematics at Pusan National University, South Korea. His main areas of expertise are equivariant geometry and topology and symplectic geometry. Dr. Jang received his Ph.D. from the University of Illinois at Urbana-
Champaign in 2015 under the supervision of Dr. Susan Tolman. After that he held a position at the Korea Institute for Advanced Study and moved to Pusan National University in 2018.