On counting by inclusion-exclusion: Moebius functions, shellability and discrete Morse theory

Patricia Hersh
Date and time: 
Thu, Jun 3 2021 - 12:15pm
Location: 
Zoom
Speaker(s):
Patricia Hersh
Department of Mathematics, University of Oregon
Host/Committee: 
  • Joe Sventek

We will tell the story of how Moebius functions may be used to count by inclusion-exclusion topologically. In particular, we will discuss combinatorial-topological tools that have been remarkably effective at doing this, namely lexicographic shellability and more recently also discrete Morse theory. Some of the most compelling applications have been to theoretical computer science, a topic we will highlight along the way. We will not assume familiarity with topology or with the more algebraic and topological sides of discrete mathematics arising in this talk.

Biography: 

Dr. Hersh is a professor in the math department at the University of Oregon. Before this, she was a math faculty member for many years at North Carolina State University and prior to that at Indiana University-Bloomington, a postdoc at MSRI, Michigan and the University of Washington. She went to grad school at MIT, and undergrad at Harvard where she studied mathematics and computer science. She spent fall 2010 visiting Cornell thanks to the very generous support of the Ruth Michler Prize of the Association for Women in Mathematics (AWM). Richard Stanley was her Ph.D. advisor, and Phil Hanlon was her NSF postdoc sponsoring scientist at Michigan; Persi Diaconis was her undergraduate advisor.

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