Seminars and Colloquia Schedule

Identifying Dehn Functions of Bestvina--Brady Groups From Their Defining Graphs

Geometry Topology Seminar
Monday, January 11, 2021 - 14:00 for 1 hour (actually 50 minutes)
Yu-Chan ChangEmory University<br />
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Meeting ID: 883 302 5617

Bestvina--Brady groups are subgroups of right-angled Artin groups, and their Dehn functions are bounded above by quartic functions. There are examples of Bestvina--Brady groups whose Dehn functions are linear, quadratic, cubic, and quartic. In this talk, I will give a class of Bestvina--Brady groups that have polynomial Dehn functions, and we can identify the Dehn functions by the defining graphs of those Bestvina--Brady groups. 

Large deviations of the greedy independent set algorithm on sparse random graphs

Combinatorics Seminar
Friday, January 15, 2021 - 15:00 for 1 hour (actually 50 minutes)
Location (To receive the password, please email Lutz Warnke)
Brett KolesnikUniversity of California, Berkeley

We study the greedy independent set algorithm on sparse Erdős-Rényi random graphs G(n,c/n). This range of p is of interest due to the threshold at c=e, beyond which it appears that greedy algorithms are affected by a sudden change in the independent set landscape. A large deviation principle was recently established by Bermolen et al. (2020), however, the proof and rate function are somewhat involved. Upper bounds for the rate function were obtained earlier by Pittel (1982). By discrete calculus, we identify the optimal trajectory realizing a given large deviation and obtain the rate function in a simple closed form. In particular, we show that Pittel's bounds are sharp. The proof is brief and elementary. We think the methods presented here will be useful in analyzing the tail behavior of other random growth and exploration processes.

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