Millican Colloquium: An ergodic advertisement for descriptive graph combinatorics- Anush Tserunyan (UIUC) | Department of Mathematics

COVID-19 updates—In an effort to keep everyone healthy, UNT's on-campus operations are closed until further notice. We're serving students remotely. Please stay connected. Stay up to date on UNT’s response to COVID-19 (Coronavirus).

Have you registered for fall classes yet? While COVID-19 has created some uncertainty for us all, UNT is committed to helping the Mean Green family turn dreams into reality. Let's get through this together!

Register for classes on
Not a UNT student yet? Apply to UNT
Having trouble registering? Get help from an advisor

Millican Colloquium: An ergodic advertisement for descriptive graph combinatorics- Anush Tserunyan (UIUC)

Event Information
Event Location: 
GAB 461
Event Date: 
Friday, March 29, 2019 - 2:00pm

Dating back to Birkhoff, pointwise ergodic theorems for probability measure preserving (pmp) actions of countable groups are bridges between the global condition of ergodicity (measure-theoretic transitivity) and the local combinatorics of the actions. Each such action induces a Borel equivalence relation with countable classes and the study of these equivalence relations is a flourishing subject in modern descriptive set theory. Such an equivalence relation can also be viewed as the connectedness relation of a locally countable Borel graph. These strong connections between equivalence relations, group actions, and graphs create an extremely fruitful interplay between descriptive set theory, ergodic theory, measured group theory, probability theory, and descriptive graph combinatorics. I will discuss how descriptive set theoretic thinking combined with combinatorial and measure-theoretic arguments yields a pointwise ergodic theorem for quasi-pmp locally countable graphs. This theorem is a general random version of pointwise ergodic theorems for group actions and is provably the best possible pointwise ergodic result for some of these actions.

Thinking about UNT?

It's easy to apply online. Join us and discover why we're the choice of over 38,000 students.

Apply now