The Midwest Mathematical Biology Seminar will be a series of virtual talks on mathematical biology featuring speakers from the Midwest region and beyond. All areas of mathematical biology will be represented in the seminar series, and a goal for this seminar is to build connections and foster research collaborations.
Schedule (Fall 2025)
(All talks at 11am Eastern Time / 10am Central Time on Tuesdays)
Zoom link: https://illinois.zoom.us/j/84907159401?pwd=JboBtq30vntVuEpj8s3yYfAdwlb258.1
September 2: Tin Phan (Los Alamos National Laboratory)
September 9: Maliha Ahmed (MIT)
September 16: Peter Thomas (Case Western Reserve University)
September 23: Maxwell Kreider (Penn State)
Title: Synchronization of Stochastic Oscillators: Arnold Tongues and Koopman Eigenfunctions
Abstract:
Phase reduction is an effective theoretical and numerical tool for studying synchronization of coupled deterministic oscillators.
Stochastic oscillators require new definitions of asymptotic phase. The Q-function, i.e., the slowest decaying complex mode of the stochastic Koopman operator (SKO), was proposed as a means of phase reduction for stochastic oscillators. In this talk, we show that the Q-function approach also leads to a novel definition of "synchronization" for coupled stochastic oscillators. A system of coupled oscillators in the synchronous regime may be viewed as a single (higher-dimensional) oscillator. Therefore, we investigate the relation between the Q-functions of the uncoupled oscillators and the higher-dimensional Q-function for the coupled system. We propose a definition of synchronization between coupled stochastic oscillators in terms of the eigenvalue spectrum of Kolmogorov's backward operator (the generator of the Markov process, or the SKO) of the higher dimensional coupled system. We observe a novel type of bifurcation reflecting (i) the relationship between the leading eigenvalues of the SKO for the coupled system and (ii) qualitative changes in the cross-spectral density of the coupled oscillators. Using our proposed definition, we observe synchronization domains for symmetrically-coupled stochastic oscillators that are analogous to Arnold tongues for coupled deterministic oscillators. Finding a Q-phase reduction for a system of coupled stochastic oscillators requires solving a high-dimensional PDE, which is numerically challenging. If time permits, we will discuss a data-driven machine learning approach to compute Q-functions for high-dimensional (n>3) systems of coupled stochastic oscillators. The talk will also build on material from Peter Thomas's talk on phase reduction for stochastic oscillators scheduled for the Midwest Mathematical Biology Seminar for September 16, 2025.
September 30: Po-Chun Kuo (Purdue University)
October 7: Naghmeh Akhavan (University of Michigan)
October 14: Hwai-Ray Tung (University of Utah)
October 21: Folashade Agusto (University of Kansas)
October 28: Hyukpyo Hong (University of Wisconsin — Madison)
November 4: Ruby Kim (University of Michigan)
November 11: Swati Patel (Oregon State University)
November 18: Cody FitzGerald (Northwestern University)
November 25: Farshad Shirani (Emory University)
December 2: Ted Loch-Temzelides (Rice University)
December 9: Binan Gu (Worcester Polytechnic Institute)
December 16: Tyler Simmons (University of Minnesota)
Schedule (Spring 2025)
(All talks at 4pm Eastern Time / 3pm Central Time on Fridays)
January 24: Bo Deng (University of Nebraska, Lincoln)
January 31: Mingchao Cai (Morgan State)
February 7: Claus Kadelka (Iowa State University)
February 14: Peter Hinow (University of Wisconsin Milwaukee)
February 21: Chengcheng Huang (University of Pittsburgh)
February 28: Veronica Ciocanel (Duke University)
SPECIAL TIME (2pm Eastern Time / 1pm Central Time)
March 7: Adrian Lam (Ohio State University)
March 14: Sabrina Streipert (University of Pittsburgh)
March 21: Merlin Pelz (University of Minnesota)
March 28: Meghan Ferrall-Fairbanks (University of Florida)
April 4: Zixuan Cang (North Carolina State University)
April 11: Jia Gou (University of California Riverside) Cancelled by the speaker.
April 18: Stephanie Dodson (Colby College)
April 25: Montie Avery (Boston University)
May 2: Bo Zhang ( Oklahoma State University)
Zoom Link: https://illinois.zoom.us/j/82616248519?pwd=CAR0v0aaIpTnIVwxJDa59wFvusobot.1.
May 9: Mario Gómez Flores (Florida State University)
Schedule (Fall 2024)
(All talks at 2pm Eastern Time / 1pm Central Time on Fridays)
September 6: Al Holder (Rose Hulman Institute of Technology)
September 13: Jichun Xie (Duke University)
September 20: Samantha Linn (University of Utah)
September 27: Guowei Wei (Michigan State)
October 4: Polly Yu (University of Illinois Urbana-Champaign)
October 11: Laurel Ohm (University of Wisconsin–Madison)
October 18: Hongsong Feng (Michigan State)
October 25: Alexandria Volkening (Purdue University)
November 1: Hyunjoong Kim (University of Cincinnati)
November 8: Kelsey Gasior (University of Notre Dame)
November 15: Wai-Tong Louis Fan (Indiana University Bloomington)
November 22: Zhe Su (Michigan State)
December 6: Gregory Handy (University of Minnesota)
December 13: Erik Amezquita Morataya (University of Missouri)
This seminar series is co-organized by Ning Wei (Purdue University) and Daniel Cooney (University of Illinois Urbana-Champaign). You can sign up for email updates on the seminar series by joining the Midwest Mathematical Biology Google Group (https://groups.google.com/g/midwest-mathematical-biology-seminar/about).