I am Associate Professor of Mathematics on the John Stewart Kennedy Foundation at Mount Holyoke College. Previously, I was an NSF Alliance for Building Faculty Diversity Postdoctoral Fellow at Iowa State University. Before that, I got my PhD in mathematics at Washington University in St. Louis. See my cv for more details.

Research

I’m interested in probability theory, stochastic processes, and dynamical systems.

Students

• In Summer 2023, I co-advised Cathy Liu, Sophie Su, and Boxiao Zhu with Alanna Hoyer-Leitzel on two projects related to stochastic differential equations with noise derived from a compound Poisson process. The group studied the problem of analyzing exit time distributions in the context of the FitzHugh-Nagumo model of neuron activity and an immunological model for sudden viral exposure.
• In Spring 2023, I co-advised Cathy Liu with Alanna Hoyer-Leitzel on a numerical study of a system differential equations with impulsive stochastic perturbations used to model the effective of sudden viral exposures on the human immune system. Some preliminary results were summarized in this slide presentation.
• In Fall 2021, I worked with Emily Rosaci and Yuxuan (Susan) Wang, continuing their work from Summer 2021. They created an interactive Shiny app on random billiards.
• In Summer 2021, I worked with Ruozhen Gong, Emily Rosaci, and Yuxuan (Susan) Wang on a project involving billiards, probability, and their interplay. Our main objects of study were polygonal billiard tables and some related Markov chains. Their work was written up in a report.
• In Spring 2021, I worked with Ruozhen Gong on the relationship between random billiard models and thermodynamics. Her work is documented in this summary report.
• In Spring 2019, I worked with Nicole Andrews on Hidden Markov models related to random billiards. Her work is documented in this write-up.
• In Fall 2018, I worked with Ziyan (Jessica) Feng on random polygonal billiards. Some of her work is documented on this web page.
• In Summer 2017, I worked with Qiran (Karen) Dong and Fanyi (Young) Yang (Mount Holyoke), on a project studying random billiard systems with non-holonomic (rolling) constraints. Here is their talk.
• In 2016, I worked with Tianle (Jeff) Yang (Iowa State) on a project studying the Lorentz gas model with random scatterer collisions.

Papers

1. T. Chumley, R. Feres, L. A. Garcia German, and G. Yablonsky. Revisiting maxwell-smoluchowski theory: low surface roughness in straight channels. Chem. Eng. Sci., 284:119477, 2024. [ arXiv ]
2. T. Chumley, J. Covey, C. Cox, and R. Feres. Chaotic lensed billiards. arXiv preprint, 2022. [ arXiv ]
3. J. Ahmed, T. Chumley, S. Cook, C. Cox, H. Grant, N. Petela, B. Rothrock, and R. Xhafaj. Dynamics of the no-slip galton board. arXiv preprint, 2022. [ arXiv ]
4. T. Chumley, R. Feres, and L. A. Garcia German. Knudsen diffusivity in random billiards: spectrum, geometry, and computation. SIAM J. Appl. Dyn. Syst., 20(3):1655–1682, 2021. [ arXiv ]
5. T. Chumley, R. Feres, and M. Wallace. Exact discretization of harmonic tensors. Potential Anal., 56(3):409–421, 2022. [ arXiv ]
6. T. Chumley and R. Feres. Entropy production in random billiards. Discrete Contin. Dyn. Syst., 41(3):1319–1346, 2021. [ arXiv ]
7. T. Chumley, S. Cook, C. Cox, and R. Feres. Rolling and no-slip bouncing in cylinders. J. Geom. Mech., 12(1):53–84, 2020. [ arXiv ]
8. O. Aydogmus, T. Chumley, A. Matzavinos, and A. Roitershtein. Moran-type bounds for the fixation probability in a frequency-dependent Wright-Fisher model. J. Math. Biol., 76(1):1–35, 2018. [ arXiv ]
9. T. Chumley, R. Feres, and H.-K. Zhang. Diffusivity in multiple scattering systems. Trans. Amer. Math. Soc., 368(1):109–148, 2016. [ arXiv ]
10. T. Chumley, S. Cook, and R. Feres. From billiards to thermodynamics. Comput. Math. Appl., 65(10):1596–1613, 2013. [ arXiv ]
11. T. Chumley. Limit Theorems for Random Billiard Models. PhD thesis, 2013.

Teaching

Current courses

• Math 206: Introduction to Proofs through Analysis (Fall 2024)
• Math 342: Probability (Fall 2024)

Past courses

• Math 101: Calculus I (Spring 2019)
• Math 102: Calculus II (Fall 2016, 2021, 2022)
• Math 203: Calculus III (Fall 2022, Spring 2023)
• Math 211: Linear Algebra (Spring 2017)
• Math 232: Discrete Math (Fall 2018)
• Math 241: Dynamical Systems (Spring 2022)
• Math 301: Real Analysis (Fall 2020, 2021, Spring 2023)
• Math 333: Differential Equations (Spring 2018)
• Math 339SP/Stat 344: Stochastic Processes (Spring 2017, 2018, 2019, 2022, 2024)
• Math 342: Probability (Fall 2016, 2017, 2018; Spring 2021, 2024)
• Stat 395: Independent study, Statistical Analysis of Networks (Fall 2017)

Prior to coming to Mount Holyoke I taught:

• Introduction to Statistics (Summer 2009, Summer 2010 at Washington University)
• Calculus I (Summer 2008 at WUSTL)
• Calculus II (Fall 2013, Fall 2015 at Iowa State University)
• Linear Algebra (Summer 2012 at WUSTL, Spring 2014 at ISU)
• Real Analysis (Fall 2014 at ISU)

Miscellaneous

• I was interviewed by the AMS Mathematical Moments program about my research on billiards and thermodynamics.
• I am honored to have appeared in the Lathisms 2020 calendar. I was also featured in an MAA Focus article about Lathisms.
• The image above is a visualization of my Math genealogy.
• Information on summer research programs for math/stat students.
• Mount Holyoke math/stat student summer activities.
• Some notes that I’ve written for myself on getting started with swarm2, the high performance computing cluster at UMass.
• I’ve made a page listing Five College equivalent math/stat courses.

Contact

Email: tchumley
Office: 423 Clapp Laboratory
Telephone: 413-538-2525
Mailing address:
     Department of Mathematics and Statistics
     Mount Holyoke College
     50 College St
     South Hadley, MA 01075