I am an Associate Professor of Mathematics 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 their applications. In the past few years I’ve worked on problems that overlap with billiard dynamical systems, differential geometry, and statistical physics.
Students
 In Summer 2023, I coadvised Cathy Liu, Sophie Su, and Boxiao Zhu with Alanna HoyerLeitzel 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 FitzHughNagumo model of neuron activity and an immunological model for sudden viral exposure.
 In Spring 2023, I coadvised Cathy Liu with Alanna HoyerLeitzel 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 writeup.
 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 nonholonomic (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

T. Chumley, R. Feres, L. A. Garcia German, and G. Yablonsky. Revisiting maxwellsmoluchowski theory: low surface roughness in straight channels. Chem. Eng. Sci., 284:119477, 2024. [ arXiv ]

T. Chumley, J. Covey, C. Cox, and R. Feres. Chaotic lensed billiards. arXiv preprint, 2022. [ arXiv ]

J. Ahmed, T. Chumley, S. Cook, C. Cox, H. Grant, N. Petela, B. Rothrock, and R. Xhafaj. Dynamics of the noslip galton board. arXiv preprint, 2022. [ arXiv ]

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 ]

T. Chumley, R. Feres, and M. Wallace. Exact discretization of harmonic tensors. Potential Anal., 56(3):409–421, 2022. [ arXiv ]

T. Chumley and R. Feres. Entropy production in random billiards. Discrete Contin. Dyn. Syst., 41(3):1319–1346, 2021. [ arXiv ]

T. Chumley, S. Cook, C. Cox, and R. Feres. Rolling and noslip bouncing in cylinders. J. Geom. Mech., 12(1):53–84, 2020. [ arXiv ]

O. Aydogmus, T. Chumley, A. Matzavinos, and A. Roitershtein. Morantype bounds for the fixation probability in a frequencydependent WrightFisher model. J. Math. Biol., 76(1):1–35, 2018. [ arXiv ]

T. Chumley, R. Feres, and H.K. Zhang. Diffusivity in multiple scattering systems. Trans. Amer. Math. Soc., 368(1):109–148, 2016. [ arXiv ]

T. Chumley, S. Cook, and R. Feres. From billiards to thermodynamics. Comput. Math. Appl., 65(10):1596–1613, 2013. [ arXiv ]

T. Chumley. Limit Theorems for Random Billiard Models. PhD thesis, 2013.
Teaching
Current courses
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)
 Math 342: Probability (Fall 2016, 2017, 2018; Spring 2021)
 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
Email: tchumley
Office: 423 Clapp Laboratory
Telephone: 4135382525
Mailing address:
Department of Mathematics and Statistics
Mount Holyoke College
50 College St
South Hadley, MA 01075