Hello there, my name is Andrew (Michael) Thomas. I am a graduate student in the Statistics department at Purdue University studying applied probability. I spend most of my research time working on the probability side of topological data analysis (TDA). I have recently completed a paper with my advisor Dr. Takashi Owada on functional limit theorems for Euler characteristic processes and my research currently consists of investigating stochastic random topology. For an introduction to the concepts of topological data analysis, including Betti numbers, please look in the miscellany section for some of my favorite introductions to TDA below. From a higher-level view, what I am interested in is the topological structure of random point clouds, especially as the number of points goes to infinity. This structure may be either the homology or persistent homology based off of simplicial complexes formed from these random point clouds. Often these point clouds are generated by point processes, so the theory thereof factors heavily into my work and is tremendously interesting.
Furthermore, I am currently the director of the organization StatCom. StatCom provides free statistical consulting services to nonprofits and local governments around Purdue University. In addition, StatCom also conducts outreach events for students in preschool to the 12th grade. Please check out our webpage here, or follow us on Facebook.
Functional limit theorems for the Euler characteristic process in the critical regime (2020).
Andrew M. Thomas and Takashi Owada
Forthcoming in Advances in Applied Probability, arXiv:1910.00751
Limit theorems for process-level Betti numbers for sparse and critical regimes (2020).
Takashi Owada and Andrew M. Thomas
Advances in Applied Probability 52, 1-31. Publisher Link.
I've appeared twice in the IMS bulletin, for solving problems in the Student Puzzle Corner. You can see here, I sent in a solution to an interesting problem on random distances on hyperspheres. Be sure to read your IMS Bulletin! Here is a link to some proofs I've compiled the last few years and have written up for my own edification. Here's video of an online talk that I gave July 1, 2020 at the Applied Algebraic Topology Research Network (AATRN).
On August 3, 2020 I gave a talk at the virtual Joint Statistical Meetings (JSM) held in virtual Philadelphia about the history of StatCom and how to keep student volunteers and clients engaged to complete projects and ensure that the volunteers have ample opportunities for service-learning. My slide deck can be accesssed here.
Below I have compiled a list of some short, invigorating yet relaxing articles on mathematical topics that will soothe your mathritis pain. Mathematical IcyHot®.