TSVP Talk: "Asymptotics for Biological Data in Non-Smooth Spaces" by Ezra Miller

Speaker: Prof. Ezra Miller (Duke University, USA)

Title: Asymptotics for Biological Data in Non-Smooth Spaces

Abstract: Biological data are often complex and geometric.  Each data object -- a 3D or 4D brain scan or a phylogenetic tree, for instance -- or the sample space parametrizing all possible data objects can be nonlinear and sometimes singular, meaning not smooth.  Statistics in these kinds of situations requires new mathematical tools to integrate geometry with analysis.  This talk tackles the central limit theorem (CLT) to understand asymptotic behavior of large-sample averages in singular settings. It starts with examples of nonlinear biological data, followed by a review of the usual linear CLT and its generalization to smooth manifolds, as seen through a lens that casts the singular CLT as a natural outgrowth.  Milestones along the way include the introduction of appropriate classes of spaces and measures as well as analogues of Gaussian random variables. Joint work with Jonathan Mattingly and Do Tran.

Profile: Ezra Miller holds a PhD in Mathematics from the University of California at Berkeley (2000) following undergraduate years at Brown University, where he earned a Bachelor of Science in Mathematics and a Bachelor of Arts in Music with a focus on theory and composition (1995). He moved to Duke University in 2009 from the University of Minnesota, where he spent six years after his postdoc at MIT. 
His research interests include geometry, algebra, topology, probability, statistics, algorithms, and combinatorics, with applications to biology and other sciences.  Miller serves on editorial boards of half a dozen journals in these and related areas and has been invited for over 250 speaking engagements ranging from local seminars to international lecture series.  He has mentored dozens of advisees at the undergraduate through postdoctoral levels and has taken part in community outreach such as collaborations on teacher training with Durham County Public Schools and interactions with television news media concerning (for example) how to present uncertainty to the public in weather forecasts or how hard it is to complete a perfect NCAA basketball tournament bracket. 
Miller has organized conferences and meetings as well as institute summer and annual programs on topics ranging from commutative algebra, combinatorics, computational geometry, and combinatorial game theory to high-dimensional statistics and computational neuroscience, some of that during an appointment as Associate Director of the Statistical and Applied Mathematical Sciences Institute (SAMSI).
He currently serves on the Fellows Selection committee of the American Mathematical Society (AMS), having previously served on the AMS Nominating Committee.  Miller was a Howard Hughes Medical Institute Scholar at the U.S. National Institutes of Health, an Alfred P. Sloan Dissertation Fellow, a Simons CRM Professor in Montréal, and a U.S. National Science Foundation CAREER awardee.  He was named a Fellow of the American Mathematical Society in 2012, the inaugural year of that fellows program.

Time: 15:00-16:00, July 16, 2025

Location: OIST, Lab 5, Floor D, Room L5D23

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Meeting ID: 947 8296 0593
Passcode: 584111

This talk is part of the Thematic Program TDA PARTI: Topological Data Analysis, Persistence And Representation Theory Intertwined.

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