I am a Postdoctoral Fellow in the Eric and Wendy Schmidt Center at the Broad Institute of MIT and Harvard, where I work with Prof. Philippe Rigollet, Prof. Caroline Uhler, and Prof. Jonathan Weissman on research in machine learning and biology. Specifically, I am developing methods to learn dynamics from multimodal biological data observed in complex systems such as tumor formation.
Prior to Fall 2023 I was a Tamarkin Assistant Professor of Mathematics and NSF Postdoctoral Fellow at Brown University, as well as a Research Affiliate at MIT. In June 2021 I completed my PhD in Mathematics at Northwestern University where I worked with with Prof. John Francis. Before that I was an undergraduate student at MIT.
Past Research
My graduate studies were in manifold topology, specifically exotic smoothings of manifold bundles. These are natural extensions of exotic smooth structures on individual manifolds, e.g. Milnor spheres, to the parametrized setting. The key invariant appearing in this area is the higher smooth torsion, an invariant studied independently by Igusa and Klein, Dwyer, Weiss, and Williams, and Bismut and Lott.
Work on these invariants was pioneered by Igusa and Waldhausen using intricate models for moduli space functors including the Whitehead space, the stable parameterized h-cobordism space, and algebraic K-theory of spaces. In my work I used excisive approximations of these functors, which I modeled using the n-Disk categories and zero-pointed spaces appearing in work of Ayala and Francis on factorization (co)homology. Coming up with refinements of the higher smooth torsion invariants in this setting allowed me to execute generalizations of theorems from classical differential topology, such as the Poincaré–Hopf theorem, to excisive functors that generalize the Euler characteristic.
This work culminated in the proof of the Rigidity Conjecture of Goette and Igusa which states that after rationalizing and stabilizing the dimension there are no exotic smoothings of bundles with even dimensional closed fibers.
Papers
Duality and vanishing theorems for topologically trivial families of smooth h-cobordisms (arXiv:2111.03188)
Teaching
I was Instructor of Record for the following courses at Brown University:
Spring 2023
Math 1620: Mathematical Statistics
Math 0520: Linear Algebra
While in graduate school I served as a teaching assistant for the following courses.
Winter 2020
336-1: Introduction to the Theory of Numbers
344-1: Introduction to Topology
Fall 2019
214-0: Single Variable Calculus III
300-0: Foundations of Higher Mathematics
Spring 2019
285-3: Accelerated Mathematics for Mathematical Methods in Social Sciences
Winter 2019
320-2: Real Analysis
344-1: Intro to Topology
Fall 2017
230-0: Differential Calculus of Multivariable Functions (two sections)
Spring 2017
224-0: Integral Calculus of One Variable Functions
331-3: Menu Abstract Algebra
Winter 2017
224-0: Integral Calculus of One Variable Functions (two sections)
Fall 2016
220-0: Differential Calculus of One Variable Functions (two sections)
Talbot Workshop
I was formerly an organizer of the MIT Talbot Workshop from 2018-2021.
In 2019 Talbot was held in Brady, TX. The topic was moduli spaces of manifolds, mentored by Prof. Soren Galatius and Prof. Oscar Randal-Williams. We made it into the local newspaper!
Here are the notes for the workshop, originally live TeX-ed by Lucy Yang, and edited by several members of the workshop including myself.
The 2020 workshop, Ambidexterity in Chromatic Homotopy Theory mentored by Prof. Jacob Lurie and Prof. Tomer Schlank, was postponed to 2021 and was held in Plymouth, MA.
In Summer 2021 we held Viva Talbot, a online retrospective workshop to mark the fifteen years of Talbot!
Travel
Here is a list of previous and upcoming travel.
2023 NEURIPS, New Orleans, Louisiana
2022 Higher algebraic structures in algebra, topology and geometry, Institut Mittag-Leffler
2020 Talbot Workshop: Ambidexterity in Chromatic Homotopy Theory, Plymouth, Massachusetts (postponed to 2021)
2021 Viva Talbot!, Online
2020 Introductory Workshop: Higher Categories and Categorification, MSRI
2019 HCM Workshop: Automorphisms of Manifolds - Hausdorff Center for Mathematics, University of Bonn
2019 Four Manifolds: Confluence of High and Low Dimensions - Fields Institute, University of Toronto
2019 Talbot Workshop: Moduli Spaces of Manifolds - Brady, TX
2018 Manifolds Workshop, Homotopy Harnessing Higher Structures Program - Isaac Newton Insti- tute, University of Cambridge
2018 Young Topologists Meeting - University of Copenhagen
2018 Seminaire de mathematiques superieures: Derived Geometry and Higher Categorical Struc- tures in Geometry and Physics - Fields Institute, University of Toronto
2017 Topological and Geometric Methods in QFT - Montana State University
2017 Floer Homology and Homotopy Theory Summer School + Conference - UCLA
2016 Talbot Workshop: Equivariant Stable Homotopy Theory and the Kervaire Invariant - Salt Lake City, Utah
2016 Young Topologists Meeting - University of Copenhagen
