I am an algebraic topologist inspired by ideas from mathematical physics.

I'm currently finishing a combined Benjamin Peirce and NSF Postdoctoral Fellowship at Harvard. In Fall of 2018, I will be at the Newton Institute in Cambridge, England, and in the Spring of 2019, I will be at MSRI. In the Fall of 2019, I will be an Assistant Professor at Texas State University.

You may have also seen me in Bonn in summer of 2015, or around the Bay Area in spring of 2014, when I was an MSRI Postdoctoral Fellow.

Statement of commitment to equity in mathematics

I support policies and activities meant to dissect and disarm mechanisms that lead to inequities in mathematical fields. To this end, I also support: conducting research into the sometimes subtle, sometimes not-so-subtle, ways in which various groups come to be underrepresented in mathematical fields; listening to needs of various communities and responding effectively to those needs; reflecting on personal actions and reactions; and enacting practices of equity in my day-to-day praxis.

Papers

  1. Associative algebras and broken lines, with Jacob Lurie. arXiv:1805.09587
  2. Surgery induces exact sequences in Lagrangian cobordisms. arXiv:1805.07424
  3. Stellar Stratifications on Classifying Spaces, with Dai Tamaki. arXiv:1804.11274
  4. Odd sphere bundles, symplectic manifolds, and their intersection theory, with Li-Sheng Tseng. To appear, Cambridge Journal of Mathematics. arXiv:1702.03423
  5. Bridgeland stability, 2-Segal spaces, and the Ran space of the line. In Proceedings of the Conference on Manifolds, K-Theory and Related Topics, Contemporary Mathematics (2017), 209--235.
  6. The Fukaya category pairs with Lagrangian cobordisms exactly. arXiv:1609.08400
  7. The Fukaya category pairs with Lagrangian cobordisms. Submitted. arXiv:1607.04976
  8. Functors (between oo-categories) that aren't strictly unital. To appear, Journal of Homotopy and Related Structures. arXiv:1606.05669
  9. Factorization homology in 3-dimensional topology, with Nikita Markarian. In Mathematical Aspects of Quantum Field Theories, Springer 2015, pp. 222-231.
  10. Factorization homology of stratified spaces, with David Ayala and John Francis. Selecta Math. (N.S.) 23 (2017), no. 1, 293--362. arXiv:1409.0848
  11. Local structures on stratified spaces, with David Ayala and John Francis. Adv. Math. 307 (2017), 903--1028. arxiv 1409.0501
  12. In simply-connected cotangent bundles, exact Lagrangian cobordisms are h-cobordisms. Submitted. arXiv:1404.6273.
  13. A stable infinity-category of Lagrangian cobordisms, with David Nadler. Submitted. arXiv:1109.4835.

In preparation:

  • Operads and broken trees (working title), joint with Jacob Lurie.
  • Exit path categories of cellular stratified spaces (working title), joint with Dai Tamaki.
  • Hamiltonian isotopies and Hochschild cochains of the Fukaya category (working title), joint with Yong-Geun Oh.
  • The integers are linear over Lagrangian cobordisms.
  • Lagrangian cobordisms are linear over L.

For more details, please see my research page. Most of my works are available as arXiv preprints, while my non-arXiv papers are all in "Proceedings" type books. Finally, here is my Google Scholar page.

Other interests

  • I am currently one of the faculty advisors for Harvard's Gender Inclusivity in Mathematics.
  • I am also one of the coaches for a local high school Mock Trial team. I coached Northwestern University's undergraduate Mock Trial team back when I was in Chicago.
  • I helped organize a Derived Geometry and Floer Theory seminar at Harvard in Fall 2016.
  • I used to volunteer with PBHA's Youth Prison Tutoring Program.
  • During spring of 2014, I volunteered for the Reading Partners program, reading one-on-one with students at an elementary school in Oakland.
  • I also organized an oo-category seminar for undergraduates at Harvard in Fall 2013.
  • Back in Chicago, I used to volunteer for the Chicago HOPES homeless education program, where I worked with students in elementary and middle schools. The organization is now called Chicago HOPES for Kids.
  • At Northwestern, I was one of two Outreach Coordinators for the Northwestern Presidential Fellows.
  • I also co-organized the Talbot Workshop from Fall 2009 to Spring 2013.
  • I helped organize the 2013 Pre-Talbot Seminar on chromatic homotopy theory.
  • I helped organize the Leverpostej seminar in Aarhus, Denmark, in 2011.
  • I helped organize the 2011 Pre-Talbot seminar on non-Abelian Hodge Theory with Sam Gunningham and Owen Gwilliam.