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

Beginning Fall of 2019, I will be an Assistant Professor at Texas State University.

You may have also seen me at the Newton Institute in Cambridge, England (Fall 2018), at MSRI (Spring 2019 and Spring 2014), at the Hausdorff Institute in Bonn (Summer 2015), or at Harvard (2013-2018) where I was a Benjamin Peirce and NSF Postdoctoral Fellow.

You can contact me at: hiroleetanaka at gmail

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 and pre-prints

  1. Continuous actions on wrapped Fukaya categories, with Yong-Geun Oh. arXiv:1911.00349
  2. Cyclic structures and broken cycles. arXiv:1907.03301
  3. Lectures on Factorization Homology, Infinity-Categories, and Topological Field Theories, with A. Amabel, A. Kalmykov, and L. Müller. arXiv:1907.00066
  4. Generation for Lagrangian cobordisms in Weinstein manifolds. arXiv:1810.10605
  5. Associative algebras and broken lines, with Jacob Lurie. arXiv:1805.09587
  6. Surgery induces exact sequences in Lagrangian cobordisms. arXiv:1805.07424
  7. Stellar Stratifications on Classifying Spaces, with Dai Tamaki. To appear, Algebraic Topology and Related Topics. arXiv:1804.11274
  8. Odd sphere bundles, symplectic manifolds, and their intersection theory, with Li-Sheng Tseng. Cambridge Journal of Mathematics (2018), 213--266. arXiv:1702.03423
  9. 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.
  10. The Fukaya category pairs with Lagrangian cobordisms exactly. arXiv:1609.08400
  11. The Fukaya category pairs with Lagrangian cobordisms. Submitted. arXiv:1607.04976
  12. Functors (between oo-categories) that aren't strictly unital. J. Homotopy Relat. Struct. (2018) 13: 273--286. arXiv:1606.05669
  13. Factorization homology in 3-dimensional topology, with Nikita Markarian. In Mathematical Aspects of Quantum Field Theories, Springer 2015, pp. 222-231.
  14. Factorization homology of stratified spaces, with David Ayala and John Francis. Selecta Math. (N.S.) 23 (2017), no. 1, 293--362. arXiv:1409.0848
  15. Local structures on stratified spaces, with David Ayala and John Francis. Adv. Math. 307 (2017), 903--1028. arxiv 1409.0501
  16. In simply-connected cotangent bundles, exact Lagrangian cobordisms are h-cobordisms. To appear, Advances in Geometry. arXiv:1404.6273.
  17. 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.
  • 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

  • From 2015 to 2018, I served as a faculty advisor for Harvard's Gender Inclusivity in Mathematics.
  • In 2018, I organized a weekly seminar for undergraduates to share their summer research projects.
  • I was a coach for a high school Mock Trial team near Boston, and 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.