(Photo credit: Ezzolo.)
Hi! I'm Hiro.
I'm a mathematician inspired by ideas from mathematical physics. I spend most of my time thinking about equitable teaching practices for students and applications of higher algebra to symplectic geometry.
Since Fall of 2019, I have been an Assistant Professor at Texas State University. Prior, I was a Benjamin Peirce Fellow at Harvard. I have also had visiting research stints at the Isaac Newton Institute, the Mathematical Sciences Research Institute, and the Hausdorff Research Institute for Mathematics.
I've been supported by the NSF GRFP, the NSF Nordic Research Opportunity program and the Danish National Research Foundation, a Northwestern University Presidential Fellowship, an NSF MSPRF, the Texas State University REP, the Texas State University Presidential Seminar Award, an NSF CAREER Award, and a Sloan Research Fellowship.
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 underserved in mathematical fields; listening to needs of various communities and responding effectively to those needs; reflecting on personal actions and reactions; and enacting principles of equity in my day-to-day praxis.
Some lecture notes
- Higher algebra in geometry. Lectures at RIKEN in Wakou-shi, Japan. Summer 2023.
- Spectra, operads, and infinity-categories (draft). Lectures at Floer Homotopy Theory summer school at University of British Columbia. Summer 2022.
- Factorization Homology, Infinity-Categories, and Topological Field Theories. Lectures at the conference Geometric Representation Theory and Low-Dimensional Topology, held at the ICMS in Edinburgh. Summer 2019.
Papers and pre-prints
- Spaces over BO are thickened manifolds. Submitted. arXiv:2307.09647
- The infinity-category of stabilized Liouville sectors, with Oleg Lazarev and Zachary Sylvan. Submitted. arXiv:2110.11754
- Localization and flexibilization in symplectic geometry, with Oleg Lazarev and Zachary Sylvan. Submitted. arXiv:2109.06069
- Smooth constructions of homotopy-coherent actions, with Yong-Geun Oh. Algebraic & Geometric Topology 22 (2022) 1177–1216. doi: 10.2140/agt.2022.22.1177. arXiv:2003.06033
- Holomorphic curves and continuation maps in Liouville bundles, with Yong-Geun Oh. Submitted. arXiv:2003.04977
- Continuous and coherent actions on wrapped Fukaya categories, with Yong-Geun Oh. Submitted. arXiv:1911.00349
- Cyclic structures and broken cycles. Submitted. arXiv:1907.03301
- Lectures on Factorization Homology, Infinity-Categories, and Topological Field Theories, with A. Amabel, A. Kalmykov, and L. Müller. SpringerBriefs in Mathematical Physics, Volume 39, 2021. ISBN 978-3-030-61162-0. doi:10.1007/978-3-030-61163-7. arXiv:1907.00066
- Generation for Lagrangian cobordisms in Weinstein manifolds. Submitted. arXiv:1810.10605
- Associative algebras and broken lines, with Jacob Lurie. arXiv:1805.09587
- Surgery induces exact sequences in Lagrangian cobordisms. Submitted. arXiv:1805.07424
- Stellar Stratifications on Classifying Spaces, with Dai Tamaki. In: Singh M., Song Y., Wu J. (eds) Algebraic Topology and Related Topics. Trends in Mathematics. Birkhauser, Singapore. doi: 10.1007/978-981-13-5742-8_15. arXiv:1804.11274
- Odd sphere bundles, symplectic manifolds, and their intersection theory, with Li-Sheng Tseng. Cambridge Journal of Mathematics (2018), 213--266. doi: 10.4310/CJM.2018.v6.n3.a1. arXiv:1702.03423
- Bridgeland stability, 2-Segal spaces, and the Ran space of the line. In Manifolds and K-Theory, Contemporary Mathematics (2017), 209--235. doi: 10.1090/conm/682.
- The Fukaya category pairs with Lagrangian cobordisms exactly. arXiv:1609.08400
- The Fukaya category pairs with Lagrangian cobordisms. Submitted. arXiv:1607.04976
- Functors (between oo-categories) that aren't strictly unital. Journal of Homotopy and Related Structures (2018) 13: 273--286. doi: 10.1007/s40062-017-0182-2. arXiv:1606.05669
- Factorization homology in 3-dimensional topology, with Nikita Markarian. In Mathematical Aspects of Quantum Field Theories, Springer 2015, pp. 222-231. doi: 10.1007/978-3-319-09949-1_7.
- Factorization homology of stratified spaces, with David Ayala and John Francis. Selecta Mathematica New Series 23 (2017), no. 1, 293--362. doi: 10.1007/s00029-016-0242-1. arXiv:1409.0848
- Local structures on stratified spaces, with David Ayala and John Francis. Advances in Mathematics 307 (2017), 903--1028. doi: 10.1016/j.aim.2016.11.032. arxiv 1409.0501
- In simply-connected cotangent bundles, exact Lagrangian cobordisms are h-cobordisms. Advances in Geometry vol. 21, no. 1, 2021, pp. 1-4. doi:10.1515/advgeom-2019-0027. arXiv:1404.6273.
- A stable infinity-category of Lagrangian cobordisms, with David Nadler. Advances in Mathematics 366 (2020). doi: 10.1016/j.aim.2020.107026. arXiv:1109.4835.
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 activities
- I have coached high school Mock Trial teams on and off throughout the years.
- I co-organized the first two iterations of the South Central Topology Conference.
- In 2020 and 2022, I led summer math research projects for high school students.
- From 2015 to 2018, I served as a faculty advisor for Harvard's Gender Inclusivity in Mathematics.
- In summer 2018, I organized a weekly seminar for undergraduates to share their summer research projects.
- 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.
- I coached Northwestern University's undergraduate Mock Trial team back when I was in Chicago.
- 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.