Contact: nmas!uda0!at!!gm!ail!!!do!tc!om (remove exclamation marks)

I graduated from Johns Hopkins in August 2024. I'll be a postdoc at Hamburg starting in October 2024. I am interested in homotopy theory, topology, category theory, and related topics. Here is my CV (last updated: September 2024)

- The algebra of categorical spectra: Categorical spectra are $(\infty, \infty)$-categorical generalization of spectra (as in homotopy theory). We introduce the (Gray-type) tensor product of categorical spectra and study the notion of stability from the viewpoint of absolute (co)limits. As an application, we derive the cobordism hypothesis with singularities from the plain version of the cobordism hypothesis. While this is the version I submitted for the thesis defense, I hope to improve it slightly before uploading to it arXiv, etc.

- Global critical chart for local Calabi-Yau threefolds [arXiv]: For an $n$-dimensional smooth variety $Y$, we describe the derived category of the total space of a $\omega_Y$-torsor as a certain deformed (n+1)-Calabi--Yau completion of the derived category of $Y$. The result is used by Tasuki Kinjo and Naoki Koseki to prove the cohomological chi-independence conjecture for Gopakumar--Vafa invariants. Joint work with Tasuki Kinjo.
- The Diagonal of the Associahedra: A new geometric/combinatorial way to understand and construct Alexander-Whitney type maps of polytopes applied to associahedra. Joint work with Hugh Thomas, Andy Tonks and Bruno Vallette.

- Tensor product of categorical spectra, 高知ホモトピー論談話会 (Kochi homotopy theory workshop), December 28, 2022 [notes]
- The diagonal of the associahedra, UPenn Deformation Theory Seminar, November 1, 2021 [notes]
- The slides for the Oral exam, March 2021.

- Here are the recordings for Ambidexterity learning seminar fall 2023 (JHU account required).
- I co-organize JHU topology seminar since fall 2022.
- I organized prismatic cohomology seminar spring 2023 with David Gepner and Milton Lin.

- eKan seminar notes on Thomason's "Algebraic K-theory and etale cohomology."
- notes for JHU Number theory learning seminar on Katz's "Serre-Tate local moduli."
- notes for JHU Number theory learning seminar on Deligne--Illusie's "Relèvements modulo p^2 et decomposition du complexe de de Rham."
- Geometric Morphism: Handwritten notes for JHU category seminar on topos theory, roughly following chapter 7 of "Sheaves in Geometry and Logic" by Mac Lane and Moerdijk.
- Seminar Notes on infinity-operads as analytic monads, liveTeXed by Emily Riehl. I gave one of the talks, following section 4 of the paper, Initial Algebras and Free Monads.
- Bar-cobar and Koszul duality for algebraic operads: Notes for JHU category seminar, may contain lots of typos. handwritten version with more pictures
- notes on past quals algebra problems from when I lead review sessions for first-year graduate students (may contain wrong solutions. large file).