Papers and preprints

• Rigid Algebras and Cospans - preprint.

The following papers, in model theory, were the two chapters of my Master's thesis:

• On Algebraically Closed Fields with a Distinguished Subfield - with Christian d'Elbée and Itay Kaplan. Israel Journal of Mathematics (2024).
• Existentially Closed Models of Fields with a Distinguished Submodule. - with Christian d'Elbée and Itay Kaplan. Journal of Symbolic Logic (to appear).

Teaching

• Algebraic topology fall 2024

Talks

• The multiplicative structure of higher bordism categories - Rehovot 2025, YTM Stockholm 2025 (slides)

  A talk about a work in progress joint with Lior Yanovski and Shai Keidar. I present higher bordism categories, their multiplicative structure defined via the Grey tensor product, and connections with the cobordism hypothesis. A recording is available here.

• Rigid algebras in (∞,2)-categories - Chicago 2025

  A longer talk about rigid algberas in a symmetric monoidal (∞,2)-category.

• Rigid algebras are right adjoint to cospans (slides) - YTM Münster 2024

  A talk about an upcoming paper on rigid algebras and cospans. I define the notion of a rigid algebras and indicate some proofs, including the adjunction with cospans.

Seminar notes

• Hirzebuch's signature theorem - Jerusalem 2024

  This talk was part of a seminar on orientations. In this talk we define the signature of a manifold, prove that it is a genus, and prove that it equal to the L-polynomial in Pontrjagin classes.

• Cyclotomic redshift - Oberwolfach 2024

  This talk was prepared for the Oberwolfach Arbeitsgemeinschaft about the disproof of the telescope conjecture. In this talk we proved cyclotomic redshift, namely that T(n+1)-localized K-theory sends height n cyclotomic extensions to height n+1 cyclotomic extension.

• Proving the chromatic nullstellensatz - Jerusalem 2024

  This talk was prepared for the Kazhdan seminar on the chromatic nullstellensatz. In this talk we gathered all the results proven throughout the semester to finalize the proof of the chromatic nullstellensatz.

• Cyclotomic and polygonic spectra - Jerusalem 2024

  This talk was prepared for a seminar on the disproof of the telescope conjecture. In this talk we define cyclotomic and polygonic spectra, and using them we define THH, TC and TR. We also prove some adjunctions.

Organization

• Homotopy Theory: Revisiting Localizations and Beyond - Mainz 2024

  Yonatan Harpaz, Shai Keidar, Tomer Schlank, Lior Yanovski and myself organized this conference in June 2024.