David Jongwon Lee

Department of Mathematics
Northwestern University
Email: davidlee@northwestern.edu

I am a Boas assistant professor at Northwestern University. I am interested in homotopy theory. Previously, I was a Phd student at MIT, advised by Jeremy Hahn. Here is my CV.

Papers

  1. The monochromatic Hahn-Wilson conjecture with Piotr Pstrągowski (2024)

    We prove the K(n)-local analogue of the Hahn-Wilson conjecture on fp-spectra, which states that the truncated Brown-Peterson spectra generate the category of fp-spectra as a thick subcategory. As a corollary, we deduce the original conjecture at height 1. Along the way, we prove the existence of K(n)-local finite complexes with particularly regular rings of homotopy groups.

  2. Uniqueness of p-local truncated Brown-Peterson spectra, to appear in Mathematische Zeitscrhift

    When p is an odd prime, we prove that the F_p-cohomology of BP⟨n⟩ as a module over the Steenrod algebra determines the p-local spectrum BP⟨n⟩. In particular, we prove that the p-local spectrum BP⟨n⟩ only depends on its p-completion BP⟨n⟩^p. As a corollary, this proves that the p-local homotopy type of BP⟨n⟩ does not depend on the ideal by which we take the quotient of BP. In the course of the argument, we show that there is a vanishing line for odd degree classes in the Adams spectral sequence for endomorphisms of BP⟨n⟩. We also prove that there are enough endomorphisms of BP⟨n⟩ in a suitable sense. When p=2, we obtain the results for n≤3.

  3. Topological Hochschild homology of the image of j with Ishan Levy, Advances in Mathematics(arxiv)

    We compute the mod (p,v_1) and mod (2,eta,v_1) THH of many variants of the image of j spectrum. In particular, we do this for j_zeta, whose TC is closely related to the K-theory of the K(1)-local sphere. For p>2, we also prove the Segal conjecture for j_zeta, and we compute the K-theory of the K(1)-local sphere in degress ≤4p-6.

  4. Integral topological Hochschild homology of connective complex K-theory, to appear in Compositio Mathematica

    We compute the homotopy groups of THH(ku) using the descent spectral sequence for the map THH(ku) to THH(ku/MU), which is the motivic spectral sequence for THH(ku) in the sense of Hahn-Raksit-Wilson. We reduce the computation of homotopy groups to the algebra of the universal formal group law, providing a systematic way to compute THH of quotients of MU. We compute the E2-page of the motivic spectral sequence computing THH(ku), and we show that it degenerates at the E2-page.

Talks

Teaching