Research and Publications

Projects

Publications

• The structure of the \(v_2\)-local algebraic tmf resolution
  Joint with Mark Behrens and Prasit Bhattacharya
  Accepted. To appear in Mathematische Zeitschrift

• Algebraic \(K\)-theory of Elliptic Cohomology
  With Gabe Angelini-Knoll, Christian Ausoni, Eva Höning, and John Rognes
  Geometry & Topology 29 (2025) 619–686

• Exotic \(K(h)\)-local Picard groups when \(2p-1=h^2\) and the Vanishing Conjecture
  Joint with Ningchuan Zhang
  Accepted

• The Motivic Lambda algebra
  Joint with J.D. Quigley and W. Balderrama
  Geometry & Topology 29 (2025) 1489–1570

• Topological Hochschild Homology of the second truncated Brown-Peterson spectrum, part 1
  Joint with Gabe Angelini-Knoll and Eva Höning Accepted. Appeared in Algebraic and Geometric Topology

• Algebraic Slice Spectral Sequences
  Joint with H. Kong and J.D. Quigley
  Accepted. Appeared in Documenta Mathematica

• The telescope conjecture at height 2 and the \(tmf\) resolution
  Joint with Behrens, Beaudry, Bhattacharya, and Xu
  Journal of Topology, 14(4), 1243–1320. (2021, December).

• On the \(K(1)\)-local homotopy of \(tmf \wedge tmf\)
  Joint with Paul VanKoughnett
  J. Homotopy Relat. Struct. 16, 367–426 (2021)

• \(kq\)-resolutions I
  Joint with JD Quigley
  Accepted. To appear in Trans. AMS

• The Adams spectral sequence for 3-local \(tmf\)
  J. Homotopy Relat. Struct. 16, 1–40 (2021)

• The \(BP\langle2\rangle\)-cooperations algebra at odd primes
  JPAA 224 (May 2020)

• On \(BP\langle2\rangle\)-cooperations
  Algebraic & Geometric Topology 19 (2019) 807-862

• On the \(E_2\)-term of the \(bo\)-Adams spectral sequence
  Joint with Mark Behrens, Agnes Beaudry, Prasit Bhattacharya, and Zhouli Xu
  J. Topology 13 (2020) 356-415

• A new basis for complex \(K\)-theory cooperations algebra
  Topology and its Applications 234 (2018) 7-25