Jiahao Hu

胡(hú) 家( jiā) 昊( hào)

I am a PhD candidate in math arrived in 2017 at Stony Brook University. I am interested in topology, especially of manifolds and algebraic varieties. My advisor is Dennis Sullivan.

  • Office: 3105, Math Department, Stony Brook University
  • Email: jiahao.hu@stonybrook.edu

    • Research

  • Almost complex manifolds with total Betti number three (accepted to Journal of Topology and Analysis)
  • (with A. Milivojević) Infinite symmetric products of rational algebras and spaces (2021, Comptes Rendus Mathématique)
  • Quaternionic Clifford modules, spin^h manifolds and symplectic K-theory (in preparation)
  • Characterization of differential K-theory by hexagon diagram (arXiv preprint)
  • (with Shamuel Aueyung and Jin-Cheng Guu) On algebra generated by mubar, delbar, del, mu (arXiv preprint)

    • Notes

  • Topological resolution of singularities for talks I gave at City University of New York Graduate Center Topology, Geometry and Physics seminar in November 2019, at University of Science and Technology of China in December 2019, and at University of Pennsylvania deformation theory seminar in February 2020.

  • Elliptic cohomology and elliptic genera for a series of talks I gave at student topology seminar in spring 2020, Stony Brook University.
  • Steenrod and Adams operations from easy algebra This is a detailed note attempting to interpret Jack Morava's point that "the dual Steenrod algebra is the automorphism group of the additive group". In particular, we solve the equations f(x+y)=f(x)+f(y) and f(x+y+xy)=f(x)+f(y)+f(x)f(y) by formal power series with coefficients in the field of p elements, and then relate the space of solutions to Steenrod and Adams operations respectively.
  • Quaternionic Clifford modules, spin^h manifolds and symplectic K-theory for a talk I gave at Topology/Geometry Zoom seminar at University of Oregon in March 2022.

  • The four components of d on almost complex manifolds for a talk I gave at City University of New York Graduate Center Differential Geometry, Topology, and special structures Seminar in September 2022. This is a supplementary note on the generalized Frölicher spectral sequence of Cirici and Wilson for almost complex manifolds.