Jiahao Hu

胡(hú) 家( jiā) 昊( hào)

I am a Ph.D. candidate in math at Stony Brook University. I am interested in algebraic topology and its applications to differential and algebraic geometry. My advisor is Dennis Sullivan.

Currently I am on job market. Here is my CV.

  • Office: 2107, Math Department, Stony Brook University
  • Email: jiahao.hu@stonybrook.edu

    • Publications

  • Almost complex manifolds with total Betti number three (2023, Journal of Topology and Analysis) arXiv version
  • (with Shamuel Aueyung and Jin-Cheng Guu) On the algebra generated by mubar, delbar, del, mu (2023, Complex Manifolds)
  • (with Aleksandar Milivojević) Infinite symmetric products of rational algebras and spaces (2021, Comptes Rendus Mathématique)

    • Preprints

  • Characterization of differential K-theory by hexagon diagram (Submitted to Journal of Topology)
  • Invariants of Real Vector Bundles (Ph.D. thesis)

    • Notes

  • A non-spin^c open 5-manifold whose compact submanifolds are all spin^c This short note records an example provided by Dennis Sullivan. Note that all orientable 4-manifolds, compact or not, are spin^c.

  • 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. I plan to improve this note in near future.

  • 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 note attempting to interpret Jack Morava's point that "the dual Steenrod algebra is the automorphism group of the additive formal 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.