# Jiahao Hu

## 胡 家
昊

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.