# Jiahao Hu

## 胡 家
昊

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.