# Welcome to my homepage

## Hailun Zheng (郑海伦)

Phone: +1 8328595243

Email: zhengh@uhd.edu

Address:

Department of Mathematics and Statistics

University of Houston-Downtown

One Main Street S749

Houston, TX 77002

I received my Ph.D from University of Washington in 2017, under the supervision of Isabella Novik. My research interests lie in geometric and topological combinatorics.

My non-mathematical hobbies include hiking and photographing. I finished a martial arts novel several years ago. I am interested in Chinese paintings and manga arts.

## Employment and Education

2022.8-present, University of Houston-Downtown, assistant professor

2020.8-2022.7, University of Copenhagen, postdoc

Mentor: Karim Adiprasito

2018.1-2020.6, University of Michigan, postdoc

Mentor: Alexander Barvinok

2017.8-2017.12, MSRI, Geometric and Topological Combinatorics Program, postdoc

Mentor: Eran Nevo

2012.9-2017.8, University of Washington, Ph.D. student

Thesis Advisor: Isabella Novik

2008.9-2012.6, Fudan University, undergraduate student

Thesis Advisor: Meng Chen (陈猛)

## Publications

Minimal balanced triangulations of sphere bundles over the circle. SIAM J. Discrete Math. 30(2016), 1259-1268.[pdf]

The flag upper bound theorem for 3- and 5-manifolds. Israel J. Math., 222(2017), 401-419. [pdf] (The extended abstract appears in DMCTS Proceedings of FPSAC 16.

A characterization of homology manifolds with $g_2\leq 2$. J. Combin. Theory Ser. A, 153(2018), 31-45. [pdf]

A lower bound theorem for centrally symmetric simplicial polytopes (with Steven Klee, Eran Nevo and Isabella Novik), Discrete Comput. Geom., 61(2019), 541-561. [pdf]

Face enumeration on flag complexes and flag spheres. Algebraic and geometric combinatorics on lattice polytopes (T. Hibi and A. Tsuchiya, eds.), World Scientific Publishing Co. Pte. Ltd, Singapore, 2019, 435-449. [pdf]

A new valuation on polyhedral cones (with Michal Zydor), Algebra i Analiz, 32(2020), 1–11. [pdf]

Ear decomposition and balanced neighborly simplicial manifolds. Electron. J. Combin., 27(2020), P1.10, 2020. [pdf]

Centrally symmetric and balanced triangulations of $S^2\times S^{d-3}$ with few vertices (with Alexander Wang). European J. Combin., 85(2020), 103043. The extended abstract with title ``Triangulations of the product of spheres with few vertices" appears in DMCTS Proceedings of FPSAC 19. [pdf]

The upper bound theorem for flag homology 5-manifolds. J. Combin. Theory Ser. A, 175(2020), 105259. [pdf]

Highly neighborly centrally symmetric spheres (with Isabella Novik). Adv. Math., 370(2020), 107238. [pdf]

The rigidity of the graphs of homology spheres minus one edge. Discrete Mathematics, 343(2020), 112135. [pdf]

A new family of triangulations of RP^d (with Lorenzo Venturello), Combinatorica, 41(2020), 127-146. [pdf]

Minimal flag triangulations of lower-dimensional manifolds (with Christin Bibby, Andrew Odesky, Mengmeng Wang, Shuyang Wang and Ziyi Zhang), Involve, 13(2020), 683-703. [pdf]

The stresses on centrally symmetric complexes and the lower bound theorems (with Isabella Novik), Algebraic Combinatorics, 4(2021), 541-549. [pdf]

Many neighborly spheres (with Isabella Novik). To appear in Mathematische Annalen. [pdf]

New families of highly neighborly centrally symmetric spheres (with Isabella Novik). To appear in Trans. Amer. Math. Soc. [pdf]

Reconstructing simplicial polytopes from their graphs and affine 2-stresses (with Isabella Novik), to appear in Israel Journal of Mathematics. [pdf]

Neighborly spheres and transversal numbers (with Isabella Novik). For the AMS volume on Open Problems in Algebraic Combinatorics, to accompany the 2022 conference held at UMN. [pdf]

Affine stresses: the partition of unity and Kalai’s reconstruction conjectures (with Isabella Novik). To appear in Discrete Comput. Geom. [pdf]

## Preprints

The merging operation and (d-i)-simplicial i-simple d-polytopes (with Isabella Novik). Submitted. [pdf]

Affine stresses, inverse systems and reconstruction problems (with Satoshi Murai and Isabella Novik). [pdf]

## Grants

NSF Grant DMS-2246739, Geometric combinatorics on polytopes and spheres, 2023-2026.

## Teaching

### Instructor

University of Houston-Downtown

Math 1301 College Algebra Spring 2023 and Autumn 2022

Math 3309 Number Theory Autumn 2022

Math 2307 Linear Algebra Autumn 2023

Math 2309 Discrete Mathematics Autumn 2023

University of Michigan

Math 214 Applied Linear Algebra. Winter and Autumn 2019

Math 115 Calculus I. Autumn 2018

Math 590 Topology. Winter 2018

Math 567 Coding theory. Winter 2020

University of Washington

Math 324 Multi-variable Calculus. Autumn 2016, Spring 2015

Math 309 Linear Analysis. Autumn 2015

Math 307 Differential Equations Spring 2017, Winter 2015

Math 124 Calculus I. Summer 2014

### Teaching Assistant

University of Copenhagen (graduate level)

Commutative Algebra Block 3, 2020-21

Invitations to Combinatorics Block 2, 2021-22

Unversity of Washington

Math 126 Calculus III. Spring 2013, Autumn 2014

Math 125 Calculus II. Winter 2013

Math 124 Calculus I. Autumn 2012

## Mentoring

### Summer REU at the University of Michigan, 2018

Project: The triangulation of the product of spheres

Students: Alexander Wang [website], Jonathon Jacobs

### Lab of Geometry at the University of Michigan, 2019

Project: Lower dimensional flag triangulated manifolds [description]

Co-mentoring with Christin Bibby [website] and Andrew Odesky.

### Senior project, University of Houston-Downtown, 2023

Project: Persistent topology and application in data science

Student: Ross Mccoy