Yilong Zhang | Department of Mathematics

Brief Introduction

I am a Golomb Visiting Assistant Professor of Mathematics at Purdue University. My mentor is Donu Arapura. I graduated from The Ohio State University in Spring 2022. My advisor was Herb Clemens.

Starting from Fall 2025, I will join University of Georgia as a Limited Term Assistant Professor.

My research is in algebraic geometry. In particular, I'm interested in Hodge theory, cubic hypersurfaces, and topology of algebraic varieties.

Here is my CV.

Research

Embedded Tubes in Hypersurfaces in P^4, with Siyang Liu, preprint available soon

Hilbert Scheme of a Pair of Skew Lines on a Cubic Hypersurface, arXiv

Elliptic-Elliptic Surfaces and Hesse Pencil, with François Greer, arXiv

Degeneration of Dual Vareties of Hypersurfaces, arXiv

Monodromy of Primitive Vanishing Cycles for Hypersurfaces in P^4, arXiv

Extension of the Topological Abel-Jacobi Map for Cubic Threefolds, arXiv

Hilbert Scheme of a pair of Skew Lines on Cubic Threefolds, to appear in Journal of Pure and Applied Algebra journal arXiv

Topological Abel-Jacobi map and Mixed Hodge Structures, Math. Res. Lett. 31, No. 4, 1215-1247 (2024) journal arXiv

Here is my thesis (modified from the original version, with errors fixed).

Seminar at Purdue

I am organizing Purdue Algebraic Geometry seminar with Takumi Murayama and Deepam Patel.

Upcoming travels/talks

Apr 23-25, University of Arkansas, algebra seminar

Apr 26-27, Purdue University, Indianapolis campus Condensed Mathematics Workshop

May 27-31, Ohio State University, Arithematics, K theory and algebraic cycles

June 9-20, Notre Dame University, Thematic Program in Discrete Groups in Topology and Algebraic Geometry

July 14-Aug 1, Colorado State University, Summer conference on algebraic geometry

Teaching

Spring 2025: MA 265 Linear Algebra

Mentoring

Summer 2024, organized a problem solving seminar. Here is the problem list.

Summer 2023, mentored two undergraduate students in REU program. It's about lines on cubic surfaces.

Summer 2023, mentored a graduate student in a reading course. The topic is on Riemann Surfaces.

Spring 2022, mentored an undergraduate student exploring a "figure-eight" phenomenon in astronomy. Here is my student's poster.

Spring 2022, mentored an undergraduate student on Stereographic Projects and Mobius Transformations

Notes

May 2021, Rationality and Stable Rationality

May 2020, O-Minimal Chow's Theorem

Dec 2019, Brieskorn's Theorem on Fundamental Groups

Last updated on April 18, 2025.