Yilong Zhang | Department of Mathematics

Brief Introduction

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

My research is in algebraic geometry. In particular, I'm interested in Abel-Jacobi map and various Hodge theory related problems. I'm also interested in geometry of cubic hypersurfaces and thinking of relevant moduli problems. Here is my research statement.

Here is my CV.

Research

Cohomology of Hypersurfaces in P^4 and Tube Mapping, 17 pages, available upon request

Topological Abel-Jacobi map and Mixed Hodge Structures, to appear in Math. Res. Lett. arXiv:2109.05717

Hilbert Scheme of Skew Lines on Cubic Threefolds and Locus of Primitive Vanishing Cycles, arXiv:2010.11622

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

Seminar at Purdue

Here is the Purdue Algebraic Geometry seminar

Upcoming travels

Apr 28 - 30, AGNES at Stony Brook

June 19 - 30, Thematic Program on Rationality and Hyperbolicity at University of Notre Dame

Teaching

Spring 2023: MA 266 Ordinary Differential Equation

Outreach

Summer 2023, I plan to lead a REU project on cubic surfaces. Detail is here.

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 23, 2023.