Yilong Zhang (張義龍)

Email: Yilong.Zhang@uga.edu
Office: Mathematical Sciences Bldg 426

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, in preparation
  • Algebraicity of Hodge classes on some Generalized Prym Varieties, with Deepam Patel, arXiv (2025)
  • Hilbert Scheme of a Pair of Skew Lines on Cubic Hypersurfaces, arXiv (2025)
  • Elliptic-Elliptic Surfaces and Hesse Pencil, with François Greer, arXiv (2024)
  • Degeneration of Dual Vareties of Hypersurfaces, arXiv (2024)
  • Monodromy of Primitive Vanishing Cycles for Hypersurfaces in P^4, arXiv (2024)
  • Extension of the Topological Abel-Jacobi Map for Cubic Threefolds, arXiv (2023)
  • Hilbert Scheme of a pair of Skew Lines on Cubic Threefolds, J. Pure Appl. Algebra 229 (2025), no. 6 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

  • July 14-25, 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 July 1, 2025.