Welcome

Hi! My name is Patricio Gallardo.

I am an assistant professor at the University of California, Riverside. My mathematical interests include algebraic geometry, singularity theory, and Hodge theory. However, I enjoy more interdisciplinary work, as well. My favorite writer is J. L. Borges, and my hobbies include dancing salsa. You can write to me to pgallard at ucr.edu.,

In Preparation

  • Moduli space of points in the projective plane (with B. Schmidt)

  • On certain families of vector-borne disease models with an arbitrary number of infected components (with J. Aguilar)

  • Moduli of Horikawa surfaces (with L. Schaffler, Z. Zhang, and G. Pearlstein).

Academic work

  1. Algebraic and analytic compactifications of moduli spaces (with M. Kerr). This note is aimed to graduate students.

  2. Quivers and moduli of their thin sincere representations in Macaulay2 (with M. Barker) Submitted.

  3. The Fulton-MacPherson compactification is not a Mori dream space (with José Luis González, Evangelos Routis) Submitted.

  4. Geometric interpretation of toroidal compactifications of moduli of points in the line and cubic surfaces (with M. Kerr and L. Schaffler) Advances in Mathematics, 381, 2021.

  5. Applications of the moduli continuity method to log K-stable pairs (with J. Martinez-Garcia and C. Spotti)Journal of the London Mathematical Society 103.2 (2021): 729-759.

  6. Moduli of cubic surfaces and their anticanonical divisors (with J. Martinez-Garcia) Revista Matematica Complutense (RMC) 32.3 (2019): 853-873

  7. Modular interpretation of a non-reductive Chow quotient (with N. Giansiracusa). Proceedings of the Edinburgh Mathematical Society.

  8. Wonderful compactifications of the moduli space of points (joint with E. Routis). European Journal of Mathematics, 3(3), 520-564.

  9. VGIT for pairs, a computational approach (with J. Martinez-Garcia). Proceeding of the AMS.

  10. Families of elliptic curves in Projective space and Bridgeland Stability (with C. Lozano-Huerta, and B. Schmidt) Michigan Mathematical Journal.

  11. On the GIT quotient of quintic surfaces. Transactions of the American Mathematical Society. 371 (2019), 4251-4275.

  12. A slice of the moduli space of lines arrangements (joint with K. Ascher) Algebra and Number theory.

  13. Compactifications of the moduli space of plane quartics and two lines (with Z. Zhang and J. Martinez-Garcia) European Journal of Mathematics, 2018, Volume 4, Issue 3.

  14. On the neighborliness of thin-sincere representations of quivers (with D. Mckenzie)