Research - the questions that guide us 

I study the behavior of families of algebro-geometric objects and the structure of the spaces that parametrize them. Within this context, my work has three primary focuses: 

Next, I list my work, accepted articles (A) and submitted preprints (P), in such areas.

Moduli spaces of points and lines in affine and projective space

A21) Polymatroids and moduli of points in flags with Javier González-Anaya, José Luis González. To appear at Forum of Mathematics Sigma . 

A20) Higher-dimensional Losev-Manin spaces and their geometry with Javier González-Anaya, José Luis González, and Evangelos Routis. IMRN, International Mathematics Research Notices, Volume 2025, Issue 23, December 2025, rnaf347, https://doi.org/10.1093/imrn/rnaf347

 A19) An explicit wall crossing for the moduli space of hyperplane arrangements with Luca Schaffler (2025). Journal of the London Mathematical Society, 111(6), e70196.

A18) Eigenperiods and the moduli of points in the line with Haohua Deng. Nagoya Mathematical Journal (2025:1-24. doi:10.1017/nmj.2025.7)

A17) Wonderful compactifications of the moduli space of points (joint with E. Routis). European Journal of Mathematics, 3(3), 520-564. 

A16) Variation of stability for moduli spaces of unordered points in the plane (with B. Schmidt), Transactions of the American Mathematical Society, (2022)

A15) The Fulton-MacPherson compactification is not a Mori dream space (with José Luis González and Evangelos Routis), Math Z, 2022.

A14) Modular interpretation of a non-reductive Chow quotient (with N. Giansiracusa).  Proceedings of the Edinburgh Mathematical Society.

A13) A slice of the moduli space of lines arrangements (joint with K. Ascher)  Algebra and Number theory.

Explicit Descriptions of Algebraic Varieties

A12) Unimodal singularities and boundary divisors in the KSBA moduli of a class of Horikawa surfaces (with L. Schaffler, G. Pearlstein, Z. Zhang). Math Nachrichten, (2023)

A11) Algebraic and analytic compactifications of moduli spaces (with M. Kerr). Notices of the American Mathematical Society 69.9 (2022).

A10)  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.

A9) 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.

A8) Moduli of cubic surfaces and their anticanonical divisors  (with J. Martinez-Garcia) Revista Matematica Complutense (RMC) 32.3 (2019): 853-873

A7) Families of elliptic curves in Projective space and Bridgeland Stability  (with C. Lozano-Huerta, and B. Schmidt), Michigan Mathematical Journal.

A6) On the GIT quotient of quintic surfaces. Transactions of the American Mathematical Society. 371 (2019), 4251-4275.

A5)  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.

Computational aspects 

A5) Agentic Lean Auformalization (ALA) v1: An LLM collaborative approach to autoformalization in LEAN with Maziar_Raissi, Ke Zhang, and Sudhir Murthy.  NeurIPS 2025 LLM Evaluation workshop poster.

A4) Enumeration of max-pooling responses with generalized permutohedra . Laura Escobar, Javier González-Anaya, José L. González, Guido Montúfar, Alejandro H. Morales. Annals of Combinatorics, 2025 https://doi.org/10.1007/s00026-025-00782-x 

A3) Quivers and moduli of their thin sincere representations in Macaulay2   with Mary Barker, JSAG, Vol. 15 (2025), 93–103, DOI: 10.2140/jsag.2025.15.93. See also the Macaulay2 package called ThinSincereQuivers 

A2) Computation of GIT quotients of semisimple groups with J. Martinez-Garcia, H-B. Moon, and D. Swinarski. Mathematics of Computation, 2026,  https://doi.org/10.1090/mcom/4152  

A1) VGIT for pairs, a computational approach (with J. Martinez-Garcia). Proceedings of the American Mathematical Society, 146(6), 2395-2408.  See also the Python package called Variations of GIT quotients.