# Research

I am an algebraic geometer with interests in moduli spaces, K-stability and birational geometry.

I work on these specific problems:

Compactification of moduli spaces and geometric invariant theory;

Computational algebraic geometry;

Classification of Fano varieties.

# Publications

Publications & Preprints

"On products of K-moduli spaces", arXiv:2403.04544.

"K-moduli of log del Pezzo pairs and Variation of GIT", (with Jesus Martinez-Garcia, and Junyan Zhao). arXiv:2406.20008

"GIT stability of divisors in products of projective spaces", (with Ioannis Karagiorgis and Theresa A. Ortscheidt) arXiv:2312.02842. *

"One dimensional components in the K-moduli of Fano 3-folds”, (with Hamid Abban, Ivan Cheltsov, Elena Denisova, Erroxe Etxabarri-Alberdi, Anne-Sophie Kaloghiros, Dongchen Jiao, Jesus Martinez-Garcia) Journal of Algebraic Geometry (to appear) arXiv: 2309.12518.

"On divisorial stability of finite covers”, (with Ruadhaí Dervan). Forum Math., Sigma 12 (2024): e65. arXiv: 2306.07151.

"K-moduli of log Fano complete intersections”, arXiv: 2212.09332.

"GIT of complete intersections and log canonical thresholds", arXiv: 2212.09332.

Software

" GIT stability of divisors in products of projective spaces" (with Ioannis Karagiorgis and Theresa A. Ortscheidt). Package. SageMath. 10.17863/CAM.104485, 2023 *

"Variations of GIT quotients for complete intersections". Package. Python/ SageMath. 10.5526/ERDR-00000155, 2022

"Segre Symbols Calculator package". Package. Python/ SageMath. 10.5526/ERDR-00000157, 2022

*part of the supervision of the summer research project titled "Computational methods in algebraic geometry" .

# Talks/ Posters

"K-moduli of log del Pezzo pairs and variations of GIT", UCLA Birational Geometry Seminar (July 18, 2024).

"Products of K-moduli spaces", University of Cambridge, Isaac Newton Institute (May 24, 2024).

"On divisorial stability of finite covers", University of Gothenburg Algebraic Geometry Seminar, University of Gothenburg, (December 14, 2023).

"On divisorial stability of finite covers", University of Nottingham Algebraic Geometry Seminar, University of Nottingham, (September 21, 21 2023).

"K-moduli of log Fano complete intersections”, Aarhus-Gothenburg Complex Geometry Seminar, Aarhus University, (May 8,8 2023).

"K-moduli of log Fano complete intersections”, Algebra and Number theory seminar, University of Glasgow, (February 22, 2023).

"Wall crossing in the K-moduli of log Fano complete intersections”, MPS conference in Higher Dimensional Geometry, Stony Brook, (August 22-26, 2022). Poster Session.

"K-moduli of log Fano complete intersections”, Cambridge Complex Geometry Afternoon, University of Cambridge, (August 11, 2022).

"K-moduli of log Fano complete intersections”, British Early Career Mathematician's Colloquium, University of Birmingham, (July 21-22, 2022).

"K-moduli of log Fano complete intersections”, Géométrie Algébrique en Liberté (GAeL) XXIX, Universite Paris-Saclay, (May 23-27, 2022).

"K-moduli of log Fano complete intersections”, Zoom Algebraic Geometry Seminar (ZAG), (April 26th 2022).

"K-moduli of log Fano complete intersections”, MPS Conference on Higher Dimensional Geometry 2022, Simons Foundation, New York, (February 23-25, 2022). Poster Session.

"GIT and K-stability for Fano varieties", Mathematics Essex Seminar Series (MESS) (December 16th 2021).

"K-moduli of log Fano complete intersections”, Edge Days Workshop "Explicit K-stability and moduli problems", University of Edinburgh (30 November-3 December 2021).

"K-moduli of log Fano complete intersections”, UC Riverside Algebraic Geometry Seminar (November 23th 2021).

"Explicit description of the moduli compactification of Fano threefold 2-25", London Mathematical Society Graduate Student Meeting Winter 2021 (November 8th 2021).

"K-moduli of log Fano complete intersection pairs”, Loughborough Geometry and Mathematical Physics Seminar (October 27th 2021).

"K-moduli of log Fano complete intersection pairs”, Cambridge Algebraic Geometry Seminar (October 20th 2021).

"Computational VGIT for Complete Intersections and a Hyperplane", Algebraic Geometry from an Algorithmic point of view, 26th Conference on Applications of Computer Algebra, (July 23-27, 2021).

"K-moduli of log Fano complete intersection pairs”, Géométrie Algébrique en Liberté (GAeL) XXVIII (July 5-9, 2021), Poster Session.

"Variational GIT for Complete Intersections and a Hyperplane Section via Sage”, Sage/Oscar Days for Combinatorial Algebraic Geometry (15-19 February 2021), Lightning Talk.

"Computational GIT for Complete Intersections", COW/EmSG/GLEN Joint Summer School (September 7-11, 2020), Poster Session.

# Research Visits

Visiting Research Fellow at the University of Glasgow (visiting Dr. Ruadhai Dervan) (03 October 2023- 02 January 2024)

Visit to Dr. Hamid Abban at the University of Loughborough (26-29 October 2021)

Visit to Dr. Ruadhai Dervan at the University of Cambridge (18-22 October 2021)