Alex Gomez

About

I am a PhD student in Mathematics at PUC-Rio, working under the supervision of Sergey Galkin. My research lies at the interface of algebraic geometry, Homological Mirror Symmetry, derived categories, Fano and log del Pezzo geometry, Landau–Ginzburg models, periods, monodromy, and arithmetic aspects of mirror symmetry.

Research interests

• Homological Mirror Symmetry
• Fano varieties and log del Pezzo surfaces
• Derived categories, semiorthogonal decompositions, and exceptional collections
• Landau–Ginzburg models, periods, and Picard–Fuchs equations
• Arithmetic geometry, monodromy, and exponential motives
• Weighted projective hypersurfaces and quotient singularities
• Modular forms

Current project

My current work studies the degree-10 weighted hypersurface X₁₀ ⊂ ℙ(1,2,3,5), a log del Pezzo surface of index one with a quotient singularity of type 1/3(1,1). I am interested in its birational geometry, minimal resolution, canonical Deligne–Mumford stack, semiorthogonal decompositions, exceptional collections, and mirror Landau–Ginzburg models.

The associated paper proves a full exceptional collection result for canonical stacks of complex log del Pezzo surfaces with 1/3(1,1)-singularities, and specializes the construction to X₁₀.

Preprints and manuscripts

• Exceptional Collections for Canonical Stacks of Log del Pezzo Surfaces with 1/3(1,1)-Singularities . arXiv:2606.18238, posted June 16, 2026; submitted to manuscripta mathematica. Latest manuscript PDF.
• Real Bruhat Intersections and Complex Open Richardson Varieties , draft communication, 2026. Part of a writing project in alequisGS/symmetrical-guide .

NotebookLM audio overviews

These are NotebookLM-generated audio overviews of my paper on exceptional collections for canonical stacks of log del Pezzo surfaces. The paper itself remains the authoritative source for its mathematical statements.

Thesis project and fellowship

I was awarded the FAPERJ Nota 10 Excellence Scholarship for my PhD thesis project, Functional Equations for Landau–Ginzburg Models and Exponential Motives . The project studies graph potentials, exponential integrals and sums, Kloosterman-type phenomena, trace formulas, and arithmetic realizations of mirror-symmetric structures.

Education

• PhD in Mathematics, PUC-Rio, Brazil, 2023–present. Advisor: Sergey Galkin.
• MSc in Mathematics, Pontificia Universidad Católica del Perú, 2019. Thesis: Modular Forms.
• BSc in Mathematics, Pontificia Universidad Católica del Perú, 2015. First Class Honors. Thesis: Elliptic Curves: Mordell–Weil, Roth and Siegel Theorems.

Honors and scholarships

• FAPERJ Nota 10 Excellence Scholarship, Rio de Janeiro, Brazil, 2024–present.
• First Class Honors, BSc in Mathematics, Pontificia Universidad Católica del Perú, 2015.

Selected talks and posters

• Exceptional Collections for Canonical Stacks of Log del Pezzo Surfaces with 1/3(1,1)-Singularities, poster presentation, RGAS Summer School, Zaragoza, 2026.
• Periods in Homological Mirror Symmetry and Kloosterman Motives, ICTP, 2025.
• A Tentative Relationship Between Homological Mirror Symmetry and Arithmetic Geometry , Arithmetic and p-adic Geometry in Chile, 2024.
• The Mordell–Weil Theorem, PUC-Rio Friday Seminar, 2024.
• Karoubian Completion of Triangulated Categories, PUC-Rio Friday Seminar, 2024.

Teaching and notes

• Graduate instructor and teaching assistant at PUC-Rio and PUCP, 2013–2026.
• Courses taught or assisted include Linear Algebra, Algebra, Real Analysis, Complex Analysis, Calculus, and Mathematics for Economists.
• Notes on quotient groups and algebraic structures.
• Notes on derived categories of sheaves.
• Notes on Geometric Invariant Theory.

Selected schools and programs

• RGAS Summer School: Mirror Symmetry and Homological Methods in Algebraic Geometry, Zaragoza, 2026.
• ICTP School and Workshop on Explicit Arithmetic Geometry, ICTP, 2025.
• Conference on Recent Developments in Topological Quantum Field Theory, BIMSA, 2024.
• The Mordell Conjecture 100 Years Later, MIT, 2024.
• ICTP String-Math, ICTP, 2024.
• CIMPA ELGA – Latin American School of Algebraic Geometry, 2024.
• Arizona Winter School, 2022 and 2023.
• IHES Summer School on the Langlands Program, 2022.
• ICTP–CIMPA Schools in Arithmetic Geometry, 2015 and 2018.

Academic service

• Co-founder and organizer of the 38 Movimientos Seminar.
• Co-organizer of the Meetings on Arithmetic and Algebraic Number Theory Seminar.

Languages

Spanish native; English advanced; Portuguese advanced; basic Chinese and French.

Music

A small personal note: one song currently on my playlist.

Contact

Email: alex.gomez@pucp.edu.pe
GitHub: github.com/alequisGS
CV: AlexGomez-CV.pdf
Thesis project: FAPERJ Nota 10 project PDF