About
I am a PhD student in Mathematics at PUC-Rio, working under the supervision of Sergey Galkin, with Vasily Golyshev as co-advisor. My research lies at the interface of algebraic geometry, birational 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
- Birational geometry of 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
I am currently studying the quantum cohomology of X10 ⊂ ℙ(1,2,3,5).
My recent paper proves full exceptional collections for canonical stacks of complex log del Pezzo surfaces with 1/3(1,1)-singularities, with X10 as a central example.
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.
- Real Bruhat Intersections and Complex Open Richardson Varieties , draft communication, 2026. Part of a writing project in alequisGS/symmetrical-guide .
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. Research advisor: Sergey Galkin. Co-advisor: Vasily Golyshev.
- 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
- Brauer–Manin and a log del Pezzo surface, Pontificia Universidad Católica de Chile, 2026.
- Exceptional Collections for Canonical Stacks of Log del Pezzo Surfaces with 1/3(1,1)-Singularities, poster, RGAS Summer School, Zaragoza, Spain, 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.
- Model structures, PUC-Rio Friday Seminar, 2024.
- A real analogue of the Moore–Tachikawa category, PUC-Rio Friday Seminar, 2024.
- Delzant’s theorem on toric symplectic manifolds, PUC-Rio Friday Seminar, 2023.
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
- Rutgers Symplectic Summer School, Rutgers University, New Brunswick, USA, 2026.
- AGRA V: School on Arithmetic, Groups and Analysis, Popayán, Colombia, 2026.
- GARLAT: Latin American School in Arithmetic Geometry, Santiago, Chile, 2026.
- RGAS Summer School: Mirror Symmetry and Homological Methods in Algebraic Geometry, Zaragoza, Spain, 2026.
- ICTP School and Workshop on Explicit Arithmetic Geometry, Trieste, Italy, 2025.
- The Mordell Conjecture 100 Years Later, MIT, USA, 2024.
- ICTP String-Math, Trieste, Italy, 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
- Teaching assistant for Métodos explícitos de Chabauty: un punto de vista computacional a los puntos racionales , AGRA V, Popayán, Colombia, 2026.
- 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