Vesselin Dimitrov
Vesselin Dimitrov
Professor of Mathematics
A.B., Harvard University, 2010; M.S., Yale University, 2014; Ph.D., 2017. Professor, Caltech, 2024-.
Research Interests: Number Theory, Diophantine Geometry, and related problems from Algebraic Geometry, Representation Theory and Harmonic Analysis
Overview
Vesselin Dimitrov is a Professor of Mathematics at Caltech. Prof Dimitrov works in the field of number theory, Diophantine geometry, and related problems from algebraic geometry, representation theory and harmonic analysis. He proved two famous conjectures from the 1970s: The Schinzel-Zassenhaus conjecture for algebraic units close to the unit circle and the "unbounded denominators" conjecture, which concerns incongruent modular forms.
Selected Awards
- New Horizons in Mathematics Prize, 2026; "for work in Diophantine geometry, including the proof of the Atkin-Swinnerton-Dyer unbounded denominators conjecture and new irrationality results for special values of Dirichlet L-series"
- American Mathematical Society Frank Nelson Cole Prize for Number Theory, 2026
- Salem Prize, 2025; "for fundamental contributions to Diophantine geometry and number theory"
- Fermat Prize, European Mathematical Society, 2025; "for major advances in number theory, Diophantine geometry and the theory of modular forms"
- The Institute of Mathematics and Informatics (IMI) of the Bulgarian Academy of Sciences, 2023; "for his outstanding contributions to number theory and Diophantine geometry"
- Oberwolfach Prize, 2022; "for his outstanding contribution to number theory and Diophantine geometry"
- David Gross Prize, 2022
Selected Awards
- New Horizons in Mathematics Prize, 2026; "for work in Diophantine geometry, including the proof of the Atkin-Swinnerton-Dyer unbounded denominators conjecture and new irrationality results for special values of Dirichlet L-series"
- American Mathematical Society Frank Nelson Cole Prize for Number Theory, 2026
- Salem Prize, 2025; "for fundamental contributions to Diophantine geometry and number theory"
- Fermat Prize, European Mathematical Society, 2025; "for major advances in number theory, Diophantine geometry and the theory of modular forms"
- The Institute of Mathematics and Informatics (IMI) of the Bulgarian Academy of Sciences, 2023; "for his outstanding contributions to number theory and Diophantine geometry"
- Oberwolfach Prize, 2022; "for his outstanding contribution to number theory and Diophantine geometry"
- David Gross Prize, 2022
PhD Thesis: Diophantine Approximation by Special Points andApplications to Dynamics and Geometry
Related Courses
Ma 110 abc. Analysis.
9 units (3-0-6); first, second, third terms, 2026-27.
Prerequisites: Ma 108 or previous exposure to metric space topology, Lebesgue measure.
First term: integration theory and basic real analysis: topological spaces, Hilbert space basics, Fejer's theorem, measure theory, measures as functionals, product measures, L^p -spaces, Baire category, Hahn- Banach theorem, Alaoglu's theorem, Krein-Millman theorem, countably normed spaces, tempered distributions and the Fourier transform. Second term: basic complex analysis: analytic functions, conformal maps and fractional linear transformations, idea of Riemann surfaces, elementary and some special functions, infinite sums and products, entire and meromorphic functions, elliptic functions. Third term: harmonic analysis; operator theory. Harmonic analysis: maximal functions and the Hardy-Littlewood maximal theorem, the maximal and Birkoff ergodic theorems, harmonic and subharmonic functions, theory of H^p -spaces and boundary values of analytic functions. Operator theory: compact operators, trace and determinant on a Hilbert space, orthogonal polynomials, the spectral theorem for bounded operators. If time allows, the theory of commutative Banach algebras.
Instructors: Makarov, Dimitrov, Isett
Instructors: Makarov, Dimitrov, Isett
Ma 120 abc. Abstract Algebra.
9 units (3-0-6); first, second, third terms, 2026-27.
Prerequisites: Ma 5 or equivalent or instructor's permission.
This course will discuss advanced topics in algebra. Among them: an introduction to commutative algebra and homological algebra, infinite Galois theory, Kummer theory, Brauer groups, semisimiple algebras, Weddburn theorems, Jacobson radicals, representation theory of finite groups.
Instructors: Sugimoto, Dimitrov
Instructors: Sugimoto, Dimitrov
Ma 135 ab. Arithmetic Geometry.
9 units (3-0-6); first, second terms, 2026-27.
Prerequisites: Ma 130.
The course deals with aspects of algebraic geometry that have been found useful for number theoretic applications. Topics will be chosen from the following: general cohomology theories (étale cohomology, flat cohomology, motivic cohomology, or p-adic Hodge theory), curves and Abelian varieties over arithmetic schemes, moduli spaces, Diophantine geometry, algebraic cycles.
Instructors: Flach, Dimitrov
Instructors: Flach, Dimitrov