Find Academic Supervisors

• Number Theory
• Modular Forms
• Galois Representations
• +5 more

Haruzo HIDA is a Distinguished Research Professor of Mathematics at the University of California, Los Angeles (UCLA). His work spans advanced topics in Number Theory, Modular Forms, Galois Representations, and Arithmetic Geometry. HIDA has held significant positions globally, including lectures and research visits at institutions in India, China, Japan, and Europe. University: University of California, Los Angeles Department: Mathematics Academic Rank: Research Professor Research Interests: HIDA’s research focuses on complex and p-adic Number Theory, Modular Forms, and their connections to Galois Representations, Iwasawa Theory, L-functions, and Automorphic Forms. His recent work addresses adjoint L-values, Selmer groups, and the interplay between arithmetic invariants and geometric structures. Publications: HIDA’s recent articles (2014-2025) explore themes like Hecke algebras, anticyclotomic Iwasawa theory, Tate-Shafarevich groups, and p-adic rigidity. His work often bridges modular forms with arithmetic geometry and automorphic representations. Students: He has supervised numerous PhD students, including Koji Kitagawa, Chandrashekhar Khare, Eknath Ghate, Ashay Burungale, and Jaclyn Lang, contributing to their research in topics like modular forms and arithmetic geometry. Grants: His research has been partially supported by NSF grants, documented across multiple publications and lecture notes.

Thomas LamView profile

Professor

• Algebraic Combinatorics
• Total Positivity
• Cluster Algebras
• +5 more

Thomas Lam is a professor of mathematics at the University of Michigan , specializing in algebraic combinatorics, total positivity, and connections to mathematical physics. His work bridges cluster algebras, positive geometry, and integrable systems, with applications to scattering amplitudes in quantum field theory. Lam has collaborated extensively with physicists such as Nima Arkani-Hamed and mathematicians like Pavlo Pylyavskyy and Mark Shimozono. Key research areas: Cluster algebras, total positivity, electrical networks, positroid varieties, and quantum cohomology. Notable contributions: Defining polypositroids, proving regularity theorems for totally nonnegative flag varieties, and establishing cluster structures in braid varieties. Recent work focuses on positive geometries , including the amplituhedron and moduli spaces of points on projective lines, with implications for particle physics. His articles often explore dual graded graphs, K-theoretic Schubert calculus, and the interplay between combinatorics and algebraic structures. Lam's research has been supported by NSF grants, including DMS-0748636 and DMS-1249708 .

Henri DarmonView profile

Professor

• Number Theory
• Algebraic Geometry
• Elliptic Curves
• +3 more

Henri Darmon is a Distinguished James McGill Professor in the Department of Mathematics and Statistics at McGill University, affiliated with the Centre Interuniversitaire en Calcul Mathématique Algébrique (CICMA) and the Centre de Recherches Mathématiques (CRM). He holds citizenships of Canada, France, and Switzerland. His research focuses on algebraic number theory, particularly elliptic curves, modular forms, and L-functions, with contributions to the Birch and Swinnerton-Dyer conjecture and Stark conjectures. Education: B.Sc. Mathematics & Computer Science, McGill University (1987) Ph.D. Mathematics, Harvard University (1991) Key Positions: Director of CICMA (1998–2024) Editorial roles at journals like Commentarii Mathematici Helvetici and Transactions of the AMS Organizer of major conferences including CNTA, ICM satellite events, and thematic programs at MSRI and CRM Research Interests: Stark-Heegner points and Euler systems p-adic L-functions and Iwasawa theory Arithmetic of modular curves and Shimura varieties His work bridges analytic and algebraic approaches to number theory, emphasizing computational and geometric methods.

Sean HoweView profile

Assistant Professor

• arithmetic geometry
• algebraic geometry
• representation theory
• +2 more

Sean Howe is an Assistant Professor in the Department of Mathematics at the University of Utah, where he has been employed since July 2019. His research is supported by NSF grants DMS-2201112 and DMS-2501816. In the academic year 2023-2024, he was a Friends of the Institute for Advanced Study Member at the special year on p-adic arithmetic geometry at the Institute for Advanced Study. Dr. Howe received his PhD from the University of Chicago in 2017 under the supervision of Matt Emerton. Prior to his position at Utah, he was an NSF Postdoctoral Scholar at Stanford University from September 2017 to June 2019. He earned a joint master's degree from Leiden University and Universite Paris-Sud 11 through the ALGANT program in 2012 and completed his undergraduate studies at the University of Arizona. Dr. Howe's research spans arithmetic and algebraic geometry, representation theory, and number theory, with a particular focus on p-adic aspects. His work often explores the connections between geometry and number theory through the lens of p-adic methods, including p-adic Hodge theory, perfectoid spaces, and the Langlands program. He has made significant contributions to understanding cohomological structures in mixed characteristic settings, the geometry of moduli spaces, and the statistical properties of L-functions. His extensive publication record demonstrates a strong trajectory in advancing p-adic geometry and its applications. Recent work shows increasing focus on cohomological smoothness in mixed characteristic, p-adic periods, and the interplay between random matrix theory and arithmetic statistics. His research often bridges abstract theoretical frameworks with concrete computational approaches. NSF Postdoctoral Scholar NSF grants DMS-2201112 and DMS-2501816 Dr. Howe is an active mentor, currently advising five PhD students: Minhua Cheng, Madison Delmoe, Shea Engle, Abhay Goel, and Suo Jun Tan. He has successfully graduated two PhD students: Matthew Bertucci (2025) and Hanlin Cai (2024). He also regularly mentors undergraduate researchers, with notable projects including Emil Geisler's work on stable multiplicities in configuration space cohomology and Daniel Koizumi's software for computing braid monodromy of cubic surfaces. His teaching portfolio includes advanced courses in algebraic topology, number theory, and algebra, reflecting his broad expertise across pure mathematics. He has taught courses such as Math 6950 (Topics in Algebraic Topology), Math 4400 (Introduction to Number Theory), and Math 6320 (Modern Algebra II).

• Algebraic Geometry
• Symplectic Geometry
• Mathematical Physics
• +1 more

Kazushi Ueda is an Associate Professor at the Graduate School of Mathematical Sciences, The University of Tokyo, where he has been since April 2015. His research spans algebraic geometry, symplectic geometry, and mathematical physics, with a focus on homological mirror symmetry and its applications to moduli spaces, Calabi-Yau manifolds, and singularities. He previously held academic positions at Osaka University from 2006 to 2015, including roles as Assistant Professor and Associate Professor. Ueda has also had visiting appointments at institutions such as the University of Oxford, Max Planck Institute for Mathematics, and Korea Institute for Advanced Study. Bachelor of Science, Kyoto University (1997-2001) Master of Science, Kyoto University (2001-2003) Doctor of Science, Kyoto University (2003-2006) Ueda's research explores the deep interplay between complex and symplectic geometry through mirror symmetry, particularly in the context of Calabi-Yau varieties, toric degenerations, and dimer models. His work addresses derived categories, stability conditions, and moduli problems, with recent contributions to noncommutative algebraic geometry and applications in mathematical physics. He has collaborated extensively with researchers like Akira Ishii, Masahiro Futaki, and Shinnosuke Okawa. His publications highlight homological mirror symmetry for K3 surfaces, Grassmannians, and singularities, as well as studies on modular forms, cluster transformations, and the Grothendieck ring. Ueda is a member of the Mathematical Society of Japan and has contributed to educational programs, including graduate lectures on mirror symmetry and symplectic geometry.

David RohrlichView profile

Professor

• Number Theory
• Algebraic Number Theory
• Arithmetic Geometry
• +3 more

David Rohrlich is a Professor of Mathematics and Statistics at Boston University, serving as Director of Graduate Studies. His primary affiliation is with the Department of Mathematics and Statistics. He specializes in Number Theory, focusing on topics such as Artin representations, arithmetic statistics, and Galois theory. His research explores areas including algebraic number theory, arithmetic geometry, and representation theory. Notable contributions include studies on self-dual Artin representations, quaternionic structures in arithmetic statistics, and the interplay between Galois representations and L-functions. Rohrlich has published extensively on topics such as Mordell-Weil groups, average multiplicities, and dihedral Artin representations. His work often involves intricate connections between algebraic structures and number-theoretic phenomena. He holds a PhD and has advised numerous graduate students (though specific names are not listed here). His office is located in CDS 433, with regular in-person and virtual office hours.

Patrick AllenView profile

Associate Professor

• Number Theory
• Galois Representations
• Automorphic Forms
• +3 more

Patrick Allen is an Associate Professor in the Department of Mathematics and Statistics at McGill University, where he contributes to research in number theory and related fields. He is affiliated with the Montreal Number Theory Group and the Centre Interuniversitaire en Calcul Mathématique Algébrique (CICMA), focusing on areas such as Galois representations, automorphic forms, and algebraic number theory. His work bridges algebraic geometry and arithmetic, with a particular emphasis on modularity lifting theorems and deformation theory. Allen's research interests include the study of CM fields, modular forms, and elliptic curves, alongside investigations into the Langlands program and p-adic methods. He has published extensively on topics such as potential automorphy, monodromy, and adjoint Selmer groups. His contributions address questions in arithmetic algebraic geometry and cohomological automorphic forms, often intersecting with representation theory. While his articles span over 20 years, recent work (2020–2023) emphasizes the modularity of Galois representations over CM fields and the application of automorphic techniques to solve problems in number theory. Allen’s research often involves collaboration with international experts in algebraic number theory and arithmetic geometry. Scientific Awards: None explicitly listed in the provided materials. Advising & Grants: No formal advisees or grant details are listed in the text. His affiliations with CICMA suggest participation in collaborative research initiatives, though specific grants are not mentioned. Labs/Teams: Active member of the Montreal Number Theory Group and CICMA, contributing to inter-university collaborative projects in algebraic number theory.

Raphaël Beuzart-PlessisView profile

Research Fellow

• Harmonic analysis
• Differential geometry
• Algebraic number theory
• +5 more

Raphaël Beuzart-Plessis is a CNRS Research Fellow affiliated with Aix-Marseille University and the Institute of Mathematics of Marseille (I2M) at Luminy Campus. He specializes in advanced areas of mathematics, including harmonic analysis, automorphic forms, representation theory, and number theory, with a focus on unitary groups and conjectures like Gan-Gross-Prasad. His work bridges algebraic geometry, differential geometry, and operator theory. Arithmetic, Geometry, Logic and Representations Group (AGLR) 2022-2027 ERC RELANTRA grant recipient Research interests span automorphic representations, L-functions, periods of automorphic forms, and harmonic analysis on real spherical spaces. He works extensively on the local and global Gan-Gross-Prasad conjectures, endoscopy, and supercuspidal representations. His recent publications analyze Plancher1el formulas, spherical characters, and congruences of automorphic forms. His 15 most recent publications (2014-2022) address topics such as the Gan-Gross-Prasad conjecture, Jacquet-Rallis's fundamental lemma, and the Asai Rankin-Selberg integrals. These works reflect his expertise in automorphic forms, representation theory, and number theory, often involving collaborations with leading mathematicians. 2016-2017 Peccot Prize for young mathematicians under 30 2022-2027 ERC RELANTRA grant for research in automorphic forms and representation theory Beuzart-Plessis has no listed students or laboratory teams but participates in the AGLR-RGR (Reduction Group Representations) team and has been an invited speaker at the 2022 International Congress of Mathematicians. His career includes guest lectures at Collège de France, including four sessions on Period factorizations and Plancherel formulas in 2017.

Frank CalegariView profile

Professor

• Algebraic Number Theory
• Langlands Programme
• Galois Representations
• +3 more

Frank Calegari is a Professor of Mathematics at the University of Chicago. His primary research interests include algebraic number theory, the Langlands program, Galois representations, and arithmetic geometry. He has made significant contributions to understanding reciprocity laws linking Galois representations to automorphic forms. His work often intersects with cohomology of arithmetic groups, motives, and the arithmetic of periods. Prof. Calegari has advised numerous PhD students, including Maria Stadnik, Shiva Chidambaram, and Eric Stubley. He serves on editorial boards for prestigious journals such as Algebra & Number Theory, Essential Number Theory, and the Annals of Mathematics. He actively participates in academic conferences and programs, including organizing the 2020 Arithmetic of the Langlands Program in Bonn. His research spans modularity theorems for abelian varieties, cohomology of arithmetic groups, and the study of L-functions. Key recent work includes resolving the unbounded denominators conjecture and advancing potential automorphy results over CM fields. Calegari frequently collaborates with leading mathematicians, including George Boxer, Vincent Pilloni, and Yilin Yang. He teaches advanced courses such as Honors Calculus (Math 16100) at the University of Chicago. His expository work includes lecture notes on motives and L-functions, as well as a blog compiling mathematical insights (Persiflage). Calegari’s contributions to number theory have been recognized through his editorial roles and invited lectures at institutions like the ICM and Clay Mathematics Institute.

Dima ArinkinView profile

Professor

• Algebraic Geometry
• Geometric Langlands Program
• Moduli Spaces
• +3 more

Dima Arinkin is a Professor in the Department of Mathematics at the University of Wisconsin–Madison, specializing in algebraic geometry with significant contributions to geometric representation theory and mathematical physics. His research focuses on: Geometric Langlands Program: Developing frameworks connecting automorphic forms and Galois representations through geometric methods Moduli Spaces: Analyzing spaces of algebraic connections, Higgs bundles, and their compactifications D-modules: Studying systems of linear differential equations via algebraic geometry Integrable Systems: Investigating geometric structures in soliton theory and Painlevé equations Irregular Singularities: Exploring connections with irregular behavior on algebraic curves Analysis of his publications (2008-2016) reveals consistent advancement in geometric Langlands through derived algebraic geometry techniques, particularly in relating singular support of sheaves to automorphic forms and establishing oper structures for connections. No scientific awards are documented in the provided materials. No information regarding student advisement or research grants appears in the source texts.

Steven B BradlowView profile

Professor

• Differential Geometry
• Gauge Theory
• Higgs Bundles
• +7 more

Steven B Bradlow is a Professor of Mathematics at the University of Illinois at Urbana-Champaign, specializing in differential geometry, gauge theory, and Higgs bundles. His work focuses on moduli spaces, geometric structures, and surface group representations. He holds a PhD from the University of Chicago (1988). Research Interests: Bradlow’s research explores advanced topics including Higgs bundles, moduli space properties, Lie group actions, and Teichmüller theory. His work bridges algebraic geometry, differential geometry, and mathematical physics, with applications to non-Abelian monopoles, spectral curves, and geometric analysis. Publications: His recent work emphasizes Cayley correspondences, Teichmüller spaces, and exotic components of SO(p,q) representations. These studies highlight his expertise in unifying geometric and algebraic perspectives. Awards: AMS Fellow (2018), Fulbright Specialist Award (2014) Collaborations: Bradlow collaborates internationally, particularly with researchers like Oscar García-Prada and Peter Gothen, advancing Higgs bundle theory and geometric representation varieties. His editorials and conference contributions further cement his role as a leader in the field.

• Algebra
• Geometry
• Topology
• +5 more

Jonas Bergström is a Professor in the Department of Mathematics at Stockholm University specializing in Algebra, Geometry, Topology, and Combinatorics. His research focuses on arithmetic geometry, moduli spaces, Siegel modular forms, and number theory, with extensive collaborations across international institutions including KTH Royal Institute of Technology. His research interests span algebraic geometry, topology, combinatorics, and number theory, with particular emphasis on moduli spaces of curves, abelian varieties, Siegel modular forms, and arithmetic geometry. Bergström's work bridges theoretical mathematics with computational approaches, often developing algorithms for complex mathematical structures. His research group actively explores commutative and homological algebra, complex and real algebraic geometry, arithmetic geometry, homotopy theory, and Ramsey theory. The most recent publications reveal a strong focus on cohomology of moduli spaces, Siegel modular forms, abelian varieties over finite fields, and L-functions. His work demonstrates a consistent pattern of combining algebraic geometry with number theory, particularly investigating arithmetic properties of algebraic varieties and developing computational methods for modular forms. The research shows increasing emphasis on algorithmic approaches and connections to theoretical physics through moduli space cohomology. Bergström has supervised several PhD students including Sjoerd de Vries (current), Stefano Marseglia, and Olof Bergvall (with Prof. Carel Faber). He currently mentors postdoctoral researchers Séverin Philip and Thomas Wennink, while former postdocs include Angelina Zheng, Valentijn Karemaker, Oliver Leigh, and Alex Samuel Bamunoba. His research is supported through collaborations with major mathematical networks including the Nordic number theory network and joint seminars with KTH. He is affiliated with the Algebra and Geometry Seminar (KTH and SU) and maintains active research connections through multiple collaborative projects, including joint work with Gerard van der Geer and Carel Faber on Hecke operators and Siegel modular forms. Bergström also contributes to open mathematical research through GitHub repositories containing computational results on cohomology of moduli spaces.

Jared WeinsteinView profile

Professor

• Number Theory
• Algebraic Geometry
• Arithmetic Geometry
• +3 more

Jared Weinstein is a Professor in the Department of Mathematics and Statistics at Boston University, serving as the Departmental Ombud. He specializes in Number Theory and Algebraic Geometry, with a focus on p-adic geometry, shtukas, and moduli spaces. His research explores connections between arithmetic geometry and homotopy theory, including contributions to the Langlands program and local Shimura varieties. Education: AB from Harvard University (undergraduate), PhD from University of California, Berkeley. Postdoctoral work at UCLA and the Institute for Advanced Study before joining BU in 2011. Research interests include arithmetic geometry, p-adic Hodge theory, and the geometry of moduli spaces. His work often intersects with topics like perfectoid spaces, diamonds, and chromatic homotopy theory. Recent articles highlight advancements in modularity of elliptic curves over function fields and the Kottwitz conjecture for local shtuka spaces. No scientific awards are explicitly listed, but his extensive publications reflect significant contributions to his field. Advising and grants details are not provided here. His work is closely tied to the v-topology and related geometric frameworks in algebraic geometry.

• Algebraic Number Theory
• Elliptic Curves
• Arithmetic Geometry
• +8 more

Professor Tim Dokchitser is the Heilbronn Chair in Algebraic/Arithmetic Geometry at the School of Mathematics, University of Bristol. His research focuses on algebraic number theory, elliptic curves, arithmetic of L-functions, Galois theory, and computational algebra. He actively explores connections between number theory and finite groups, using computer experiments to advance conjectures like the Birch-Swinnerton-Dyer Conjecture. BSc, Lund University MSc, Lund University PhD, University of Utrecht MA, University of Cambridge His research spans hyperelliptic curves over local fields, Weil representations, tame Galois torsion, and finite group character formulas. Recent work includes computational approaches to Frobenius traces and étale cohomology in hyperelliptic curve quotients. Articles (2023-2025) highlight advancements in arithmetic geometry, zero-knowledge cryptography, and Galois representation theory. Scientific awards include a University Research Fellowship (2011-2014) for elliptic curves and L-functions. He leads projects like the 2015-2018 study on hyperelliptic curves and contributes to collaborations across arithmetic geometry. His computational methods have inspired conjectures in motivic cohomology and modular deformations.

Maxim KontsevichView profile

Professor

• Mathematical Physics
• Algebraic Geometry
• Deformation Quantization
• +5 more

Maxim Kontsevich is a permanent professor at the Institut des Hautes Études Scientifiques (IHÉS), holding the AXA Chair for Mathematics since 1995 and a visiting chair at Rutgers University (one month annually since 1997). Born in 1964 in Khimki, USSR, he earned his PhD from Bonn University in 1992. His career includes visiting positions at Harvard, the Institute for Advanced Study, and Berkeley, where he was a professor from 1993 to 1995. His research spans mathematical physics, algebraic geometry, and non-commutative geometry. Notable contributions include deformation quantization, mirror symmetry, and motivic integration. His work bridges algebraic structures with geometric and physical concepts, influencing areas like topological field theories, string theory, and integrable systems. Awardees of Fields Medal (1998), Crafoord Prize (2008), and Breakthrough Prize (2014), he also holds editorial roles at Compositio Mathematica and Publications Mathématiques IHÉS. His over 50 publications explore advanced topics such as quantum cohomology, Hodge theory, and categorical structures in geometry.