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Jack ThorneView profile

Professor

• Number Theory
• Arithmetic Geometry
• Automorphic Forms
• +3 more

Jack Thorne is a Professor of Number Theory in the Department of Pure Mathematics and Mathematical Statistics (DPMMS) at the University of Cambridge, within the Faculty of Mathematics. His office is located in room E1.18 at the department, and he can be contacted at thorne@dpmms.cam.ac.uk or by telephone at 01223 764283. Professor Thorne's primary research interests lie in Number Theory and Arithmetic Geometry , with significant contributions to the understanding of automorphic forms, Galois representations, and the Langlands program. His work spans theoretical developments in modularity, symmetric power functoriality, and the study of Selmer groups, demonstrating deep connections between algebraic geometry and number-theoretic phenomena. Analysis of Professor Thorne's recent publications reveals a consistent focus on advanced topics in modern number theory. His research demonstrates particular expertise in automorphy lifting theorems, potential automorphy over various fields, and the intricate relationships between Galois representations and automorphic forms. The publications show a progression toward increasingly sophisticated applications of the Langlands program to concrete arithmetic problems, with notable work on symmetric powers, level-raising phenomena, and the arithmetic of elliptic curves. Professor Thorne maintains an active research profile with numerous high-impact publications in leading mathematical journals including Annals of Mathematics, Publications mathématiques de l'IHÉS, and Journal of the American Mathematical Society. His collaborative work with prominent mathematicians such as Patrick Allen, Chandrashekhar Khare, and James Newton highlights his position within the international number theory community.

Sug Woo ShinView profile

Professor

• Number Theory
• Automorphic Forms
• Algebraic Geometry
• +6 more

Sug Woo Shin is a Professor of Mathematics at the University of California, Berkeley ( Math Genealogy , MathSciNet Profile ). His research focuses on Number Theory and Automorphic Forms, with significant contributions to the Langlands Program, Shimura varieties, and cohomology of arithmetic spaces. Editorial roles: Astérisque , Manuscripta Mathematica , Journal of the Korean Mathematical Society Recent research explores cohomological properties of locally symmetric spaces, tempered A-packets for classical groups, and modularity of symplectic Galois representations Collaborators include Ana Caraiani, Mark Kisin, Arno Kret, and Peter Scholze He has supervised PhD theses on topics like affine Deligne-Lusztig varieties, specialization maps in Scholze's category of diamonds, and statistical properties of automorphic representations. Teaching includes graduate courses on Number Theory (254A/254B), undergraduate Linear Algebra (110), and Calculus (1A), as well as seminars on global Langlands reciprocity and p-adic cohomology theories. Co-organized conferences include the BIRS workshop on Langlands programs (2025), PRIMA algebraic number theory sessions (2022), and KAST Symposium on automorphic forms (2021). His work appears in journals like Annals of Mathematics, Duke Mathematical Journal, and Compositio Mathematica.

Stephen S. KudlaView profile

Professor

• Automorphic Forms
• Arithmetic Geometry
• Theta Functions
• +4 more

Stephen S. Kudla is a Professor in the Department of Mathematics at the University of Toronto, located in the Bahen Centre for Information Technology. He holds the prestigious distinction of being a Fellow of the Royal Society of Canada (FRSC), reflecting his significant contributions to mathematical research. Professor Kudla's research focuses on the deep connections between number theory and geometry, with particular expertise in automorphic forms, arithmetic geometry, and theta functions. His work bridges abstract mathematical theory with concrete geometric structures, exploring how modular forms can encode arithmetic information about algebraic varieties. Analysis of Kudla's publication record reveals a sustained research program centered on the relationship between derivatives of Eisenstein series and arithmetic geometry. His work consistently explores how modular and automorphic forms can be used to study arithmetic cycles on Shimura varieties. A notable pattern in his research is the interplay between analytic objects (like Eisenstein series) and geometric structures (such as arithmetic cycles), with applications to understanding heights, intersection theory, and special values of L-functions. Fellow of the Royal Society of Canada (FRSC) While specific details about Kudla's advising activities aren't provided in the available materials, his extensive publication record with prominent collaborators like Michael Rapoport and Tonghai Yang suggests he has likely mentored numerous graduate students and postdoctoral researchers throughout his career. His participation in major mathematical conferences including the International Congress of Mathematicians (ICM) indicates recognition by the broader mathematical community. Kudla's research has clearly been supported by significant funding, as evidenced by his ability to maintain a sustained publication record in top mathematical journals.

Tasho KalethaView profile

Professor

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

Tasho Kaletha is a Professor in the Department of Mathematics at the University of Michigan. His research focuses on the Langlands program, intersecting number theory, representation theory, algebraic geometry, and analysis. He holds a Ph.D. from the University of Chicago (2010). Key research interests include representation theory of reductive groups, harmonic analysis, Galois cohomology, and automorphic representations. Education: Ph.D., University of Chicago (2010). Research interests revolve around the Langlands conjectures, endoscopy, and the structure of reductive groups. His work addresses representation theory of real/p-adic groups, cohomology of Galois groups, and automorphic spectra. Recent publications explore Bruhat-Tits theory, discrete series L-packets, and global rigid inner forms. He has authored a monograph with Gopal Prasad and contributed to foundational papers in Duke Mathematical Journal and Inventiones Mathematicae . Notable contributions include studies on supercuspidal L-packets, endoscopic classification, and commensurability growth in algebraic groups. His work bridges abstract algebraic structures with analytic techniques, advancing the Langlands program's goals.

Dinesh S. ThakurView profile

Professor

• Number Theory
• Arithmetic Geometry
• Function Field Arithmetic
• +7 more

Professor Dinesh S. Thakur holds the position of Professor in the Department of Mathematics at the University of Rochester. He earned his PhD from Harvard University and has made significant contributions to number theory, arithmetic geometry, and function field arithmetic. His research focuses on developing theories related to zeta functions, Drinfeld modules, and p-adic analysis in finite characteristic environments. Education: PhD in Mathematics, Harvard University Research Interests: Thakur’s work integrates advanced topics such as elliptic curves, modular forms, Diophantine equations, and the arithmetic of function fields. He has pioneered studies on multizeta values, p-adic continued fractions, and the distribution of Diophantine exponents in finite characteristic. His research bridges classical number theory with modern algebraic geometry and p-adic analysis. Teaching & Mentorship: Thakur has taught a wide range of courses, including graduate-level topics in function field arithmetic, algebraic geometry, and number theory. He has advised 11 PhD students and several master’s students, whose theses span themes like elliptic Carmichael numbers, Drinfeld modular forms, and multizeta relations. Notable advisees include Javier Diaz-Vargas (1996), George Todd (2015), and Yao-Rui Yeo (2021). Outreach & Contributions: Thakur participates in initiatives like the Arizona Winter School and Olympiad training programs in India. He maintains an active seminar series at UR on topics such as L-values, Fermat’s Last Theorem, and automatic sequences. His work is accessible through his personal page and MathSciNet.

Aise Johan de JongView profile

Professor

• Algebraic Geometry
• Arithmetic Geometry
• Stacks Theory
• +4 more

Aise Johan de Jong is a Professor in the Department of Mathematics at Columbia University, where he teaches courses including representations of finite groups and organizes the algebraic geometry seminar. He is a leading figure in algebraic geometry with a particular focus on stacks theory and arithmetic aspects of algebraic varieties. Institution: Columbia University, Department of Mathematics Research Focus: Algebraic stacks, arithmetic geometry, moduli spaces Major Project: The Stacks Project (open-source collaborative textbook) De Jong's research primarily centers on algebraic stacks, arithmetic geometry, and the foundations of algebraic geometry. His work bridges abstract theoretical frameworks with concrete computational aspects, particularly in positive characteristic. He has made significant contributions to understanding Brauer groups, period-index problems, and the geometry of moduli spaces. His research often connects number theory with geometric structures, exploring how arithmetic properties manifest in geometric settings. His publication record shows a consistent focus on fundamental structures in algebraic geometry, with particular emphasis on stacks theory (evident in The Stacks Project), Brauer groups, rational connectivity, and arithmetic properties of algebraic varieties. The trajectory of his work demonstrates increasing sophistication in handling complex geometric structures while maintaining connections to arithmetic questions. His most recent work continues to explore the interplay between algebraic geometry and number theory, particularly through the lens of stacks and moduli spaces. De Jong actively mentors graduate students, with numerous descendants listed in the Mathematics Genealogy Project. His academic lineage includes researchers working across various subfields of algebraic geometry. He has organized multiple conferences including "Moduli spaces and moduli stacks" (2012) and "Spaces of curves and their interaction with diophantine problems" (2009), demonstrating his leadership in the field. He leads The Stacks Project, a major collaborative open-source initiative that has become an essential reference for algebraic geometers worldwide. This project provides comprehensive foundations for algebraic stacks and related concepts, with regular updates and community contributions. De Jong also maintains the Stacks Project Blog where he discusses mathematical topics related to the project and shares updates.

Elden ElmantoView profile

Assistant Professor

• Algebraic Geometry
• Homotopy Theory
• Algebraic K-theory
• +3 more

Elden Elmanto is an Assistant Professor in the Department of Mathematics at the University of Toronto, affiliated with the Faculty of Arts and Science. His research focuses on advanced areas of algebraic geometry and homotopy theory, particularly through a motivic perspective. He investigates algebraic cycles, vector bundles, and motivic cohomology, often leveraging techniques from derived algebraic geometry and p-adic geometry. Recently, he co-developed a motivic cohomology theory for singular schemes with Matthew Morrow. His work spans topics like algebraic K-theory, motivic homotopy theory, and the interplay between topology and arithmetic geometry. He actively participates in seminars such as the Toronto Algebraic Geometry Seminar and has led research on topological cyclic homology, equivariant algebraic K-theory, and motivic infinite loop spaces. Elmanto collaborates widely, contributing to fields like étale motivic spectra, Voevodsky’s convergence conjecture, and the Quillen-Lichtenbaum dimension. His research emphasizes foundational questions in modern algebraic geometry, with applications to arithmetic and geometric contexts.

Kartik PrasannaView profile

Professor

• Number Theory
• Automorphic Forms
• Algebraic Cycles
• +6 more

Kartik Prasanna is a Professor in the Department of Mathematics at the University of Michigan , affiliated with the College of Literature, Science and the Arts . He received his PhD from Princeton University in 2003 under the supervision of Andrew Wiles. Research Interests: His work lies at the intersection of number theory , algebraic cycles , and automorphic forms , focusing on the Langlands program , L-functions , algebraic cycles , and Iwasawa theory , particularly through the lens of the Bloch-Beilinson and Bloch-Kato conjectures . His recent publications explore periods of automorphic forms and the arithmetic of Shimura varieties. Grants & Awards: Simons Fellowship (2014-15) von Neumann Fellowship at the Institute for Advanced Study (2014-15) Current NSF Grants : DMS 2001293 and RTG DMS 1840234 Previous NSF grants: DMS 1600494, DMS 1160720, DMS 1015173, DMS 0801191, DMS 0854900 Academic Contributions: He has advised or collaborated with numerous postdoctoral researchers including Christopher Lyons , Ruochuan Liu , and Cameron Franc . Prasanna organized the 2011 FRG/RTG Workshop on L-functions, Galois Representations and Iwasawa Theory at the University of Michigan.

Matthew EmertonView profile

Professor

• Number Theory
• Arithmetic Geometry
• Automorphic Forms
• +3 more

Matthew Emerton is a Professor in the Department of Mathematics at the University of Chicago, part of the Physical Sciences Division. He specializes in number theory, arithmetic geometry, and the Langlands program. His research focuses on automorphic forms, Galois representations, and p-adic methods in arithmetic geometry. Education: BSc (Hons) from the University of Melbourne (1993), PhD in Mathematics from Harvard University (1998), advised by Barry Mazur. Research Highlights: Pioneered work on the p-adic Langlands program, moduli stacks of Galois representations, and prismatic cohomology. Authored over 50 publications, including foundational works on p-adic Hodge theory and local-global compatibility. Awards: Alfred P. Sloan Doctoral Dissertation Fellowship (1997-98), Rackham Summer Faculty Fellowship (1999). Grants: Multiple NSF awards (e.g., DMS-2201242 for 'Arithmetic Aspects of the Langlands Program', DMS-1952705 for geometric aspects of the p-adic Langlands program). Students: Mentored 25+ PhD students and postdocs, many contributing to number theory and representation theory.

Guido KingsView profile

Professor

• Special Values of L-functions
• Tamagawa Number Conjecture
• Polylogarithms
• +3 more

Prof. Dr. Guido Kings is a Professor of Pure Mathematics at the Faculty of Mathematics, University of Regensburg. His research focuses on Special Values of L-functions , Tamagawa Number Conjecture , and Polylogarithms , with significant contributions to Iwasawa Theory and Arithmetic Geometry . He has held leadership roles in research projects such as the CRC Higher Invariants. Prof. Kings has authored influential papers on topics like Eisenstein-Kronecker classes , p-adic interpolation , and regulators in arithmetic geometry . He received the Frontier of Science Award in recognition of his work. His team includes doctoral students and postdoctoral researchers, such as Bernadette Melichar and Julio de Mello Bezerra. Current Affiliations: Faculty of Mathematics, University of Regensburg Recent Courses Taught: Analysis II, Advanced Seminar in Arithmetic Geometry, and Modular Forms Research Group: Comprises scientific staff (e.g., Han-Ung Kufner) and doctoral students working on number theory and algebraic geometry. His publications are widely cited in Annals of Mathematics , Duke Mathematical Journal , and Inventiones Mathematicae , reflecting his expertise in connecting motivic cohomology with p-adic analysis.

• Algebraic Number Theory
• Modular Forms
• Galois Representations
• +3 more

Jaclyn Lang is the Selma Lee Bloch Brown Assistant Professor of Mathematics at Temple University. Her research centers on algebraic number theory, focusing on modular forms, Galois representations, elliptic curves, motives, and p-adic methods. Education: Ph.D. in Mathematics, UCLA (2016), advised by Haruzo Hida Part III of the Mathematical Tripos, University of Cambridge (2010), supervised by Tom Fisher MA in Mathematics, Bryn Mawr College (2009), supervised by Helen Grundman Research Interests: She works on advanced problems in number theory, including the Eisenstein ideal, pseudorepresentations, and arithmetic geometry of elliptic curves. Her work often bridges algebraic geometry and automorphic forms using p-adic techniques. Scientific Awards: Churchill Scholarship (2009–2010) Clare Booth Luce Scholarship (2007–2009) NSF Graduate Research Fellowship (2010–2015) Charles E. and Sue K. Young Graduate Student Award (2015) NSF Mathematical Sciences Postdoctoral Research Fellowship (2016–2020) AWM Travel Grant (2023) Fulbright U.S. Student Program Grant (2016) Simons Travel Support for Mathematicians (2023–2028) Grants: She has received NSF Standard Grant DMS-331117 (2023–2026) and participated in programs like the Park City Math Institute and Women in Numbers Europe (WINE3).

• 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.

• Arithmetic Geometry
• Algebraic Geometry
• Number Theory
• +4 more

Dr. Niranjan Ramachandran is a Professor of Mathematics at the University of Maryland, College Park, specializing in the deep structural connections between Arithmetic Geometry and Number Theory. His work centers on motives, zeta functions, and algebraic cycles, with significant contributions to foundational conjectures in modern mathematics. His primary research domains include: Arithmetic Geometry Algebraic Geometry Number Theory Motives Zeta Functions Cohomology K-theory Prof. Ramachandran's research explores the intricate relationships between algebraic cycles, special values of L-functions, and motivic cohomology, advancing understanding of the Birch and Swinnerton-Dyer conjecture, Artin-Tate conjecture, and higher Euler characteristics through innovative approaches to zeta functions and motivic complexes. Analysis of his 15 most recent publications reveals sustained focus on zeta function special values (2023), derived categories of elliptic curves (2022), and Artin-Tate conjecture proofs (2022), with recurring themes in fiber integration of gerbes (2020), higher Euler characteristics (2016), and motivic measure exponentiation (2014). His work consistently bridges abstract motivic frameworks with concrete arithmetic problems. No scientific awards were documented in the provided materials. Information regarding academic advising, Ph.D. students, or research grants was not specified in the available text.

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).