Langlands programme Professors and Supervisors | ApplySharif

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Urs HartlView profile

Professor

University of MünsterGermany

Prof. Dr. Urs Hartl is a faculty member in the Department of Mathematics and Computer Science at the University of Münster, affiliated with the Faculty of Mathematics and Computer Science. He is an Investigator in Mathematics Münster and a member of the Collaborative Research Centre (CRC) 1442 'Geometry: Deformations and Rigidity.' His research focuses on arithmetic geometry, representation theory, algebraic number theory, and arithmetic of function fields. He holds a prominent position in the field, contributing to areas such as Shimura varieties, p-adic Hodge theory, and the Langlands program. Affiliations: Member of CRC 1442 Geometry Investigator in Mathematics Münster Research Interests: Arithmetic algebraic geometry Algebraic number theory Arithmetic of function fields Structure theory of Shimura varieties p-adic Hodge theory p-adic Langlands programme Model theory Recent Publications: Hartl's recent work includes studies on moduli stacks of global G-shtukas, periods of Drinfeld modules, and p-adic Galois representations. His research emphasizes foundational contributions to arithmetic geometry and number theory, often involving collaborations with leading mathematicians such as Rajneesh Kumar Singh and Eva Viehmann. Grants & Advising: Hartl’s involvement in CRC 1442 reflects his leadership in geometric research. While specific advising details are not provided, his extensive publications suggest active mentorship in advanced mathematical research. Labs/Teams: Collaborates within the Mathematics Münster research group and the CRC 1442 team, focusing on geometric and arithmetic structures.

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Frank CalegariView profile

Professor

University of ChicagoUnited States

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.

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Vasily PestunView profile

Professor

Paris-Saclay UniversityFrance

Vasily Pestun is a Permanent Professor of theoretical physics at the Institut des Hautes Études Scientifiques (IHÉS) in Bures-sur-Yvette, France, a position he has held since 2014. Previously he was a member at the Institute for Advanced Study (2011–2014) and a Junior Fellow of the Harvard Society of Fellows (2008–2011). Education Ph.D. in Physics, Princeton University (2008). Thesis: Wilson loops in supersymmetric gauge theories under the supervision of Edward Witten. B.S. & M.S. in Physics (summa cum laude), Moscow Institute of Physics and Technology (MIPT) (2003). Research Interests Pestun’s research lies at the intersection of quantum field theory, string theory and integrable systems . He is renowned for developing supersymmetric localization techniques that yield exact results in strongly-coupled supersymmetric gauge theories placed on curved manifolds. His recent work explores deep connections between quiver gauge theories , conformal field theories , quantum algebras and integrable systems , with applications to the geometric Langlands programme . Selected Awards & Honours Hermann Weyl Prize (2016) ERC Starting Grant QUASIFT (2015–2020) Junior Fellow, Harvard Society of Fellows (2008–2011) Porter Ogden Jacobus Fellowship, Princeton University (2007–2008) Centennial Fellowship, Princeton University (2003–2008) Joseph Henry Merit Prize, Princeton University (2003) Pomeranchuk Fellowship, ITEP (2003) Russian Federation President Fellowship (1997) Gold Medal, 28th International Physics Olympiad (1997) Grants & Funding Principal Investigator, ERC Starting Grant Quantum Algebraic Structures In Field Theories (QUASIFT) – €1.5 million (2015-2020) Professional Service & Outreach Pestun serves as an editor for Letters in Mathematical Physics and regularly referees for leading journals. He has organised several high-profile meetings and schools, including the 2018 month-long programme “Localization Techniques in Quantum Field Theories” at Stony Brook, and the 2019 IHES conference “Higher Structures in Holomorphic and Topological Field Theory”. He has given more than 100 invited lectures and seminar talks world-wide.

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Konstantin ArdakovView profile

Lecturer

University of OxfordUnited Kingdom

Konstantin Ardakov is a Tutorial Fellow in Mathematics at Brasenose College and University Lecturer in Pure Mathematics at the University of Oxford. He holds an MMath from the University of Oxford and a PhD from the University of Cambridge. His academic background includes positions at the Universities of Sheffield, Nottingham, Queen Mary University of London before returning to Oxford in 2013. Dr. Ardakov's research focuses on applying techniques from algebraic geometry and noncommutative algebra to study problems in representation theory arising from areas of algebraic number theory such as non-commutative Iwasawa theory and the Langlands programme. His work explores the geometric representation theory of p-adic groups and the development of p-adic analogues of Beilinson-Bernstein localization.

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Eugen HellmannView profile

Professor

University of MünsterGermany

Prof. Dr. Eugen Hellmann is a full Professor at the Mathematical Institute of the University of Münster , within the Department of Mathematics and Computer Science . He is a leading researcher in arithmetic geometry and representation theory, actively contributing to the CRC 1442 Geometry: Deformations and Rigidity and Mathematics Münster excellence cluster. His work focuses on the p-adic aspects of the Langlands program, moduli spaces of Galois representations, and p-adic Hodge theory. Research Interests: His primary research areas include Arithmetic Algebraic Geometry , the Langlands Program (especially its p-adic and categorical formulations), p-adic Hodge Theory , p-adic Galois Representations , and p-adic Automorphic Forms . His work often involves the study of (phi,Gamma)-modules, eigenvarieties, and deformation spaces, aiming to understand the deep connections between automorphic forms and Galois representations in the p-adic setting. Publication Trends: His most recent publications (2022–2023) show a strong focus on the derived and categorical aspects of the p-adic Langlands program, including the derived category of Hecke algebras and a categorical framework for the entire program. Earlier works established foundational results on the smoothness of eigenvarieties, the geometry of trianguline varieties, and the structure of moduli spaces for Galois representations. His research consistently bridges abstract algebra, number theory, and algebraic geometry. Scientific Awards: No specific awards or fellowships are mentioned in the provided texts. Advising and Grants: While a list of former research group members (e.g., Dr. Claudius Heyer, Dr. Damien Junger) is provided, their exact status as PhD advisees is not explicitly confirmed. He leads significant research projects funded by the DFG, including CRC 1442 - A01: Automorphic forms and the p-adic Langlands programme and CRC 1442 - A02: Moduli spaces of p-adic Galois representations , as well as a project within the EXC 2044 - A1: Arithmetic, geometry and representations cluster. He is also a co-author on a preprint titled "Patching and multiplicities of p-adic eigenforms," indicating active collaboration on grant-funded research. Labs and Teams: He is a central figure in the arithmetic geometry group at Münster. He organizes and leads the Research Seminar "p-adic arithmetic" and the Mittagsseminar "Arithmetic" , which serve as key forums for his research group and collaborators to present and discuss current work. His research team has included several postdoctoral researchers and doctoral students, contributing to a vibrant research environment focused on cutting-edge problems in number theory.

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Gergely ZábrádiView profile

Associate Professor

Eötvös Loránd UniversityHungary

Gergely Zábrádi is an Associate Professor and Head of the Department of Algebra and Number Theory at the Institute of Mathematics, Eötvös Loránd University (ELTE), Budapest. He earned his PhD from Trinity College, University of Cambridge, and conducted postdoctoral research at Westfälische Wilhelmsuniversität Münster. His academic focus lies at the intersection of algebraic number theory, Iwasawa theory, and the p-adic Langlands programme. Education: PhD in Mathematics, Trinity College, University of Cambridge (2008) Habilitation, Eötvös Loránd University (2016) Research Interests: Zábrádi's research spans algebraic number theory , particularly noncommutative Iwasawa theory for elliptic curves, and the p-adic Langlands programme . He explores deep connections between Galois representations , automorphic forms , and L-functions , utilizing tools like (φ,Γ)-modules and perfectoid spaces . Publications Overview: His recent work includes studies on generalized Montréal functors , matrix Kloosterman sums , and sup-norm problems for automorphic forms. These publications reflect a consistent engagement with foundational questions in arithmetic geometry and representation theory. Advising and Grants: Zábrádi has supervised numerous PhD, Master's, and Bachelor's theses, guiding students through topics ranging from Iwasawa theory to p-adic Galois representations . His mentorship has produced award-winning research, including first-prize recognition at the Hungarian Student Research Competition (OTDK). Research Groups and Labs: He leads a vibrant research group at ELTE, fostering collaboration with international scholars and participating in networks like the CENTRAL programme. His team focuses on advancing the p-adic Langlands correspondence and related arithmetic questions.

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Haluk SengunView profile

Senior Lecturer

University of SheffieldUnited Kingdom

Dr. Haluk Sengun is a Senior Lecturer of Pure Mathematics at the School of Mathematical and Physical Sciences, University of Sheffield. He is also a member of the One University Committee and holds a position in the Number Theory Group. His research focuses on cohomology and K-theory of arithmetic groups, automorphic forms, abelian varieties, Galois representations, and the Langlands Programme, with a particular emphasis on Bianchi groups within PSL(2,C). He has held post-doctoral positions at institutions including Barcelona, Bonn, Essen, and Warwick. Education: BSc from Istanbul Bilgi University and PhD from the University of Wisconsin-Madison. His work combines theoretical research with computational experiments to explore these areas. He teaches courses such as MAS220 Algebra and MAS430 Analytic Number Theory. Grants: Recipient of an EPSRC grant for 'A torsion Jacquet-Langlands Transfer via K-theory'. His research has been published in journals like Duke Mathematical Journal, Selecta Mathematica, and Commentarii Mathematici Helvetici. He maintains an active homepage with resources on his research and collaborations.

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Justin TriasView profile

Researcher

University of East AngliaUnited Kingdom

Justin Trias is a Senior Research Associate at the School of Mathematics , University of East Anglia (UEA) , with a focus on Algebra, Number Theory, and the Langlands Programme. He was previously a postdoctoral researcher at UEA (2019–2021) under Shaun Stevens , followed by a postdoc at Imperial College London (2021–2023) with David Helm . His current research is supported by an Engineering and Physical Sciences Research Council (EPSRC) grant (2022–2025), collaborating with Stevens on local theta correspondence and ℓ-modular representations. Education Doctor of Science (2015–2019), Sorbonne Université (Jussieu), Paris Master in Pure Mathematics (2013–2015), Université Pierre et Marie Curie (Jussieu), Paris Bachelor in Pure Mathematics (2010–2012), École Normale Supérieure, Cachan, France Agrégation Exam (2012–2013), France Research Interests Trias works at the intersection of Algebra and Number Theory, particularly within the Langlands Programme . His research emphasizes the modular representation theory of p-adic groups and its connections to the local Langlands Programme, with a special focus on local theta correspondence and its applications to representation theory. He explores tools like Harish-Chandra theory and Weil modules in characteristic not p to advance understanding of automorphic forms and dual pairs. Publications His work includes preprints on Local theta correspondences of supercuspidal representations (in preparation) and The universal Harish-Chandra character (with Gil Moss, in preparation). Recent publications span topics such as ℓ-modular local theta correspondence (2025), theta correspondence in families (2023), and Whittaker functionals in non-p characteristic (2022).

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Shaun StevensView profile

Professor

University of East AngliaUnited Kingdom

Shaun Stevens is Professor of Mathematics at the University of East Anglia, affiliated with the School of Engineering, Mathematics and Physics. He leads the Algebra, Number Theory, Logic, and Representations (ANTLR) research group and is actively involved in PhD supervision and research leadership. Education: Bachelor's in Mathematics, Gonville and Caius College, Cambridge PhD in Mathematics, King's College London, supervised by Prof. Colin Bushnell Postdoctoral experience at Université de Paris-Sud and Westfälische Wilhelms-Universität Münster His research lies at the intersection of Number Theory and Representation Theory , particularly focusing on the local Langlands correspondence , representations of p-adic groups , Hecke algebras , and buildings . He aims to make the Langlands correspondence explicit for classical groups such as orthogonal and symplectic groups. The recent publications highlight a strong trend in explicit constructions in representation theory, especially concerning supercuspidal and ℓ-modular representations of classical p-adic groups. His work often involves deep algebraic structures and connections to automorphic forms and arithmetic geometry. Scientific Awards and Recognition: EPSRC Leadership Fellowship (2010–2015) for “Explicit Correspondences in Number Theory” He has supervised ten PhD students and multiple postdoctoral researchers. His research has been supported by multiple EPSRC grants, including projects on the local theta correspondence and categorification of p-adic groups. He contributes to the academic community through editorial and peer-review roles. He is a member of the EPSRC Peer Review College and previously served as co-editor of the Bulletin of the London Mathematical Society (2009–2014). He also held leadership roles at UEA, including Head of School of Mathematics (2015–16, 2017–21).

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James NewtonView profile

Professor

University of OxfordUnited Kingdom

James Newton is a Professor of Number Theory at the University of Oxford's Mathematical Institute and Tutorial Fellow at Merton College. His research focuses on number theory, algebra, and geometry, particularly the Langlands programme and p-adic automorphic forms. He has held prior roles at King's College London, Cambridge, and Imperial College London. He currently serves as an editorial board member for Crelle's Journal, Essential Number Theory, Proceedings of the LMS, and Quarterly Journal of Mathematics. Research Interests: Newton's work centers on algebraic number theory, including p-adic automorphic forms, Galois representations, and their interactions with algebraic geometry. He explores symmetries of algebraic equations through the Langlands programme, advancing understanding of arithmetic structures and their geometric manifestations. Teaching & Advising: Newton supervises doctoral students in algebraic number theory and has taught courses at Oxford, King's, and Imperial College, including Group Representation Theory, Modular Forms, and Linear Algebra. His current advisees include Charlotte Clare-Hunt (co-supervised), Zachary Feng, and Håvard Damm-Johnsen. Labs/Teams: Engaged in collaborative research projects through editorial roles and international networks, contributing to advancements in number theory and representation theory.

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Dmitri WhitmoreView profile

Research Fellow

University of CambridgeUnited Kingdom

Dmitri Whitmore is a Research Fellow at Gonville and Caius College, University of Cambridge, within the Faculty of Mathematics and the Department of Pure Mathematics and Mathematical Statistics (DPMMS). His research centers on number theory, representation theory, and algebraic geometry through the Langlands programme framework. His academic background includes: PhD in Mathematics, University of Cambridge, 2024. Thesis: "The Taylor-Wiles method for reductive groups", supervised by Professor Jack Thorne. Whitmore's research explores profound connections between automorphic forms and Galois representations, with emphasis on reductive groups and modularity lifting. His work bridges abstract algebraic structures with analytic number theory, particularly through the lens of the Langlands correspondence, addressing foundational questions in arithmetic geometry and representation stability. His recent preprints reveal a cohesive trajectory in advancing the Langlands programme, focusing on Taylor-Wiles methodology extensions, automorphy criteria for local systems, and irreducibility properties of polarized representations. These contributions collectively strengthen the theoretical infrastructure for modularity theorems across diverse algebraic settings. Dr. Whitmore actively fosters academic collaboration at Cambridge through seminar organization, including a 2024 reading group on Caraiani-Newton's modularity work over imaginary quadratic fields and a 2023 preprint seminar, demonstrating leadership in community-driven mathematical research.

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Frazer JarvisView profile

Professor

University of SheffieldUnited Kingdom

Dr Frazer Jarvis is a Professor in Pure Mathematics and Mathematics Programme Lead at the School of Mathematical and Physical Sciences, University of Sheffield. His research focuses on algebraic number theory, modular forms, elliptic curves, and Galois representations, with contributions to the Langlands Program and generalizations of Fermat's Last Theorem. He has held a grant from the EPSRC on modularity of elliptic curves over totally real fields. Research Interests: Dr Jarvis explores advanced topics in number theory, including the interplay between modular forms and elliptic curves, Galois representations, and arithmetic geometry. He investigates extensions of Fermat's Last Theorem to other fields and equations, leveraging techniques from algebraic geometry and representation theory. Publications span 20+ years, including work on isogenies, theta lifts, and combinatorial problems like Sudoku enumeration. Teaching responsibilities include modules like MAS111 Mathematics Core II and MAS369 Machine Learning. Member of the Number Theory research group at the University of Sheffield. His recent articles address cutting-edge questions in number theory, such as the modularity of elliptic curves, p-adic analysis, and applications to algebraic structures. He actively contributes to both theoretical advancements and pedagogical innovations.

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Payman KassaeiView profile

Professor

King’s College LondonUnited Kingdom

Professor Payman Kassaei is a leading academic in Number Theory at King's College London, Department of Mathematics. He holds the rank of Professor and specializes in Arithmetic Geometry, focusing on the interplay between modular forms, Galois representations, and Shimura varieties. His research emphasizes p-adic methods, including overconvergent modular forms and their role in the p-adic Langlands programme. Kassaei obtained his PhD from MIT in 1999 and has held positions at institutions like McGill University before joining King's in 2006. Education: PhD in Mathematics from MIT (1999) Affiliations: Member of the Number Theory group at King's College London His research explores congruences between modular forms modulo primes, leveraging cohomology studies over Shimura varieties. Key topics include Hilbert modular forms, canonical subgroups, and mod p dynamics of Hecke operators. Kassaei has contributed to major projects like the Langlands Programme and has held EPSRC grants. His work appears in prestigious journals such as Compositio Mathematica and Astérisque . Recent publications highlight advancements in Jacquet-Langlands relations, minimal weights of Hilbert modular forms, and p-adic dynamics. His 2023 paper on Jacquet-Langlands relations and Serre filtration exemplifies his innovative use of geometric methods. Kassaei has organized conferences and delivered invited lectures, including a 2024 inaugural lecture on 'Arithmetic and Geometry.' Grants include leadership in the EPSRC-funded 'Langlands reciprocity and the geometry of Shimura varieties.' Collaborations with scholars like Fred Diamond and Shu Sasaki underscore his international impact in arithmetic geometry.

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Yiwen DingView profile

Associate Professor

Max Planck Institute for MathematicsGermany

Yiwen Ding is an Associate Professor at the Beijing International Center for Mathematical Research (BICMR), Peking University. His research focuses on advanced topics in pure mathematics, particularly the intersection of number theory and representation theory. He specializes in the p-adic Langlands program, exploring its arithmetic applications through innovative approaches to Galois representations and automorphic forms. Research Interests: Dr. Ding's work centers on: Number Theory : Especially p-adic aspects and arithmetic applications Representation Theory : With emphasis on locally analytic representations of p-adic groups p-adic Langlands Programme : Bridging automorphic forms and Galois representations L-invariants & Local-Global Compatibility : Fundamental constructs in modern arithmetic geometry His publications demonstrate consistent focus on p-adic methods in representation theory, featuring advancements in: L-invariants, locally analytic representations, deformation theory, and the geometric Langlands correspondence. Recent work (2023-2024) shows deepened exploration of crystabelline representations and weight structures in p-adic contexts. No scientific awards, student advisees, or grant information are mentioned in available materials.

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Judith LudwigView profile

Professor

Heidelberg UniversityGermany

Judith Ludwig is a Professor of Mathematics at Heidelberg University. Her research focuses on the Langlands programme through the lens of arithmetic geometry, particularly exploring the interplay between representation theory and non-archimedean geometry within the theory of p-adic automorphic forms. No educational background, academic awards, grants, or supervised students are explicitly mentioned in the provided text. She does not appear to be associated with specific laboratories or research teams based on the available information.

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