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

Prof. Peter Scholze is a leading mathematician at the University of Bonn and the Max Planck Institute for Mathematics (MPIM). He holds a professorship in the Mathematical Institute at the University of Bonn and is affiliated with MPIM as a principal investigator. His research focuses on arithmetic geometry, representation theory, and p-adic geometry, with notable contributions to perfectoid spaces, prismatic cohomology, and the geometrization of the local Langlands correspondence. Scholze has organized several advanced seminars (ARGOS) and taught courses on topics like condensed mathematics, p-adic geometry, and algebraic geometry. He collaborates widely with researchers such as Laurent Fargues and Bhargav Bhatt. His recent work includes groundbreaking papers on wild Betti sheaves, motivic geometrization of the local Langlands correspondence, and the Habiro ring of number fields. Scholze has pioneered the use of prismatic cohomology to unify p-adic Hodge theories and has developed foundational frameworks in derived algebraic geometry. His research also intersects with representation theory and topological cyclic homology. Affiliations: University of Bonn (Mathematical Institute), Max Planck Institute for Mathematics (MPIM) Research Groups: Arbeitsgruppe Arithmetische Geometrie und Darstellungstheorie Teaching: Recent courses include 'Selected Topics in Algebraic Geometry' and 'Six-Functor Formalisms'. His work frequently explores connections between algebraic geometry and number theory, with a focus on geometric approaches to arithmetic problems. Scholze is a key figure in modern arithmetic geometry, influencing both foundational theory and applied areas like the Langlands program.

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.

• Algebraic Geometry
• Arithmetic Geometry
• Number Theory
• +5 more

Prof. Peter Scholze is a leading mathematician at the Max Planck Institute for Mathematics in Bonn, specializing in algebraic geometry and arithmetic geometry. He holds the academic rank of Professor and is part of the Arbeitsgruppe Algebraische Geometrie und Darstellungstheorie. His research focuses on foundational questions in algebraic geometry, number theory, and representation theory, particularly through the lens of the Langlands program, p-adic Hodge theory, and perfectoid spaces. Scholze has pioneered geometric approaches to the local Langlands correspondence and introduced revolutionary concepts like prismatic cohomology and condensed mathematics. He actively contributes to academia through advanced courses on topics such as geometrization of the Langlands program, étale cohomology, and condensed mathematics. His work bridges algebraic geometry with representation theory, addressing fundamental problems in arithmetic geometry and p-adic analysis. Scholze’s research outputs include seminal papers on perfectoid spaces, prismatic cohomology, and the geometrization of local Langlands correspondence. He collaborates extensively with leading mathematicians globally, contributing to collaborative research initiatives like the ARGOS seminar and the Habiro ring project. His teaching engagements include advanced lectures on algebraic geometry, representation theory, and p-adic geometry, reflecting his commitment to training the next generation of researchers. Despite no explicitly listed awards in the provided text, Scholze is widely recognized as a Fields Medalist (2018) and a leading figure in modern mathematics.

Brian ConradView profile

Professor

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

Brian Conrad is a Professor of Mathematics at Stanford University, specializing in number theory and arithmetic geometry. He holds a position in the Department of Mathematics and has contributed extensively to algebraic geometry, algebraic number theory, and representation theory. His research encompasses foundational work on reductive groups, pseudo-reductive groups, and their applications in arithmetic contexts. Dr. Conrad is an editor for the Journal of the AMS, Algebra and Number Theory, and IMRN. He has organized numerous learning seminars, including those on étale cohomology and the BSD conjecture, and has taught advanced courses on algebraic geometry, class field theory, and modular forms. His work bridges classical algebraic geometry with modern arithmetic applications, emphasizing foundational proofs and geometric intuition. His editorial roles and seminar leadership reflect his commitment to advancing mathematical exposition and education. Education details are not explicitly provided in the texts, but his academic trajectory includes significant contributions to the field through publications and mentorship. Dr. Conrad's research has led to advancements in areas such as the classification of algebraic groups, étale cohomology, and the arithmetic of elliptic curves. His collaborative work with mathematicians like Chai, Oort, and Prasad has produced influential monographs, including Pseudo-reductive Groups and Complex Multiplication and Lifting Problems .

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.

David NadlerView profile

Professor

• Geometric Representation Theory
• Symplectic Geometry
• Langlands Duality
• +3 more

David Nadler is a Professor in the Department of Mathematics at the University of California, Berkeley, appointed in 2012. His research centers on geometric representation theory and symplectic geometry, with significant contributions to the Langlands program, microlocal sheaf theory, and symplectic topology. He maintains an active research group and teaches courses ranging from undergraduate linear algebra to graduate algebraic topology and geometry. Nadler's research explores the interface of algebraic geometry, topology, and representation theory. His work in geometric representation theory focuses on Langlands duality, Springer theory, and Betti geometric Langlands. In symplectic geometry, he investigates microlocal sheaves, Fukaya categories, and Weinstein structures. His recent publications demonstrate a consistent focus on categorical methods in geometric Langlands correspondence and symplectic arborealization. His publications consistently emphasize categorical and geometric approaches to representation theory. Recent works cluster in three areas: (1) extensions of the geometric Langlands program to Betti cohomology settings, (2) microlocal analysis of sheaves on symplectic manifolds, and (3) combinatorial models in symplectic topology. This reflects sustained development of 'Betti geometric Langlands' as a distinct research program bridging topology and automorphic forms. Nadler has advised over a dozen PhD students since 2012, with dissertations spanning geometric representation theory, symplectic geometry, and algebraic topology. Student projects frequently investigate categorical aspects of geometric Langlands, microlocal sheaves, and combinatorial models in symplectic topology.

Eva ViehmannView profile

Professor

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

Prof. Dr. Eva Viehmann is a leading mathematician at the University of Münster within the Faculty of Mathematics and Computer Science and a key figure in the Mathematics Münster cluster. She was awarded the prestigious Gottfried Wilhelm Leibniz Prize 2024 for her groundbreaking work in arithmetic algebraic geometry and representation theory within the Langlands program . University: University of Münster Department: Mathematical Institute Her research focuses on the intersection of algebra , geometry , and analysis , particularly through the lens of Shimura varieties and moduli spaces of local G-shtukas . She has pioneered the study of affine Deligne-Lusztig varieties in equal and mixed characteristics, advancing understanding of their dimension , connectedness , and irreducible components . Recent publications highlight her work on Newton stratification , Harder-Narasimhan theory , and p-adic moduli spaces . Her scientific advisory contributions include mentoring former doctoral student Stefania Trentin and collaborating with Prof. Urs Hartl over 15 years. Awards and honors include the Leibniz Prize 2024 , reflecting her status as a trailblazer in arithmetic geometry and p-adic geometry . Her research projects span the CRC 1442 and EXC 2044 , aiming to unify Galois representations , automorphic forms , and geometric methods .

Urs HartlView profile

Professor

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

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.

• Mathematics
• Machine Learning
• Quantum Topology
• +9 more

Sergei Gukov is the John D. MacArthur Professor of Theoretical Physics and Mathematics at the California Institute of Technology (Caltech), where he has been a faculty member since 2005. He serves in the Division of Physics, Mathematics and Astronomy, with primary affiliation in the Department of Mathematics. His research bridges the fields of mathematics and theoretical physics, focusing on deep connections between geometry, topology, and quantum field theory. Gukov received his B.S. from Moscow Institute of Physics and Technology in 1997, followed by an M.S. and Ph.D. from Princeton University in 2001. He joined Caltech as an Associate Professor in 2005, was promoted to Professor in 2007, and was named the John D. MacArthur Professor in 2021. His research spans several interconnected areas at the frontier of mathematics and physics. A central theme is the exploration of quantum topology and its connections to mathematical physics. He has made significant contributions to the geometric Langlands program, gauge theory, and the categorification of knot and 3-manifold invariants. His recent work increasingly incorporates machine learning approaches to mathematical problems, reflecting his interest in the intersection of traditional mathematical research and modern computational techniques. Gukov's work often reveals deep connections between seemingly disparate areas of mathematics and physics, such as the relationship between Rozansky-Witten geometry and Coulomb branches in supersymmetric gauge theories. Gukov's publications demonstrate a consistent focus on the mathematical structures underlying quantum field theories and their topological implications. His recent work shows an increasing emphasis on computational approaches to mathematical problems, particularly through his interest in mathematics and machine learning. The recurring themes across his research include the application of physical insights to solve mathematical problems and the discovery of new mathematical structures through physical reasoning. He serves on the editorial boards of several prestigious journals including the Journal of Knot Theory and Its Ramifications, Communications in Mathematical Physics, and Letters in Mathematical Physics. Gukov is also active in the academic community, having delivered plenary talks at major conferences such as the First International Congress of Basic Science and presenting at String Math 2023 on the potential impact of AI on mathematical research. Gukov teaches Ma 146 ab, Introduction to Knot Theory and Quantum Topology, a course that reflects his research interests. He also runs a seminar on Mathematics and Machine Learning, held Tuesdays from 2-3pm in East Bridge Conference room 114, demonstrating his commitment to fostering interdisciplinary research at the intersection of mathematics and computational methods.

Ana CaraianiView profile

Professor

• Number Theory
• Arithmetic Geometry
• Langlands Program
• +3 more

Ana Caraiani is a Royal Society University Research Fellow and Professor in the Department of Mathematics at Imperial College London, specializing in Number Theory and Arithmetic Geometry. She is a member of the Number Theory group, focusing on the Langlands program, Shimura varieties, and p-adic Galois representations. Her work bridges arithmetic geometry and representation theory, with contributions to modularity lifting theorems, cohomology of Shimura varieties, and local-global compatibility in the Langlands program. Education: She earned a Ph.D. in Mathematics from Harvard University in 2012. She held positions as a Veblen Research Instructor (2013–2015) and Veblen Fellow (2015–2016) at the Institute for Advanced Study's School of Mathematics. Research Interests: Her research emphasizes the classical and p-adic Langlands programs, Shimura varieties, arithmetic geometry, and moduli stacks of Galois representations. Specific topics include vanishing theorems for cohomology, modularity of elliptic curves over CM fields, and applications of perfectoid spaces. Key Contributions: Caraiani has advanced the proof of modularity of elliptic curves over imaginary quadratic fields, established vanishing theorems for Shimura varieties with torsion coefficients, and contributed to the potential automorphy of Galois representations over CM fields. Her work links geometric approaches to arithmetic conjectures, such as the Sato-Tate and Ramanujan conjectures. Awards and Recognition: Royal Society University Research Fellowship (202?), Veblen Research Instructor/Fellowships (2013–2016), and contributions to major collaborative projects like the Potential Automorphy over CM Fields paper in the Annals of Mathematics.

David SavittView profile

Professor

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

David Savitt is a Professor and Chair of the Department of Mathematics at Johns Hopkins University, affiliated with the Krieger School of Arts & Sciences. His research focuses on algebraic number theory, with emphasis on Galois representations, modular forms, and p-adic Hodge theory. He holds a PhD from Harvard University and has served on the board of directors for Canada/USA Mathcamp, a summer program for high school students. His work spans theoretical contributions to arithmetic geometry, including studies on moduli stacks of Galois representations and geometric aspects of the p-adic Langlands program. Education: PhD in Mathematics from Harvard University. Research interests include the interplay between Galois representations and modular forms, p-adic Hodge theory, and moduli spaces. His recent work explores geometric structures in the Emerton-Gee stack and the Breuil-Mézard conjecture. Over 20 years of research has produced influential papers on topics like Serre weight conjectures and crystalline lifts of Galois representations. Professional contributions include editorial roles for journals and books, such as co-editing p-adic Geometry: Lectures from the 2007 Arizona Winter School . His involvement with Mathcamp highlights his dedication to nurturing young talent in mathematics.

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.

Benjamin GammageView profile

Research Fellow

• Geometry
• Algebra
• Mathematical physics
• +6 more

Benjamin Gammage is a Benjamin Peirce Fellow in the Department of Mathematics at Harvard University. Beginning in Summer 2025, he will transition to an Assistant Professor position at the University of Toronto. His academic journey includes a PhD from UC Berkeley under David Nadler, where his thesis focused on microlocal sheaves and mirror symmetry, and an undergraduate degree with honors from the University of Chicago. Dr. Gammage's research centers on quantum geometry, exploring the deep connections between geometry, algebra, and mathematical physics. His work particularly focuses on homological mirror symmetry and 3d mirror symmetry, investigating how quantum field theories reveal profound relationships between seemingly different geometric spaces. He has made significant contributions to understanding how the structure of SYZ fibrations mediates mirror symmetry and how perverse schobers can categorify aspects of geometric representation theory. His research has followed a clear trajectory from foundational work on mirror symmetry for affine hypersurfaces toward increasingly sophisticated structures in 3-dimensional field theories. The most recent publications demonstrate a progression from studying 1- and 2-dimensional quantum field theories toward fully categorified 3d mirror symmetry, revealing deep structural connections between representation theory and symplectic geometry. 2023-present: Principal Investigator, NSF DMS grant #2305257 2020: NSF Postdoctoral Research Fellowship 2019: Kenneth Ribet and Lisa Goldberg Award in Algebra 2015: NSF Graduate Research Fellowship 2014: Paul R. Cohen Prize Dr. Gammage has served as a minor thesis advisor for Grant Barkley (2022) and has been actively involved in mentoring through Harvard's Graduate Admissions Committee and as a Math Includes mentor. His research is supported by significant grant funding, including his current NSF grant. He has organized numerous seminars including the Open Neighborhood Seminar, Relative Langlands seminar, and various topics in mirror symmetry and string theory. His collaborative work spans multiple institutions, with frequent collaborations at institutions including the University of Toronto, UC Berkeley, and various international research centers. His research program bridges pure mathematics with theoretical physics, creating new frameworks for understanding geometric structures through quantum field theory perspectives.

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.

Peter SchneiderView profile

Professor

• Arithmetic geometry
• Representation theory
• Cohomology theories
• +7 more

Prof. Dr. Peter Schneider is a faculty member at the University of Münster, affiliated with the Faculty of Mathematics and Computer Science and the Department of Mathematics and Computer Science . He is a principal investigator in the CRC 1442 Geometry: Deformations and Rigidity and contributes to the Mathematics Münster cluster. University: University of Münster School: Faculty of Mathematics and Computer Science Department: Department of Mathematics and Computer Science Academic Rank: Professor His research focuses on arithmetic geometry and representation theory , particularly the p-adic Langlands program , cohomology theories in mixed characteristics, and noncommutative algebraic structures. He investigates derived categories of p-adic representations, moduli spaces of Galois representations, and geometric approaches to automorphic forms. He has supervised numerous students, including Torsten Schoeneberg (2009), Marten Bornmann (2009), and Marius Kley (2016, 2019). His collaborative works with Rachel Ollivier, Otmar Venjakob, and Marie-France Vigneras explore modular Hecke algebras, Iwasawa theory, and (phi, Gamma)-modules. Emails: pschnei@wwu.de pschnei@uni-muenster.de Workshops Organized: Noncommutative Algebras (2006) Instructional workshop on noncommutative main conjectures (2011) International workshop on K-types for p-adic groups (2003)