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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.

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

• Number Theory
• Representation Theory
• 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 .

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

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

• Number Theory
• Arithmetic Geometry
• Automorphic Forms
• +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.

• Geometric Representation Theory
• Symplectic Geometry
• Langlands Duality
• +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).

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

• Algebraic Combinatorics
• Total Positivity
• Cluster Algebras
• +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.

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

• Number Theory
• Algebraic Number Theory
• Arithmetic Geometry
• +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.

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

Elena Mantovan is the Taussky-Todd-Lonergan Professor of Mathematics at the California Institute of Technology (Caltech), within the Department of Mathematics under the Division of Physics, Mathematics and Astronomy. She holds a Laurea from the University of Padova (1995), an M.A. from Harvard University (1998), and a Ph.D. from Harvard (2002). Her research focuses on Arithmetic Geometry and Number Theory, particularly the study of moduli spaces of abelian varieties, Barsotti-Tate groups, and the arithmetic theory of Shimura varieties. Her work contributes to the Langlands program, exploring connections between automorphic forms and Galois representations. Elena joined Caltech as an Assistant Professor in 2005, advancing to Associate Professor (2010), full Professor (2010-2023), and her current title (2023-). She served as Executive Officer for the Department of Mathematics from 2016 to 2019. Her research interests emphasize Shimura varieties, Newton stratifications, and cohomological studies, reflecting her expertise in algebraic geometry and number theory. Despite no listed awards, her scholarly contributions include foundational work on Rapoport-Zink spaces and Igusa varieties. Elena’s advising and grants are not explicitly detailed in the provided texts, though her role as an academic leader suggests involvement in mentorship and institutional projects. She maintains an office in Sloan Hall and collaborates on initiatives like the Southern California Number Theory Day Conference and the Number Theory seminar.

• Arithmetic Geometry
• Number Theory
• Moduli Spaces
• +3 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).

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

• Algebraic Geometry
• Geometric Langlands Program
• Moduli Spaces
• +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.

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