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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.

• 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.

Christopher DeningerView profile

Professor

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

Christopher Deninger is a distinguished Professor in the Mathematical Institute at the University of Münster, Germany, where he leads research in Arithmetic Geometry and Representation Theory. His office is located in Room 413 of the Einsteinstr. 62 building, and he maintains active teaching responsibilities including courses in Representation Theory of Finite Groups, Linear Algebra, and specialized topics like Adic Spaces. Deninger's research spans multiple interconnected domains of modern mathematics, with a consistent focus on the deep connections between number theory and geometry. His work has evolved from classical arithmetic geometry to incorporate increasingly sophisticated connections with p-adic analysis, dynamical systems, and more recently proalgebraic fundamental groups. A unifying theme throughout his career has been exploring analogies between different mathematical structures, particularly those connecting analytic number theory with dynamical systems on foliated spaces. His recent publications reveal a continued expansion of his research program into new territories while maintaining connections to his foundational work. The most recent papers show increasing integration of algebraic topology concepts with arithmetic geometry, particularly through proalgebraic fundamental groups and their applications. The consistent thread throughout his decades of publications is the search for deeper structural connections between seemingly disparate areas of mathematics, particularly those bridging analysis, geometry and number theory. Professor Deninger has mentored an extensive number of doctoral students and postdoctoral researchers, as evidenced by the comprehensive list of former members in his working group. His collaborations span the international mathematical community, with numerous joint publications with leading mathematicians across Europe and beyond. While specific grant information isn't detailed in the available materials, his sustained publication record across decades suggests consistent research support for his mathematical investigations. The Mathematical Institute at Münster provides the institutional home for Deninger's research activities, where he maintains an active working group focused on arithmetic geometry and related fields. His office environment includes support staff and colleagues working in closely related mathematical domains, creating a vibrant research community centered around advanced topics in pure mathematics.

Lars HesselholtView profile

Professor

• Algebraic Topology
• K-Theory
• Homological Algebra
• +3 more

Lars Hesselholt is a Professor at the Department of Mathematical Sciences, University of Copenhagen, and a key member of the Copenhagen Centre for Geometry and Topology (GeoTop). His research focuses on the intersection of algebraic topology, K-theory, and arithmetic geometry, with significant contributions to topological Hochschild homology and its applications to number theory and algebraic geometry. His recent work includes advancements in Dirac geometry, connections between topological cyclic homology and the Fargues–Fontaine curve, and studies on the K-theory of division algebras over local fields. These publications highlight his role in bridging homotopy theory with arithmetic structures. Hesselholt maintains an active research profile, with 36 research outputs documented, including collaborations with mathematicians like Thomas Nikolaus, Morten Larsen, and Ayelet Lindenstrauss. His work spans topological methods in algebraic geometry, cyclic homology, and noncommutative geometry. For correspondence, he can be reached at larsh@math.nagoya-u.ac.jp or via phone at +4551319971. His office is located at Universitetsparken 5, 2100 København Ø, Denmark.

• Algebraic Topology
• K-theory
• Group Theory
• +8 more

Irakli Patchkoria is a Lecturer in the Department of Mathematics at the University of Aberdeen, affiliated with the School of Natural and Computing Sciences. His research focuses on algebraic topology, K-theory, and homological algebra, with contributions to equivariant stable homotopy theory and Witt vectors. Research Interests: Algebraic Topology, K-Theory, Group Theory, Homological Algebra, Morava K-Theory, Algebraic Models for Homotopy Theories, Witt Vectors, de Rham-Witt Complex, TC and THH Computations, Equivariant Stable Homotopy Theory. The recent publications highlight his work on Adams spectral sequences, Witt vectors with coefficients, cyclic homology of differential graded algebras, and geometric fixed points of real topological cyclic homology. These contributions intersect algebraic topology, homotopy theory, and noncommutative geometry. Irakli is responsible for public outreach in his department and organizes the Aberdeen Topology Seminar. He has secured an EPSRC grant for research on classifying spaces and stable homotopy theory.

• Algebraic Number Theory
• p-adic Analysis
• Iwasawa Theory
• +6 more

Prof. Dr. Johannes Sprang is a Professor at the University of Duisburg-Essen, Faculty of Mathematics, leading the Research Group Sprang (RG Sprang). His research focuses on algebraic number theory, p-adic analysis, and Iwasawa theory, with notable contributions to zeta values, elliptic polylogarithms, and cohomological realizations. He advises two PhD students: Guillermo Gamarra Segovia and Riccardo Tosi. His academic background includes a PhD in Mathematics (2017) from the University of Duisburg-Essen, with a thesis on Eisenstein series via the Poincaré bundle and applications. His research interests span p-adic L-functions, transcendence theory, and complex geometry, with a particular emphasis on modular forms and abelian varieties. Teaching responsibilities include courses such as Algebraic Number Theory , Complex Geometry , and Iwasawa Theory . Recent courses highlight his expertise in number theory and geometric methods. His work frequently intersects with algebraic topology and arithmetic geometry, addressing topics like syntomic cohomology and topological modular forms. Prof. Sprang’s publications emphasize the irrationality of zeta values, p-adic interpolation, and cohomological comparisons. His research group collaborates internationally, with projects involving co-authors such as Guido Kings, Wadim Zudilin, and Nobuaki Naumann. No scientific awards are explicitly listed, though his contributions are widely recognized in number theory circles.

Sanath DevalapurkarView profile

Research Fellow

• Algebraic Topology
• Geometric Representation Theory
• Chromatic Homotopy Theory
• +2 more

Sanath Devalapurkar is a Dickson instructor in the Department of Mathematics at the University of Chicago for the 2025-26 academic year, with upcoming positions at the Institute for Advanced Study (Fall 2026) and Johns Hopkins University (as Assistant Professor thereafter). His academic career spans prestigious institutions including Harvard University and MIT. His educational background includes: PhD in Mathematics from Harvard University (completed 2025), advised by Mike Hopkins and Dennis Gaitsgory Undergraduate degree in Mathematics (Course 18) with a minor in Physics (Course 8) from MIT (completed 2020) Devalapurkar's research spans multiple interconnected areas of modern mathematics. His primary interests lie in algebraic topology, particularly chromatic homotopy theory and its connections to other fields. He investigates characteristic p geometry, exploring deep connections between homotopy theory and arithmetic geometry. His work in geometric representation theory focuses on the geometric Langlands program and its generalizations, especially through the lens of higher category theory and derived algebraic geometry. A unifying theme in his research is the application of homotopical methods to solve problems in representation theory and algebraic geometry, often revealing unexpected connections between seemingly disparate mathematical domains. His work demonstrates sophisticated use of spectral sequences, EHP sequences, and Hopf fibrations to bridge abstract homotopy theory with concrete geometric problems. His publication record demonstrates a consistent trajectory from foundational work in unstable homotopy theory toward increasingly sophisticated applications in geometric representation theory. Early publications established results in chromatic phenomena and Thom spectra, while more recent work explores intricate connections between geometric Langlands duality and generalized cohomology theories. His research shows particular strength in identifying and exploiting analogies between different mathematical structures, such as the relationship between the geometric Satake equivalence and chromatic homotopy theory. His papers frequently combine deep technical results with broader conceptual frameworks that illuminate connections across mathematical disciplines. As an educator, Devalapurkar has taught a variety of courses including Math 99r on integrable systems (Spring 2024) and Math 1b (Calculus, Series, and Differential Equations) at Harvard (Fall 2022). He has served as a teaching assistant for advanced courses in algebraic number theory (Math 223a) and algebraic topology (Math 231b). He has mentored numerous reading projects through Harvard's Directed Reading Program, covering topics from surfaces and Chern classes to prismatic cohomology. He also actively mentors high school students through the PRIMES USA program, demonstrating commitment to nurturing mathematical talent at all levels. Additionally, he organizes seminars including one on "Arnold's trinities" with Thomas Brazelton and another on relative Langlands duality with Ben Gammage.

• Arithmetic Geometry
• p-adic Cohomology
• p-adic Hodge Theory
• +4 more

Oliver Gregory is a Heilbronn Research Fellow in the Department of Mathematics at Imperial College London, affiliated with the Faculty of Natural Sciences. His research focuses on arithmetic geometry, particularly p-adic cohomology, p-adic Hodge theory, and applications to algebraic cycles, K-theory, and motivic cohomology. He has authored multiple influential papers in journals like Journal of Pure and Applied Algebra and Canadian Mathematical Bulletin . Dr. Gregory’s academic contributions include work on torsion cycles in abelian varieties, log-motivic cohomology for semistable varieties, and Hodge-Witt decompositions. He completed his PhD on crystals of relative displays and Grothendieck-Messing deformation theory. In late 2023, he taught an advanced LTCC course on Beilinson's Conjectures, with lecture notes and exercise sheets publicly available. His research interests bridge algebraic geometry and number theory, with particular emphasis on p-adic methods, cohomological approaches to arithmetic problems, and geometric structures in mixed characteristic settings. He has collaborated with prominent mathematicians such as Prof. Achim Langer and Prof. Christian Liedtke.

• Algebraic Geometry
• Number Theory
• Homological Algebra

Alexander Petrov is a Clay Research Fellow at the Massachusetts Institute of Technology (MIT), conducting research at the intersection of algebraic geometry, number theory, and homological algebra. He completed his PhD in Mathematics at Harvard University in 2022 under the supervision of Professor Mark Kisin. Education PhD in Mathematics, Harvard University, 2022 (Advisor: Mark Kisin) Research Interests Petrov's work centers on advanced problems in arithmetic geometry, particularly in positive characteristic settings. His research investigates structural properties of de Rham complexes, p-adic Hodge theory, and the arithmetic of algebraic varieties, with significant contributions to understanding Galois representations, Brauer groups, and cyclic homology through homological algebra techniques. His methodologies often bridge abstract algebraic frameworks with concrete geometric applications. Publications Overview His publication record (2017-2025) reveals a consistent focus on foundational questions in arithmetic geometry, featuring deep explorations of cohomology theories, spectral sequences for algebraic groups, and p-adic local systems. Key trends include the decomposition of de Rham complexes in positive characteristic, violations of Hodge symmetry in rigid-analytic contexts, and universal properties of Galois actions. Collaborations with leading mathematicians like Alexei Skorobogatov and Vadim Vologodsky underscore his integration into the global mathematics community. Awards and Honors Clay Research Fellow (current) Advising and Collaborations As a postdoctoral fellow, Petrov was previously advised by Mark Kisin during his doctoral studies at Harvard. No current advisees are mentioned, but his extensive co-authorship network—including frequent work with Skorobogatov and Vologodsky—demonstrates active collaborative research. His publications appear in premier journals such as Duke Mathematical Journal, Compositio Mathematica, and Selecta Mathematica, reflecting significant contributions to the field.

• Algebraic Topology
• Algebraic K-Theory
• p-adic Arithmetic Geometry
• +4 more

Akhil Mathew is an Associate Professor in the Department of Mathematics at the University of Chicago. He completed his PhD at Harvard University under Jacob Lurie in 2017. His research focuses on algebraic topology, algebraic K-theory, and p-adic arithmetic geometry, with contributions to prismatic cohomology and derived algebraic geometry. He organizes workshops like the Workshop on p-adic Geometry and contributes to editorial boards of Compositio Mathematica and Nagoya Mathematical Journal . Teaching includes advanced courses such as Honors Basic Algebra III and topics in commutative algebra. His work bridges homotopy theory and arithmetic geometry, with recent collaborations on syntomic complexes and étale cohomology. Education: PhD in Mathematics (2017), Harvard University Research Interests: Homotopy theory, arithmetic geometry, prismatic cohomology Recent Activities: Organized 2024 p-adic Geometry workshop; co-authored papers on syntomic complexes and K-theory Teaching Highlights: Courses include Algebra II, Honors Basic Algebra, and special topics in condensed mathematics. His lectures and seminars on geometric Langlands and derived algebraic geometry are widely recognized.

Hélène EsnaultView profile

Professor

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

Hélène Esnault is a Professor at the University of Duisburg-Essen, where she directs a research group focused on algebraic geometry. She holds an honorary doctorate (Dr. h.c.) and has supervised over 20 doctoral students and postdoctoral researchers. Her research spans algebraic geometry, arithmetic geometry, Hodge theory, singularity theory, and fundamental groups, with significant contributions to D-modules and algebraic cycles. Her work frequently explores connections between characteristic zero and positive characteristic settings, with emphasis on rational points over finite fields, fundamental group schemes, and cohomological methods. She maintains active collaborations with prominent mathematicians globally. Awards & Honors: Dr. h.c. (honorary doctorate) Research Group: Leads the Research Group Esnault at Essen Seminar, mentoring students and postdocs in algebraic geometry.

Ravi FernandoView profile

Research Professor

• Algebraic Geometry
• p-adic Cohomology
• Arithmetic Geometry
• +1 more

Ravi Fernando is a Research Professor in the Department of Mathematics at the University of Illinois Urbana-Champaign, where he has held the J.L. Doob Research Assistant Professorship since 2023. He obtained his Ph.D. from UC Berkeley under Martin Olsson and completed his undergraduate studies at Stanford University. His research focuses on: p-adic cohomology theories in mixed characteristic Algebraic geometry over characteristic p De Rham-Witt complexes and related structures Fernando's publications demonstrate consistent focus on arithmetic geometry, evolving from combinatorial group theory to advanced p-adic methods. His 2023 thesis represents significant contributions to cohomology theory. He has organized several academic events: 2018 & 2021 Berkeley Arithmetic Geometry RTG Workshops 2020 Berkeley Undergraduate Number Theory Conference Since 2019, he serves as mathematical advisor for PrimeGrid, a distributed computing project for prime number discovery.