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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.

Zsolt PatakfalviView profile

Associate Professor

• Algebraic Geometry
• Commutative Algebra
• Birational Geometry
• +3 more

Zsolt Patakfalvi is an Associate Professor at École Polytechnique Fédérale de Lausanne (EPFL), holding positions in the School of Basic Sciences (SB) within the Department of Mathematics (MATH). He is affiliated with the Chair of Algebraic Geometry (CAG) and the Section of Mathematics for Engineers (SMA-ENS). Additionally, he serves as Director of SMA-GE and holds roles in academic governance bodies like the Conference of Section Directors (CDS) and SB Faculty Management. His research focuses on Algebraic Geometry, particularly in birational geometry, positive characteristic methods, moduli theory, and mixed characteristic algebra. He explores topics such as Hodge theory, singularities, and applications to arithmetic geometry. Notable contributions include work on the minimal model program, test ideals, and counterexamples to classical conjectures in positive characteristics. He supervises doctoral students in areas like algebraic geometry and commutative algebra, including Jefferson Baudin, Léo Navarro Chafloque, and Linus Rösler. His past advisees include Emelie Arvidsson and Quentin Posva. Patakfalvi’s publications frequently address foundational questions in geometry, with recent work extending into perfectoid spaces and globally-regular varieties. He coordinates courses such as 'Algebra III - Rings and Fields' and 'Perfectoid spaces' at EPFL, reflecting his commitment to both research and education. His academic service includes managing educational programs within SB-SMA and contributing to institutional decision-making through CDS membership.

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)

Qile ChenView profile

Associate Professor

• Algebraic Geometry
• Moduli Spaces
• Logarithmic Geometry
• +3 more

Qile Chen is an Associate Professor in the Department of Mathematics at Boston College . His research focuses on Algebraic Geometry , particularly in Logarithmic Geometry , Moduli Spaces , and Gromov-Witten Theory . He has made significant contributions to understanding A^1-connectedness , Stable Log Maps , and Virtual Cycles in geometric contexts. His publications include collaborations with leading mathematicians such as Dan Abramovich , Felix Janda , Yi Zhu , and Dawei Chen . Key topics span Logarithmic GLSM , Multi-scale Differentials , and Spin/Hyperelliptic Structures . Recent Articles : Punctured logarithmic maps (2025), Gorenstein contractions (2024), Campana rational connectedness (2024) Co-advised Student : Zijian Han (Ph.D. in progress at Boston College)

Gyujin OhView profile

Assistant Professor

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

Gyujin Oh is a Ritt Assistant Professor in the Department of Mathematics at Columbia University's Faculty of Arts and Sciences. He received his PhD in mathematics from Princeton University in 2022 under the supervision of Christopher Skinner and Akshay Venkatesh. Prior to joining Columbia, he was a postdoctoral member of the SLMath/MSRI program Algebraic Cycles, L-Values, and Euler Systems in Spring 2023. Dr. Oh's research spans multiple areas of number theory and arithmetic geometry. His primary interests include Algebraic Number Theory, the Langlands Program, Modular Forms, Galois Representations, and Arithmetic Geometry. His work often bridges classical number theory with modern geometric approaches, exploring connections between automorphic forms, cohomology theories, and arithmetic structures. He has made contributions to understanding rigid local systems, the Néron-Ogg-Shafarevich criterion, and various aspects of the Langlands correspondence. His recent publications demonstrate a strong focus on advanced topics in number theory, particularly exploring the intersection of modular forms, Shimura varieties, and Galois representations. His work on generalized Whittaker models, moduli stacks of crystals, and arithmetic quantum local systems reflects his interest in both classical and cutting-edge approaches to number-theoretic problems. The pattern in his research shows a consistent theme of connecting geometric structures with arithmetic phenomena. Dr. Oh is an active educator who has developed comprehensive lecture notes for both undergraduate and graduate courses in Algebraic Number Theory. In Spring 2025, he is teaching Graduate Algebraic Number Theory (MATH GR6657) at Columbia University, covering local and global class field theory, Langlands program connections, and related advanced topics. He has also been involved in organizing and participating in numerous learning seminars including the Moduli of Langlands Parameters seminar, Theta learning seminar, and Deformation theory learning seminar.

Tom CoatesView profile

Professor

• Pure Mathematics
• Algebraic Geometry
• Mirror Symmetry
• +5 more

Tom Coates is a Professor of Pure Mathematics in the Department of Mathematics at Imperial College London's Faculty of Natural Sciences. He holds affiliations with the Artificial Intelligence Network, the CNRS-Imperial Abraham de Moivre UMI, and the Pure Mathematics research group. His office is located in the Huxley Building (662) on the South Kensington Campus, London SW7 2AZ, and he can be contacted via email at t.coates@imperial.ac.uk or phone at +44 (0)207 594 3607. Professor Coates' research spans pure mathematics with emphasis on algebraic geometry, mirror symmetry, and Gromov-Witten theory. He investigates quantum cohomology and Fano variety classification to construct a 'Periodic Table for shapes' through computational algebra, data mining, and machine learning. His work integrates geometric methods with cluster-scale computing to identify structural patterns in algebraic varieties, focusing on quantum periods, toric degenerations, and Laurent polynomial applications. His recent publications (2021-2024) demonstrate a strong trend toward computational classification of Fano varieties and polytopes, leveraging machine learning for dimension prediction and database construction. Key themes include mirror symmetry via Laurent inversion, toric geometry applications, and connections between Gromov-Witten invariants and modular forms. These works often utilize custom tools like PCAS and Fanosearch for large-scale algebraic computations. While specific student names are not listed, Professor Coates mentors PhD and Master's students in algebraic geometry and computational mathematics. His research is supported by the Simons Foundation, member institutions, and contributors, enabling international collaborations through networks like the CNRS-Imperial Abraham de Moivre UMI. He leads a research team developing the Periodic Table for shapes framework, utilizing high-performance computing resources. The team maintains open-source tools including PCAS (Periodic Table for Algebraic Shapes) and Fanosearch for Fano variety exploration, with code repositories hosted on Bitbucket and quantum period databases published in Scientific Data.

Tim BrowningView profile

Professor

• Number Theory
• Analytic Number Theory
• Diophantine Geometry
• +4 more

Tim Browning is a Professor of Number Theory at the Institute of Science and Technology Austria (IST Austria). He leads the Browning Group, focusing on analytic number theory and its interfaces with algebraic geometry. His research addresses Diophantine equations, rational points on algebraic varieties, and the distribution of arithmetic objects. He organizes the Algebraic Geometry & Number Theory Seminar and the Women in Math Day. Previously, he held roles at the University of Bristol and University of Oxford. He has authored over 100 publications and received accolades including the Ferran Sunyer i Balaguer Prize and an ERC Starting Grant. His group includes PhD students and postdocs working on topics like rational points, sieve methods, and arithmetic statistics. Education: PhD in Mathematics, University of Oxford (2002) Postdoctoral Fellowships at University of Oxford and Université de Paris-Sud Research Interests: Analytic and arithmetic methods in number theory, Diophantine geometry, rational points on varieties, circle method, sieve theory, and arithmetic statistics. His work often combines geometric and analytic techniques, such as the circle method and algebraic geometry to solve problems like Manin's conjecture and the distribution of solutions to polynomial equations. Grants & Leadership: ERC Starting Grant (2012) Serves on editorial boards of journals like Compositio Mathematica and Commentarii Mathematici Helvetici Organizes international conferences and workshops Labs/Teams: Leads the Browning Group at IST Austria, which includes postdocs and PhD students working on number theory and algebraic geometry. Collaborates with researchers globally on topics like the arithmetic of Fano varieties and rational curves.

• Algebraic Geometry
• Algebraic Topology
• Motivic Homotopy Theory
• +2 more

Ryomei Iwasa serves as Associate Professor in the Department of Mathematical Sciences at the University of Copenhagen, where his research bridges algebraic geometry and algebraic topology through advanced investigations in motivic homotopy theory and cohomology frameworks. His core research spans Algebraic Geometry, Algebraic Topology, Motivic Homotopy Theory, and K-Theory, with specialized focus on motivic spectra, algebraic cobordism, and the structural relationships between cohomology theories and moduli spaces. Recent publications demonstrate deep engagement with foundational aspects of Milnor excision, cdh descent, and modulus conditions in cycle theory. Analysis of his publication trajectory reveals a concentrated effort toward geometrization of cohomology theories, particularly evident in his 2025 Journal of the American Mathematical Society paper on Conner-Floyd isomorphisms and ongoing seminar work. Collaborations with leading mathematicians including Toni Annala, Marc Hoyois, and Wataru Kai underscore his position at the forefront of these mathematical frontiers. Scientific recognition includes: ERC MOSHOT grant He actively directs a weekly seminar on geometrization of cohomology theories, structuring comprehensive explorations from filtered modules to de Rham cohomology and prismatization. The seminar program—featuring presentations by Qingyuan Bai, Adrien Morin, and Florian Riedel—demonstrates his commitment to advancing collective understanding and mentoring emerging researchers in specialized mathematical domains.

Ravi VakilView profile

Professor

• Algebraic Geometry
• Enumerative Geometry
• Moduli Spaces
• +3 more

Ravi Vakil is the Robert Grimmett Professor of Mathematics at Stanford University and the President of the American Mathematical Society (AMS). He specializes in algebraic geometry, with contributions to enumerative geometry, moduli spaces, intersection theory, and Schubert calculus. His research interests also extend to mathematics education and public outreach. He earned his Ph.D. from Harvard University under Joe Harris. Vakil is renowned for his book The Rising Sea: Foundations of Algebraic Geometry , set for publication by Princeton University Press in 2025. He co-founded MathOverflow and Proof School, and serves on editorial boards of journals like Algebra and Number Theory and Involve . His awards include the AMS Centennial Fellowship, Coxeter-James Prize, Sloan Fellowship, and the Chauvenet Prize for mathematical exposition. He has advised numerous Ph.D. students and is known for his dedication to teaching, receiving the Dean’s Award for Distinguished Teaching. Vakil actively participates in academic service, including roles on the AMS Board and the National Math Stars advisory board. His research explores foundational questions in algebraic geometry, often with connections to combinatorics and representation theory.

• Algebraic Geometry
• Arithmetic Geometry
• Topology
• +5 more

Siqing Zhang is a Gibbs Assistant Professor at Yale University, where he conducts research in algebraic geometry. From 2023 to 2025, he is a Postdoctoral Member at the Institute for Advanced Study (IAS), mentored by Bhargav Bhatt. He completed his Ph.D. at Stony Brook University in 2023 under Mark Andrea de Cataldo and holds a B.S. in Mathematics and Philosophy from NYU Shanghai (2018). Research Interests: Dr. Zhang's work bridges algebraic geometry, arithmetic, and topology. His research focuses on moduli stacks, characteristic p geometry, perverse sheaves, and geometric applications to the P=W conjecture and non-Abelian Hodge theory. He explores phenomena in positive characteristic, including harmonic metrics, liftings mod p², and logarithmic poles. Publications: His recent articles address cohomological structures in positive characteristic, semistability in non-Abelian Hodge theory, and moduli spaces for Higgs bundles and t-connections. These studies often intersect with geometric invariant theory, algebraic stacks, and topological methods in algebraic geometry. Scientific Contributions: Dr. Zhang has been invited to speak at institutions like the Simons Center, Harvard-MIT, and Clay Mathematics Institute on topics including étale homotopy, non-Abelian Hodge theorems, and characteristic p geometry.

Melanie Matchett WoodView profile

Professor

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

Melanie Matchett Wood is the William Caspar Graustein Professor of Mathematics at Harvard University. Her research spans number theory, arithmetic statistics, algebraic geometry, and probability theory, with a focus on distributions of class groups, Galois groups of unramified extensions, and random algebraic structures. She has been supported by prestigious awards including the Packard Fellowship, the NSF Waterman Award, and the MacArthur Fellowship. Her work connects number theory to topology through function field analogs, studying moduli spaces of curves and their statistical properties. She has made significant contributions to understanding the universality of random matrix cokernels and their applications to sandpile groups of graphs. Her editorial roles include the Journal of the American Mathematical Society and Algebra and Number Theory . Recent publications emphasize arithmetic topology, proving universality theorems for 3-manifold groups, and developing new heuristics for class group torsion. She organizes seminars on arithmetic statistics and topology-number theory interactions. Her teaching includes advanced courses like Algebraic Number Theory and Class Field Theory, with research supervision spanning PhD and undergraduate projects. Scientific Awards: Packard Fellowship for Science and Engineering National Science Foundation Waterman Award MacArthur Fellowship

Martin OlssonView profile

Professor

• Algebraic Geometry
• Arithmetic Geometry
• K3 Surfaces
• +7 more

Martin Olsson is a Professor in the Department of Mathematics at the University of California, Berkeley , where he has been a faculty member since 2006. He currently serves as the Department Chair and is affiliated with the Simons Collaboration on Perfection in Algebra, Geometry, and Topology . His research focuses on Algebraic Geometry and Arithmetic Geometry , exploring topics such as K3 surfaces , abelian varieties , Brauer groups , motives , and moduli spaces . He has supervised numerous PhD theses on advanced topics in these fields. Martin Olsson's work is funded by the National Science Foundation , including FRG grant 2151946 and RTG grant 1646385. He has mentored students including Roy Zhao, Ravi Fernando, Michael Christianson, and others, with theses spanning 2009–2023.

Joe WaldronView profile

Assistant Professor

• Algebraic Geometry
• Birational Classification
• Positive Characteristic
• +3 more

Joe Waldron is an Assistant Professor in the Department of Mathematics at Michigan State University (MSU), located in C335 Wells Hall. His research focuses on algebraic geometry, particularly the birational classification of algebraic varieties in positive and mixed characteristic, with connections to commutative algebra and arithmetic geometry. He holds a PhD from the University of Cambridge under Caucher Birkar, followed by postdoctoral positions at Princeton University and the École Polytechnique Fédérale de Lausanne (EPFL). His work is supported by NSF Grant #2401279 and a Simons Foundation Gift #850684. Waldron is actively involved in academic outreach, co-organizing the First-Generation/Low-Income (FGLI) mentorship program in MSU's mathematics department. This initiative connects FGLI students with faculty and graduate student mentors to support their academic and career goals. He also contributes to the Michigan algebraic geometry symposium and the MSU algebra seminar. His research interests include advanced topics such as Mori fibre spaces, test ideals in mixed characteristic, and the log minimal model program (LMMP) for threefolds. He has published extensively on geometrically non-reduced varieties, singularities in positive characteristics, and purely inseparable Galois theory. Waldron’s grants fund explorations into foundational algebraic geometry problems, emphasizing cross-disciplinary connections with commutative algebra. His involvement in departmental initiatives reflects his commitment to fostering inclusive academic environments and mentoring underserved student populations.

Yunfeng JiangView profile

Professor

• Algebraic Geometry
• Mathematical Physics
• Moduli Spaces
• +3 more

Yunfeng Jiang is a Professor of Mathematics at the University of Kansas, affiliated with the Department of Mathematics in the College of Liberal Arts & Sciences. His research focuses on algebraic geometry, with a particular emphasis on moduli spaces of stable maps, sheaves, and their enumerative invariants such as Gromov-Witten and Donaldson-Thomas invariants. His work intersects theoretical physics, including string theory and gauge theory, exploring connections between algebraic structures and physical theories. Recent research has addressed smoothing of surface singularities, equivariant geometry, and the interplay between birational geometry and enumerative invariants. He has contributed to the study of moduli spaces of general type surfaces, Vafa-Witten invariants, and S-duality conjectures on K3 surfaces. His work often involves advanced techniques like virtual fundamental classes and obstruction theories. Jiang has taught extensively at KU, including courses on linear algebra, calculus, algebraic topology, and specialized topics in algebraic geometry. His research is supported by the NSF (DMS-2401484) and has been disseminated through over 50 peer-reviewed publications in top journals like *Mathematische Annalen*, *Advances in Mathematics*, and *Pure and Applied Mathematics Quarterly*. His research trends emphasize geometric structures in higher dimensions, moduli problems, and applications to physics, with notable contributions to the quantum cohomology of moduli spaces and the study of root stacks in algebraic geometry.

• Algebraic Topology
• Moduli Spaces
• Homology Spheres
• +5 more

Søren Galatius is a Visiting Professor at the Department of Mathematical Sciences, University of Copenhagen. His research focuses on algebraic topology with an emphasis on moduli spaces, homology spheres, K-theory, and cobordism categories. He holds a PhD and has established himself as a leading figure in geometric topology and algebraic structures in mathematics. Recent research has explored topics such as general linear groups over finite fields, Pontryagin classes, and tropical geometry applications to moduli spaces. His work bridges pure algebraic topology with geometric and combinatorial methods, contributing foundational insights into modern mathematical frameworks. Key collaborations include projects with Oscar Randal-Williams and Martin Hairer, advancing understanding of cobordism categories and topological field theories. His articles consistently appear in top-tier journals like Annales Scientifiques de l'Ecole Normale Superieure and Inventiones Mathematicae . No scientific awards or grants are explicitly listed in the provided materials, though his publication record speaks to significant academic contributions. No advisee students are documented here.