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Jack ThorneView profile

Professor

• Number Theory
• Arithmetic Geometry
• Automorphic Forms
• +3 more

Jack Thorne is a Professor of Number Theory in the Department of Pure Mathematics and Mathematical Statistics (DPMMS) at the University of Cambridge, within the Faculty of Mathematics. His office is located in room E1.18 at the department, and he can be contacted at thorne@dpmms.cam.ac.uk or by telephone at 01223 764283. Professor Thorne's primary research interests lie in Number Theory and Arithmetic Geometry , with significant contributions to the understanding of automorphic forms, Galois representations, and the Langlands program. His work spans theoretical developments in modularity, symmetric power functoriality, and the study of Selmer groups, demonstrating deep connections between algebraic geometry and number-theoretic phenomena. Analysis of Professor Thorne's recent publications reveals a consistent focus on advanced topics in modern number theory. His research demonstrates particular expertise in automorphy lifting theorems, potential automorphy over various fields, and the intricate relationships between Galois representations and automorphic forms. The publications show a progression toward increasingly sophisticated applications of the Langlands program to concrete arithmetic problems, with notable work on symmetric powers, level-raising phenomena, and the arithmetic of elliptic curves. Professor Thorne maintains an active research profile with numerous high-impact publications in leading mathematical journals including Annals of Mathematics, Publications mathématiques de l'IHÉS, and Journal of the American Mathematical Society. His collaborative work with prominent mathematicians such as Patrick Allen, Chandrashekhar Khare, and James Newton highlights his position within the international number theory community.

• Algebraic Geometry
• Syzygies of Algebraic Varieties
• Secant Varieties
• +6 more

Jinhyung Park is an Associate Professor in the Department of Mathematical Sciences at KAIST, Daejeon, Korea. He obtained his Ph.D. from KAIST in 2014 under Prof. Sijong Kwak and was mentored as a CMC Fellow at KIAS (2014–2019). His research focuses on Algebraic Geometry , particularly syzygies of algebraic varieties , secant varieties , and positivity of line bundles . Education: Ph.D., KAIST (2014); MS/BS, KAIST and University of Chicago (2002/2001). Research Interests: His work explores geometric properties of projective manifolds, singularities in algebraic geometry, and applications of Okounkov bodies to divisors and syzygies. Recent trends include Castelnuovo-Mumford regularity bounds (e.g., for threefolds with rational singularities) and subadditivity of Okounkov bodies in fiber spaces. Teaching: Courses include Matrix Groups, Algebraic Geometry, and Calculus. He previously taught at Sogang University and Purdue University. Professional Affiliations: Member of the Korean Mathematical Society, American Mathematical Society, and other international societies. Organized the 8th East Asia Number Theory Conference at KAIST (2019).

• Topological Data Analysis
• Data Visualization
• Computational Topology
• +5 more

Bei Wang Phillips is an Associate Professor in the School of Computing and a faculty member at the Scientific Computing and Imaging (SCI) Institute at the University of Utah. She holds a Ph.D. in Computer Science from Duke University and an undergraduate degree from the University of Bridgeport. Her research focuses on Topological Data Analysis (TDA), data visualization, computational topology, and machine learning, with applications in scientific data exploration and analysis. She has received prestigious awards including the NSF CAREER Award (2022) and the PECASE Award (2025). Her work spans projects funded by NSF, NIH, and DOE, including multiparameter TDA and topology-aware data compression. She advises numerous students and collaborates on interdisciplinary initiatives in astrophysics, climate science, and AI fairness. Education: Ph.D. in Computer Science, Duke University (2010) B.S. in Computer Science and Mathematics, University of Bridgeport (2003) Research Interests: Topological techniques for large-scale data analysis Integration of topological, geometric, and machine learning methods Applications in visualization, bioinformatics, and network analysis Key Projects: NSF-funded TDA research (DMS-2301361, OAC-2313124) DOE project on topology-preserving data compression Collaborations with NASA, Argonne National Lab, and Carnegie Institution of Washington Awards: Presidential Early Career Award for Scientists and Engineers (2025) NSF CAREER Award (2022) DOE Early Career Research Program (2020) Advising and Grants: Mentored over 30 students and postdocs Recipient of multiple NSF and DOE grants totaling millions

• General Relativity
• Theoretical Physics
• Black Hole Mechanics
• +6 more

Harvey Reall is a Professor of Theoretical Physics at the University of Cambridge , affiliated with the Department of Applied Mathematics and Theoretical Physics (DAMTP) and a Fellow of Trinity College . His research focuses on General Relativity and Effective Field Theory , particularly in the context of black hole mechanics , higher-dimensional gravity , and cosmic censorship . He has held prestigious positions including a Royal Society University Research Fellowship from 2005 to 2013. Education: PhD from DAMTP, University of Cambridge. Previous Appointments: Lecturer at the University of Nottingham (2005-2007); Postdoctoral positions at the Kavli Institute (2003-2005), Queen Mary University of London (2000-2003), and University of California, Santa Barbara (2003-2005). Reall's work explores the uniqueness and stability of black holes , causality in gravitational theories , and effective field theory approaches to gravity . His recent publications address nonperturbative second law formulations , event horizon dynamics , and axisymmetry theorems in extended theories of gravity. He has supervised numerous researchers including Aidan McSharry (2025-) , Maxime Gadioux (2022-) , and Iain Davies (2020-24) , contributing to the training of the next generation of physicists. Scientific Awards: Royal Society University Research Fellow (2005-2013)

Stephen S. KudlaView profile

Professor

• Automorphic Forms
• Arithmetic Geometry
• Theta Functions
• +4 more

Stephen S. Kudla is a Professor in the Department of Mathematics at the University of Toronto, located in the Bahen Centre for Information Technology. He holds the prestigious distinction of being a Fellow of the Royal Society of Canada (FRSC), reflecting his significant contributions to mathematical research. Professor Kudla's research focuses on the deep connections between number theory and geometry, with particular expertise in automorphic forms, arithmetic geometry, and theta functions. His work bridges abstract mathematical theory with concrete geometric structures, exploring how modular forms can encode arithmetic information about algebraic varieties. Analysis of Kudla's publication record reveals a sustained research program centered on the relationship between derivatives of Eisenstein series and arithmetic geometry. His work consistently explores how modular and automorphic forms can be used to study arithmetic cycles on Shimura varieties. A notable pattern in his research is the interplay between analytic objects (like Eisenstein series) and geometric structures (such as arithmetic cycles), with applications to understanding heights, intersection theory, and special values of L-functions. Fellow of the Royal Society of Canada (FRSC) While specific details about Kudla's advising activities aren't provided in the available materials, his extensive publication record with prominent collaborators like Michael Rapoport and Tonghai Yang suggests he has likely mentored numerous graduate students and postdoctoral researchers throughout his career. His participation in major mathematical conferences including the International Congress of Mathematicians (ICM) indicates recognition by the broader mathematical community. Kudla's research has clearly been supported by significant funding, as evidenced by his ability to maintain a sustained publication record in top mathematical journals.

Jelani NelsonView profile

Professor

• Theoretical Computer Science
• Algorithms
• Data Streams
• +8 more

Jelani Nelson is a Professor and Department Chair in the UC Berkeley EECS Department (College of Engineering). His work focuses on theoretical computer science , particularly algorithms , data streams , dimensionality reduction , and privacy-preserving computation . Advising : Current students include Ishaq Aden-Ali, Xin Lyu, Mihir Singhal, and Hongxun Wu (co-advised with leading researchers). Education : PhD from MIT (George M. Sprowls Award), M.Eng from MIT. Research Highlights : Developed foundational results in Johnson-Lindenstrauss dimensionality reduction (optimality, sparse embeddings). Advancements in differential privacy (lower bounds, private mean estimation, threshold learning). Pioneering work on streaming algorithms for heavy hitters, norm estimation, and graph problems. Innovations in compressed sensing and oblivious subspace embeddings . Scientific Awards : PODS Best Paper Award (2011, 2022) IBM Pat Goldberg Memorial Best Paper Award (2011) George M. Sprowls Award for MIT doctoral thesis (2009) NeurIPS 2020 Spotlight Presentation

Mark D. HaimanView profile

Professor

• Algebra
• Combinatorics
• Algebraic Geometry
• +12 more

Mark D. Haiman is a Professor at the University of California, Berkeley, Department of Mathematics, with research interests spanning algebra, combinatorics, and algebraic geometry. His work connects symmetric function theory with geometric objects like Hilbert schemes and algebraic structures such as Cherednik algebras and Hecke algebras. Appointed: 2001 Contact: mhaiman@math.berkeley.edu Teaching: Math 256B—Algebraic Geometry (Spring 2025), Math 249—Algebraic Combinatorics (Spring 2024), and others in calculus and Lie groups. Research Interests : Haiman's research focuses on Macdonald polynomials, LLT polynomials, Hilbert schemes of points in the plane, and their combinatorial and geometric implications. His work includes resolving the Macdonald positivity conjecture and the n! conjecture through algebraic geometry. Publications : Haiman has contributed to foundational papers in combinatorial and algebraic structures, including generalizations of the shuffle theorem and positivity results for LLT polynomials. His articles often bridge representation theory, symmetric functions, and geometric methods. Students : He has supervised numerous PhD students, including Magda Hlavacek (2023), Foster Tom (2022), Jeremy Meza (2021), Maryam Farahmand-Asil (2018), Maria Monks Gillespie (2016), and others working on combinatorial algebraic geometry and related fields.

Brent PymView profile

Associate Professor

• Mathematical Physics
• Algebraic Geometry
• Noncommutative Geometry
• +3 more

Brent Pym is an Associate Professor in the Department of Mathematics and Statistics at McGill University. His research focuses on the intersection of differential, algebraic, and noncommutative geometry, with a particular emphasis on Poisson varieties and deformation quantization. He has held academic positions at the University of Edinburgh, University of Oxford, and was a Postdoctoral Fellow at McGill and the University of Toronto. Education: BScE in Engineering Physics, Queen's University (2007) MSc in Mathematics, University of Toronto (2008) PhD in Mathematics, University of Toronto (2013) Research Interests: Pym studies Poisson structures, their quantizations, and connections to mathematical physics. His work involves classical/derived algebraic geometry, D-modules, moduli spaces, the Stokes phenomenon, and multiple zeta values. Recent projects include holonomic Poisson manifolds, log symplectic structures, and software for symbolic calculations in deformation quantization. Awards: Lichnerowicz Prize (2018) Advising & Grants: Pym has openings for graduate students (admission 2026) and undergraduate projects (2026–27). He develops the Star Products software package for symbolic calculations in Poisson brackets and quantization. His work is supported by research collaborations and institutional grants. Labs & Teams: Pym collaborates with researchers in geometry and mathematical physics, contributing to projects in noncommutative algebra and geometric quantization. His software tools enhance symbolic computation in these fields.

Fatma Kılınç-KarzanView profile

Associate Professor

• Mathematical Optimization
• Convex Optimization
• Non-convex Optimization
• +7 more

Fatma Kılınç-Karzan is an Associate Professor of Operations Research at Carnegie Mellon University's Tepper School of Business, with a courtesy appointment as Associate Professor of Computer Science. She is also affiliated with the Algorithms Combinatorics and Optimization (ACO) PhD Program and was a Visiting Scientist at Berkeley's Simons Institute for the Theory of Computing during Fall 2017. Her educational background includes a PhD from Georgia Institute of Technology's H. Milton Stewart School of Industrial & Systems Engineering with a minor in Mathematics, supervised by Prof. Arkadi Nemirovski. She earned her B.S. and M.S. degrees from the Industrial Engineering Department of Middle East Technical University with a minor in Information Systems. Dr. Kılınç-Karzan's research spans mathematical optimization with emphasis on convex and non-convex optimization theory, algorithms, and applications. Her work bridges theoretical foundations with practical implementations in optimization under uncertainty (robust optimization, chance constraints, distributionally robust optimization), machine learning (preference learning from limited data), and business analytics. She develops foundational theory for large-scale optimization problems with applications in decision making under uncertainty and high-dimensional statistical inference. Analysis of her recent publications reveals a strong focus on convex hull characterizations, semidefinite programming relaxations, distributionally robust optimization, and online convex optimization frameworks. Her work demonstrates increasing integration of optimization theory with machine learning applications, particularly in developing data-driven approaches for decision making under uncertainty. NSF CAREER Award (2015) INFORMS Optimization Society Young Researcher Prize (2015) INFORMS Junior Faculty Interest Group (JFIG) Best Paper Award (2014) BP Junior Faculty Chair (2014-2015) Faculty Giving Chair (2012-2013) Wimmer Fellowship (2012-2013) Dr. Kılınç-Karzan has successfully mentored numerous PhD students who have received prestigious awards, including the 2021 INFORMS Optimization Society Best Student Paper (1st prize) and multiple honorable mentions. Her research has been supported by significant grants including an NSF CAREER Award, an ONR grant (with S. Küçükyavuz), and an AFOSR grant. She serves on editorial boards for Mathematical Programming, Operations Research, Mathematics of Operations Research, and other leading journals, and has held leadership positions in professional societies including the Mathematical Optimization Society and INFORMS Computing Society. Through her affiliations with CMU's Tepper School, Computer Science Department, and ACO Program, she collaborates across disciplines to advance optimization theory and its applications. Her professional service includes committee chair roles for major INFORMS competitions and program committee leadership for international optimization conferences.

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.

Hrvoje JasakView profile

Professor

• Computational Fluid Dynamics (CFD)
• Continuum Mechanics
• Numerical Simulation Methods
• +5 more

Hrvoje Jasak is a Professor of Continuum Physics at the Department of Physics (Cavendish Laboratory), University of Cambridge. He holds a fellowship at Christ’s College. His academic journey includes a BSc in Mechanical Engineering from the University of Zagreb (1992) and a PhD in CFD from Imperial College London (1996). Prior to academia, he held engineering roles at CD-adapco (now Siemens PLM), Nabla Ltd, and Ansys-Fluent Inc., contributing to CFD software development. His research focuses on numerical simulation methods, continuum physics, multiphase flows, naval hydrodynamics, and software development. He co-created OpenFOAM, chairs its Numerics Technical Committee, and leads the Computational Continuum Mechanics (CCM) research group within the Laboratory for Scientific Computing. His work integrates advanced numerical techniques like the partially rotating grid method, finite volume algorithms, and multiphysics coupling frameworks. Jasak is a seasoned developer with 25+ years of C++ expertise, having authored ~1 million lines of code. His group’s projects include the Naval Hydro Pack , fluid-structure interaction solvers, and the Eulerian multi-fluid model for dense sprays. He actively collaborates on international initiatives like the NUMAP-FOAM Summer School and the OpenFOAM community. His teaching spans MPhil programs, PhD supervision, and specialized CFD courses. Current research explores wave-ice interaction, lubricated contact modeling, and open-source software innovation. The CCM group’s work bridges academia and industry, addressing challenges in marine engineering, energy systems, and computational mechanics.

Joan BrunaView profile

Professor

• Machine Learning
• Deep Learning
• Signal Processing
• +5 more

Joan Bruna is a Full Professor of Computer Science, Data Science, and affiliated Mathematics at New York University's Courant Institute and Center for Data Science. He leads the CILVR group and co-founded the MaD group. His research focuses on mathematical foundations of machine learning, deep learning, signal processing, and their applications in computational science, climate modeling, and geophysics. He holds a Ph.D. in Applied Mathematics from École Polytechnique and has held roles at UC Berkeley, the Institute for Advanced Study, and the Flatiron Institute. Education: Ph.D. (2013) and M.Sc. (2005) in Applied Mathematics, École Polytechnique and ENS Cachan; dual B.Sc./M.Sc. in Telecommunications and Mathematics from UPC Barcelona (2002–2004). Awards include the NSF CAREER Award (2019) and Alfred P. Sloan Fellowship (2018). Research interests span theoretical aspects of deep learning, optimization, and statistical methods, with applications to climate science and inverse problems. He has advised numerous PhD students and postdocs, contributing to seminal work on scattering networks, geometric deep learning, and neural ODEs. Professional service includes editorial roles at TMLR, JMLR, and TPAMI, plus program chairs for major conferences. His work bridges mathematics and machine learning, emphasizing rigorous analysis and real-world impact.

Imre LeaderView profile

Professor

• Extremal Combinatorics
• Ramsey Theory
• Combinatorial Number Theory
• +3 more

Professor Imre Leader is a distinguished mathematician at the University of Cambridge, where he serves as Professor of Pure Mathematics in the Department of Pure Mathematics and Mathematical Statistics (DPMMS), which is part of the Faculty of Mathematics. His office is located in room C2.02 at the DPMMS building. Professor Leader's research primarily focuses on Extremal Combinatorics and Ramsey Theory , two fundamental areas of discrete mathematics. His work explores deep connections between combinatorial structures, set theory, and algebraic properties. He has made significant contributions to understanding partition regularity, monochromatic structures, extremal set theory, and combinatorial geometry. His research often bridges the gap between pure combinatorics and applications in computer science and theoretical mathematics. Over his prolific career, Professor Leader has published numerous influential papers in top mathematical journals, collaborating with leading mathematicians worldwide. His work spans various aspects of combinatorics including hypergraph theory, geometric combinatorics, additive number theory, and combinatorial game theory. He has been particularly active in advancing our understanding of Ramsey-type phenomena in infinite structures and developing new techniques in extremal combinatorics. Research Group: Combinatorics Email: I.Leader@dpmms.cam.ac.uk Telephone: 01223 765902 Personal homepage: https://www.dpmms.cam.ac.uk/~ibl10

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 .

David BindelView profile

Associate Professor

• Applied Numerical Linear Algebra
• Eigenvalue Problems
• Network Analysis
• +5 more

David Bindel is an Associate Professor in the Department of Mathematics at Cornell University, affiliated with the College of Arts and Sciences, College of Engineering, and Cornell Ann S. Bowers College of Computing and Information Science. He earned his Ph.D. in Mathematics from the University of California, Berkeley in 2006. His research focuses on applied numerical linear algebra, eigenvalue problems, and their applications in plasma physics, network analysis, and nonlinear systems. He develops methods for analyzing complex systems, including magnetic confinement in stellarators, stability of MHD systems, and community detection in networks. His work bridges theoretical foundations with practical computational tools, such as formal verification of linear algebra algorithms and scalable Gaussian process models. Bindel’s research explores the interplay between structure and computation, leveraging eigenvalue analysis to address challenges in computer vision, opinion dynamics, and engineering design. He has contributed to advancements in numerical methods for large-scale systems, including iterative solvers, spectral approximation techniques, and stochastic optimization. His interdisciplinary approach spans applied mathematics, computer science, and physics, with applications in fusion energy, machine learning, and network science. Recent work highlights include high-order expansions for magnetic confinement, adaptive filtering for dynamical systems, and Bayesian optimization strategies. His publications emphasize rigorous analysis alongside computational scalability, addressing both theoretical and practical aspects of modern scientific computing. Despite no explicitly listed awards, his contributions reflect significant impact in his fields.