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.
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نمایش ۱-۱۵ از ۵۵۵ استاد راهنما
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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.
- Algebra
- Combinatorics
- Algebraic Geometry
- +۱۲ مورد دیگر
Victor Ginzburg is a Professor in the Department of Mathematics at the University of Chicago. His research focuses on geometric representation theory and noncommutative geometry, with contributions to areas such as Hecke algebras, quantum groups, and mirror symmetry. He currently advises seven graduate students, though their specific projects vary widely. His work intersects with algebraic geometry, string theory, and mathematical physics. Key research themes include the application of algebraic geometry to representation theory, including studies on D-modules, quiver varieties, and symplectic reflection algebras. He has authored influential papers such as Non-commutative Symplectic Geometry (2001) and Symplectic reflection algebras (2002). His interests also extend to Calabi-Yau categories and operads, reflecting a deep engagement with modern geometric and algebraic structures.
Mona Merlingمشاهده پروفایل
دانشیار
Mona Merling is an Associate Professor in the Department of Mathematics at the University of Pennsylvania, affiliated with the School of Arts and Sciences. She holds a Ph.D. from the University of Chicago (2014) under Peter May. Prior to Penn, she was a J.J. Sylvester Assistant Professor at Johns Hopkins University. Her research focuses on algebraic K-theory, its applications to number theory and manifold theory, and equivariant stable homotopy theory. She has held research positions at institutions like the Mathematical Sciences Research Institute (MSRI) and the Max Planck Institute for Mathematics. Merling teaches advanced courses in algebraic topology, homotopy theory, and calculus, including innovative programs like the Penn Directed Reading Program and collaborations with the Prison Teaching Initiative to provide education in incarcerated settings. She organizes conferences and workshops, such as the Algebraic Topology Bridge Summer Workshop, fostering accessibility in topology education. Her research explores cutting-edge topics like scissors congruence K-theory, equivariant infinite loop space theory, and parametrized cobordism categories. Recent work includes collaborations on derived scissors congruence and multiplicative equivariant K-theory, with applications to geometric and algebraic structures. Her grants include funding for social justice initiatives in education.
Jeremy Hahnمشاهده پروفایل
استادیار
Jeremy Hahn is an Assistant Professor at the Massachusetts Institute of Technology (MIT), affiliated with the Department of Mathematics within the School of Science. His research focuses on Algebraic Topology, particularly structured ring spectra, chromatic homotopy theory, and equivariant homotopy theory. Supported by grants from the Sloan Foundation and the National Science Foundation (DMS-1803273), his work has contributed to foundational advances in topological K-theory, algebraic K-theory, and manifold topology. Education details are not explicitly listed, though past teaching roles at Harvard University suggest prior academic training. His research interests span topics including: Structured ring spectra constructions (e.g., truncated Brown-Peterson spectra) Chromatic redshift phenomena and algebraic K-theory Equivariant orientations and C_p actions Applications of homotopy theory to manifold classification Notable recent work includes counterexamples to Ravenel's telescope conjecture, advancements in motivic filtrations of topological cyclic homology, and the construction of multiplicative structures on classical spectra. Collaborations with researchers such as Robert Burklund, Dylan Wilson, and Allen Yuan reflect his active engagement in the global topology research community. Teaching includes advanced courses like Algebraic Topology I (18.905) and past roles as a teaching assistant for Linear Algebra (18.06) and multivariable calculus at MIT. His research has been supported by multiple NSF grants and the Sloan Fellowship, indicating sustained academic excellence and leadership in the field.
Megan Kerr serves as the Katharine and Claudine Malone '63 Professor of Mathematics at Wellesley College, where she teaches across the mathematics curriculum from calculus to advanced topics in geometry. Her academic home is within the Mathematics & Statistics Department at this prestigious women's liberal arts college. Her educational journey began as an undergraduate at Wellesley College, where she later returned as faculty, completing a full circle in her academic career. She earned her Ph.D. from the University of Pennsylvania under the supervision of Wolfgang Ziller, with research focused on Homogeneous Einstein Metrics. Professor Kerr's research centers on global differential geometry, particularly exploring the interplay between curvature constraints and large symmetry groups. She specializes in homogeneous and low-cohomogeneity spaces, investigating fundamental questions about the existence of geometric structures, their rarity or commonality, and potential obstructions. Her work bridges the analytic concept of curvature with the algebraic framework of Lie groups, and she has recently expanded into geometric analysis where topology plays a significant role. Analysis of her publication record reveals a consistent focus on homogeneous Einstein metrics across three decades, with particular attention to curvature properties, symmetry constraints, and classification problems in both positive and negative curvature settings. Her research has evolved from foundational work on symmetric spaces to more complex non-symmetric examples and specialized curvature conditions, demonstrating both depth and breadth in differential geometry. Katharine and Claudine Malone '63 Professor of Mathematics Radcliffe Institute Fellowship As an alumna of Wellesley College, Professor Kerr maintains a strong commitment to encouraging women in mathematics. She teaches a diverse range of courses including calculus, linear algebra, combinatorics, real analysis, non-Euclidean geometry, differential geometry, topology, knot theory, and matrix groups as an introduction to Lie groups. Her teaching philosophy emphasizes developing mathematical understanding and confidence that benefits students regardless of their major. Her research has taken her to international destinations including Australia, Germany, and Mexico, reflecting the global nature of her scholarly collaborations.
Igor Kriz is a Professor of Mathematics at the University of Michigan, specializing in algebraic topology. He is affiliated with the Department of Mathematics within the College of Literature, Science, and the Arts (LSA). His research focuses on advanced topics in algebraic topology, particularly stable homotopy theory and related areas. Kriz received his Ph.D. from Charles University in 1988. His academic journey has led him to become a prominent researcher in algebraic topology, with significant contributions to the field over several decades. Professor Kriz's primary research interests lie in algebraic topology , which studies topological spaces through algebraic invariants. He specializes in equivariant stable homotopy theory, Mackey functors, cobordism, and motivic homotopy theory . His work involves calculations of stable homotopy groups and other generalized homology theories, including Morava K-theories of classifying spaces of finite groups. He has made significant contributions to the study of operads and structures up to homotopy, with applications extending to differential geometry and physics, particularly string theory. His research often bridges multiple mathematical disciplines, creating connections between topology, algebra, and geometry. His recent publications (2022-2025) demonstrate a strong focus on equivariant topology and its connections to algebraic structures. Kriz frequently collaborates with researchers like P. Hu, P. Somberg, and others, producing work that explores the intersection of homotopy theory with representation theory and algebraic geometry. His research program shows consistent evolution from foundational work in stable homotopy to more recent applications in motivic contexts and topological Hochschild homology. Professor Kriz teaches both undergraduate and graduate courses at the University of Michigan. His teaching portfolio includes Math 425 (Introduction to Probability), Math 592 (Introduction to Algebraic Topology), and advanced graduate courses Math 695 and Math 696 (Algebraic Topology I and II). His course materials are regularly updated, reflecting his commitment to education in mathematical topology. Based in East Hall (room 3846) at the University of Michigan, Professor Kriz maintains an active research program while contributing to the academic community through teaching and mentorship. His work continues to advance our understanding of complex topological structures and their algebraic representations.
Sergei Gukov is the John D. MacArthur Professor of Theoretical Physics and Mathematics at the California Institute of Technology (Caltech), where he has been a faculty member since 2005. He serves in the Division of Physics, Mathematics and Astronomy, with primary affiliation in the Department of Mathematics. His research bridges the fields of mathematics and theoretical physics, focusing on deep connections between geometry, topology, and quantum field theory. Gukov received his B.S. from Moscow Institute of Physics and Technology in 1997, followed by an M.S. and Ph.D. from Princeton University in 2001. He joined Caltech as an Associate Professor in 2005, was promoted to Professor in 2007, and was named the John D. MacArthur Professor in 2021. His research spans several interconnected areas at the frontier of mathematics and physics. A central theme is the exploration of quantum topology and its connections to mathematical physics. He has made significant contributions to the geometric Langlands program, gauge theory, and the categorification of knot and 3-manifold invariants. His recent work increasingly incorporates machine learning approaches to mathematical problems, reflecting his interest in the intersection of traditional mathematical research and modern computational techniques. Gukov's work often reveals deep connections between seemingly disparate areas of mathematics and physics, such as the relationship between Rozansky-Witten geometry and Coulomb branches in supersymmetric gauge theories. Gukov's publications demonstrate a consistent focus on the mathematical structures underlying quantum field theories and their topological implications. His recent work shows an increasing emphasis on computational approaches to mathematical problems, particularly through his interest in mathematics and machine learning. The recurring themes across his research include the application of physical insights to solve mathematical problems and the discovery of new mathematical structures through physical reasoning. He serves on the editorial boards of several prestigious journals including the Journal of Knot Theory and Its Ramifications, Communications in Mathematical Physics, and Letters in Mathematical Physics. Gukov is also active in the academic community, having delivered plenary talks at major conferences such as the First International Congress of Basic Science and presenting at String Math 2023 on the potential impact of AI on mathematical research. Gukov teaches Ma 146 ab, Introduction to Knot Theory and Quantum Topology, a course that reflects his research interests. He also runs a seminar on Mathematics and Machine Learning, held Tuesdays from 2-3pm in East Bridge Conference room 114, demonstrating his commitment to fostering interdisciplinary research at the intersection of mathematics and computational methods.
- Mathematics
- Machine Learning
- Quantum Topology
- +۹ مورد دیگر
Jianqi Liuمشاهده پروفایل
پژوهشگر ارشد
Jianqi Liu is a Hans Rademacher Research Fellow in the Department of Mathematics at the University of Pennsylvania, affiliated with the School of Arts and Sciences. His research focuses on vertex operator algebras (VOAs) and 2D conformal field theory (CFT), with an emphasis on algebraic structures such as fusion rules, Zhu’s algebras, Borel-type subalgebras, and connections to the classical Yang-Baxter equation. He also explores geometric aspects of VOAs and their physical interpretations. He earned his Ph.D. in Mathematics from the University of California, Santa Cruz (2018–2023), under the supervision of Chongying Dong. Prior to his current role, he held teaching roles at both UPenn and UCSC, instructing courses ranging from advanced linear algebra to complex analysis and number theory. His research publications address topics such as twisted conformal blocks, Rota-Baxter operators, and the interplay between algebraic structures and integrable systems. Liu collaborates with researchers like Angela Gibney and Daniel Krashen, focusing on advancing theoretical frameworks in mathematical physics and algebraic geometry.
Yi Laiمشاهده پروفایل
استادیار
Yi Lai is an Assistant Professor in the Department of Mathematics at the University of California, Irvine (UCI). He earned his Ph.D. from UC Berkeley in 2021 under Richard Bamler and served as a Szego Assistant Professor at Stanford University (2021–2024), mentored by Otis Chodosh. His research centers on geometric analysis, with a focus on Ricci flows, steady gradient solitons, and the geometry of 3-manifolds. Dr. Lai's work explores the construction and classification of geometric structures like flying wing solitons, convergence properties of Ricci flow, and curvature behavior in low-dimensional manifolds. His publications frequently address long-time existence of geometric flows and symmetry in solitons, blending PDE theory with differential geometry. At UCI, he teaches courses such as Linear Algebra (Math 121A). No awards, grants, or supervised students are mentioned in available sources.
Melanie Weberمشاهده پروفایل
استادیار
Melanie Weber is an Assistant Professor of Applied Mathematics and Computer Science at Harvard University's John A. Paulson School of Engineering and Applied Sciences (SEAS), leading the Geometric Machine Learning Group. Her research focuses on leveraging geometric structures in data for designing efficient machine learning and optimization algorithms with theoretical guarantees. She holds a PhD from Princeton University (2021) and has held fellowships at the Mathematical Institute of Oxford, Brasenose College, and the Simons Institute. Her work bridges geometry, optimization, and machine learning, with funding from NSF, Sloan Foundation, and Harvard initiatives. Education : PhD in Applied Mathematics, Princeton University (2021) BSc/MSc in Mathematics and Physics, University of Leipzig (2016) Research Interests : Dr. Weber's research integrates geometric principles into machine learning and optimization, focusing on non-Euclidean spaces, graph structures, and manifold-based methods. Key areas include optimization on Riemannian manifolds, curvature-based analysis (e.g., Ricci curvature), and developing algorithms resilient to data geometry challenges like over-smoothing in graph neural networks. Her work emphasizes theoretical foundations while addressing practical scalability in high-dimensional data. Awards & Recognition : 2024 Sloan Research Fellowship 2023 Leslie Fox Prize in Numerical Analysis 2023 NSF Grant for Geometric Optimization Grants & Funding : Supported by National Science Foundation (NSF), Alfred P. Sloan Foundation, Aramont Foundation, Harvard Dean’s Fund, and Harvard Data Science Initiative. Labs & Collaborations : Leads the Geometric Machine Learning Group at SEAS, collaborating with institutions like MIT, Max Planck Institute, and industry labs (Facebook, Google, Microsoft). Active in organizing workshops on geometric methods and curvature analysis.
Nathan Reading is a Professor in the Department of Mathematics at North Carolina State University (NCSU). He holds a Ph.D. in Mathematics from the University of Minnesota (2002) and a B.S. in Physics from Stanford University (1995). His research focuses on algebraic and geometric combinatorics, particularly in Coxeter groups, cluster algebras, and lattice-theoretic approaches. He has been actively involved in organizing the Triangle Lectures in Combinatorics, a biannual research conference. His research interests include noncrossing partitions, cluster scattering diagrams, and the lattice theory of torsion classes. Recent work explores connections between Coxeter groups and combinatorial structures on surfaces. Reading has authored numerous papers on topics such as semidistributive lattices, scattering diagrams, and Cambrian frameworks. He teaches advanced combinatorics courses (e.g., MA 724: Combinatorics II) and has advised graduate students. His work has been supported by grants from the National Science Foundation (NSF), including DMS-1500949. Reading maintains an active presence in the mathematics community through publications, conference organization, and pedagogical contributions.
Steven B Bradlow is a Professor of Mathematics at the University of Illinois at Urbana-Champaign, specializing in differential geometry, gauge theory, and Higgs bundles. His work focuses on moduli spaces, geometric structures, and surface group representations. He holds a PhD from the University of Chicago (1988). Research Interests: Bradlow’s research explores advanced topics including Higgs bundles, moduli space properties, Lie group actions, and Teichmüller theory. His work bridges algebraic geometry, differential geometry, and mathematical physics, with applications to non-Abelian monopoles, spectral curves, and geometric analysis. Publications: His recent work emphasizes Cayley correspondences, Teichmüller spaces, and exotic components of SO(p,q) representations. These studies highlight his expertise in unifying geometric and algebraic perspectives. Awards: AMS Fellow (2018), Fulbright Specialist Award (2014) Collaborations: Bradlow collaborates internationally, particularly with researchers like Oscar García-Prada and Peter Gothen, advancing Higgs bundle theory and geometric representation varieties. His editorials and conference contributions further cement his role as a leader in the field.
- Differential Geometry
- Gauge Theory
- Higgs Bundles
- +۷ مورد دیگر
Timothy Riley is a Professor in the Department of Mathematics at Cornell University, affiliated with the College of Arts and Sciences. His research focuses on geometric group theory, studying infinite discrete groups through geometric lenses such as Riemannian manifolds, graphs, and cell complexes. Key interests include curvature, geometric features of group presentations, and algorithmic complexity. He holds a D.Phil. from Oxford University (2002). Research spans geometric aspects of the word problem, hyperbolic groups, Dehn functions, and applications to cryptography and topology. His work integrates algebraic, topological, and computational perspectives. Notable collaborations include studies on hydra groups, Cayley graphs, and asymptotic cones. Publications emphasize geometric topology and group theory, with contributions to understanding filling invariants and geometric algorithmic properties. His office is 403 Malott Hall, and he maintains an active personal web page. No explicit awards are listed in the provided text, though he was part of news items related to teaching honors in 2024.
Matt Kerr is a Professor of Mathematics at Washington University in St. Louis, where he has been affiliated since 2010. He holds a doctorate in Mathematics from Princeton University (2003) and has held prior positions at UCLA, the Max Planck Institute, the University of Chicago, and Durham University. His research focuses on Algebraic Geometry, Hodge Theory, and Mathematical Physics, with notable contributions to period maps, normal functions, and the arithmetic of motives. He has been awarded the Guido L. Weiss Teaching and Service Award (2024), a Simons Foundation Travel Grant (2024-2029), and the Barry M. Goldwater Scholarship (1996-1997). Dr. Kerr has organized numerous conferences, including the Western Algebraic Geometry Symposium (2023), and co-edited volumes such as Period Domains, Algebraic Cycles, and Arithmetic . He currently supervises four Ph.D. students (Xiaojiang Cheng, RJ Acuna, Devin Akman, Rachel Wu) and has mentored postdoctoral researchers like Ivan Horozov and Patricio Gallardo. His teaching spans advanced graduate courses (e.g., Complex Analysis, Algebraic Geometry) and undergraduate programs, including contributions to the Washington University Math Circle and the National Alliance for Doctoral Studies mentorship initiative. His work bridges pure mathematics and theoretical physics, particularly through studies of Feynman integrals, Calabi-Yau varieties, and quantum curves. He is actively involved in academic service, including roles on hiring committees, grant reviewing, and mentoring programs. Recent research themes include regulators of algebraic cycles, singularities in Hodge theory, and compactifications of moduli spaces. Grants: NSF grants (2011–2024), FRG grants, Simons Foundation awards, and EPSRC funding. Awards: Multiple teaching and service recognitions, including the 2024 Weiss Award. Publications: Over 40 peer-reviewed articles and books, including collaborations with leading mathematicians like Phillip Griffiths and Spencer Bloch.