جستجوی استاد راهنمای دانشگاهی

• Arithmetic Geometry
• Algebraic Geometry
• Representation Theory
• +۴ مورد دیگر

Prof. Peter Scholze is a leading mathematician at the University of Bonn and the Max Planck Institute for Mathematics (MPIM). He holds a professorship in the Mathematical Institute at the University of Bonn and is affiliated with MPIM as a principal investigator. His research focuses on arithmetic geometry, representation theory, and p-adic geometry, with notable contributions to perfectoid spaces, prismatic cohomology, and the geometrization of the local Langlands correspondence. Scholze has organized several advanced seminars (ARGOS) and taught courses on topics like condensed mathematics, p-adic geometry, and algebraic geometry. He collaborates widely with researchers such as Laurent Fargues and Bhargav Bhatt. His recent work includes groundbreaking papers on wild Betti sheaves, motivic geometrization of the local Langlands correspondence, and the Habiro ring of number fields. Scholze has pioneered the use of prismatic cohomology to unify p-adic Hodge theories and has developed foundational frameworks in derived algebraic geometry. His research also intersects with representation theory and topological cyclic homology. Affiliations: University of Bonn (Mathematical Institute), Max Planck Institute for Mathematics (MPIM) Research Groups: Arbeitsgruppe Arithmetische Geometrie und Darstellungstheorie Teaching: Recent courses include 'Selected Topics in Algebraic Geometry' and 'Six-Functor Formalisms'. His work frequently explores connections between algebraic geometry and number theory, with a focus on geometric approaches to arithmetic problems. Scholze is a key figure in modern arithmetic geometry, influencing both foundational theory and applied areas like the Langlands program.

• Algebraic Geometry
• Singularities of Algebraic Varieties
• Hodge Theory
• +۴ مورد دیگر

Mircea Mustata is a Professor in the Department of Mathematics at the University of Michigan. His research focuses on singularities of algebraic varieties and their role in higher-dimensional geometry, with significant work on invariants like log canonical thresholds, minimal log discrepancies, multiplier ideals, and Hodge ideals derived from Saito's mixed Hodge modules. He collaborates extensively, notably with Mihnea Popa on Hodge ideals and with other researchers on topics such as square-free polynomials and F-thresholds. Contact: 3064 East Hall, mmustata@umich.edu Education: Ph.D. from UC Berkeley (2001) Research Interests: Mustata's work bridges algebraic geometry and singularity theory, utilizing tools from resolutions of singularities, jet schemes, D-modules, and positive characteristic methods. His long-term collaboration with Popa explores Hodge ideals, while other projects address Du Bois complexes, stable rationality, and cohomological dimension. Teaching: Courses include Algebraic Geometry I/II, D-modules, commutative algebra, and advanced linear algebra. Lecture notes for topics like toric varieties, rationality, and cohomology are publicly available. Editorial & Organizational Roles: Managing editor of the Michigan Mathematical Journal and member of editorial boards for Compositio Mathematica, Journal de l'École polytechnique-Mathématiques, and Journal of Singularities. Organized events like the Spring School in Ann Arbor and conferences on algebraic geometry.

Renjie Fengمشاهده پروفایل

پژوهشگر ارشد

• Probability Theory
• Random Matrix Theory
• Machine Learning
• +۵ مورد دیگر

Renjie Feng is a Research Fellow in Mathematics and AI at the School of Mathematics and Statistics and the Sydney Mathematical Research Institute , University of Sydney. His work bridges probability theory, statistics, and applications in machine learning, deep learning, and artificial intelligence. His research interests focus on probability theory and its applications to machine learning , random matrix theory , and statistical physics . He investigates extreme value problems, spectral properties of random matrices, and topological features of random fields over Riemannian manifolds. Recent publications highlight trends in random matrix theory (GUE, GOE, GSE), extreme gap problems , determinantal point processes , and Wiener chaos . Collaborative works with F. Götze, D. Yao, and R. Adler emphasize U-statistics , multivariate linear statistics , and random topology inspired by Poisson point process studies.

• General Relativity
• Theoretical Physics
• Black Hole Mechanics
• +۶ مورد دیگر

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)

Jeffrey F. Brockمشاهده پروفایل

استاد

• Low-dimensional geometry
• Hyperbolic geometry
• Topology
• +۳ مورد دیگر

Jeffrey F. Brock is the Dean of the School of Engineering & Applied Science and the William S. Massey Professor of Mathematics at Yale University. He holds the Zhao and Ji Chair in Mathematics. His research focuses on low-dimensional geometry and topology, particularly hyperbolic geometry and its applications to data analysis. He completed his undergraduate studies at Yale and earned his Ph.D. from UC Berkeley. He held positions at Stanford, the University of Chicago, and Brown University, where he chaired the Mathematics Department from 2013 to 2017 and founded Brown’s Data Science Initiative in 2016. He joined Yale in 2018, serving as inaugural Dean of Science in the Faculty of Arts and Sciences until assuming his current role in 2022. He is a Guggenheim Fellow and Fellow of the American Mathematical Society. His research spans hyperbolic 3-manifolds, Teichmüller dynamics, and geometric methods in data science. Notable contributions include work on Thurston’s geometrization program, classification of hyperbolic manifolds, and applications of geometric topology to complex datasets. He co-authored foundational papers on ending laminations, Weil-Petersson geometry, and renormalized volume. His recent work bridges pure mathematics with applied challenges, such as algorithmic detection of medical imaging patterns. Awarded the Guggenheim Fellowship (2008) and AMS Fellow (2017), Brock has also led interdisciplinary initiatives at Brown and Yale. His administrative roles include overseeing engineering, natural sciences, and data science programs. Beyond academia, he co-founded the Vijay Iyer Trio, showcasing his passion for music performance and creativity.

Stephen S. Kudlaمشاهده پروفایل

استاد

• Automorphic Forms
• Arithmetic Geometry
• Theta Functions
• +۴ مورد دیگر

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.

Lukas Brantnerمشاهده پروفایل

پژوهشگر ارشد

• Geometry
• Topology
• Algebraic Topology
• +۴ مورد دیگر

Lukas Brantner is a Royal Society University Research Fellow at the Mathematical Institute of the University of Oxford. His research focuses on geometry, topology, and derived algebraic structures, with a particular emphasis on partition Lie algebras, deformation theory, and higher algebraic frameworks. His recent work spans topics such as derived foliations, Poincaré-Birkhoff-Witt theorems, and the complexity of geometric objects like Calabi-Yau varieties in characteristic p. This reflects a deep interplay between algebraic topology, homotopy theory, and modern algebraic geometry. Major Themes: Derived Algebraic Geometry, Homotopy Theory, Deformation Theory, Galois Theory Collaborators: Magidson, Nuiten, Antolín-Camarena, Heuts, Taelman, Campos, Waldron, Hahn, Knudsen, Mathew, Arone, Manners Scientific Awards & Honors: Royal Society University Research Fellow Brantner actively contributes to foundational research in algebraic topology and derived structures, often bridging pure algebra with topological phenomena. His publications highlight the evolution of partition Lie algebras, configuration spaces, and Goodwillie calculus in modern mathematics.

Brent Pymمشاهده پروفایل

دانشیار

• Mathematical Physics
• Algebraic Geometry
• Noncommutative Geometry
• +۳ مورد دیگر

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.

Aise Johan de Jongمشاهده پروفایل

استاد

• Algebraic Geometry
• Arithmetic Geometry
• Stacks Theory
• +۴ مورد دیگر

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
• Mathematical Physics
• Mirror Symmetry
• +۷ مورد دیگر

Maxim Kontsevich has been a permanent professor at the Institut des Hautes Études Scientifiques (IHÉS) since 1995, holding the AXA-IHES Chair for Mathematics . He is also Professor at Rutgers University (one month per year since 1997) and was Professor at University of California, Berkeley (1993–1995). Born 25 August 1964 in Khimki, former USSR, he became a French citizen in 1999. Education: Ph.D. in Mathematics, University of Bonn, March 1992. Research Interests: Prof. Kontsevich’s work lies at the intersection of algebraic geometry , mathematical physics , and quantum theory . He introduced revolutionary ideas in mirror symmetry , non-commutative geometry , and deformation quantization , creating new algebraic structures that have found applications far beyond their original contexts. His current ERC Synergy Grant “ReNew Quantum” (2019-2025) explores recursive and exact new quantum theory . Publications & Trends: Across more than 50 influential papers, Kontsevich has consistently pushed the boundaries of enumerative geometry , motivic integration , and topological field theory . His recent work delves into symplectic aspects of homological algebra , motivic Donaldson-Thomas invariants , non-archimedean geometry , and integrable systems , revealing deep connections between geometry, algebra, and physics. Scientific Awards & Honors: Fields Medal (1998) Crafoord Prize (2008) Shaw Prize in Mathematical Sciences (2012) Breakthrough Prize in Fundamental Physics (2012) Breakthrough Prize in Mathematics (2014) ERC Synergy Grant “ReNew Quantum” (2019) AMS Moore Prize (2025) Doctor Honoris Causa: Aarhus University (2014), Universität Wien (2015), Syddansk Universitet (2023) Member of Académie des Sciences, Institut de France, Academia Europaea, National Academy of Sciences (foreign), London Mathematical Society (honorary) Grants & Leadership: As Principal Investigator of the ERC Synergy Grant “ReNew Quantum” (€10 million, 2019-2025), Kontsevich coordinates an international team advancing exact methods and resurgence in quantum field and string theories. Editorial Service & Community Roles: He serves on the editorial boards of Compositio Mathematica , Publications Mathématiques IHÉS , Journal of Noncommutative Geometry , and several other leading journals, shaping the direction of contemporary mathematical research.

• Commutative Algebra
• Algebraic Geometry
• Hyperplane Arrangements
• +۴ مورد دیگر

Ştefan Tohăneanu is a Professor in the Department of Mathematics and Statistical Science at the University of Idaho , affiliated with the College of Science. His academic journey includes a Ph.D. in Mathematics from Texas A&M University (2007), and M.S. degrees in Algebra (2001) and Analysis (2001) from the University of Bucharest, where he also earned a B.S. in Mathematics (1997). Research Focus: Commutative Algebra, Hyperplane Arrangements, Matroid Theory, and applications to Coding Theory, including generalized Hamming weights, Orlik-Terao algebras, and homological properties of ideals. Publications: Recent work explores Betti numbers, Jacobian ideals, logarithmic derivations, and connections between algebraic invariants and coding theory problems like minimum distance computation and error correction. Collaborations: Engages with global research networks through affiliations with institutions such as Texas A&M University, University of Bucharest, and University of Idaho.

Elden Elmantoمشاهده پروفایل

استادیار

• Algebraic Geometry
• Homotopy Theory
• Algebraic K-theory
• +۳ مورد دیگر

Elden Elmanto is an Assistant Professor in the Department of Mathematics at the University of Toronto, affiliated with the Faculty of Arts and Science. His research focuses on advanced areas of algebraic geometry and homotopy theory, particularly through a motivic perspective. He investigates algebraic cycles, vector bundles, and motivic cohomology, often leveraging techniques from derived algebraic geometry and p-adic geometry. Recently, he co-developed a motivic cohomology theory for singular schemes with Matthew Morrow. His work spans topics like algebraic K-theory, motivic homotopy theory, and the interplay between topology and arithmetic geometry. He actively participates in seminars such as the Toronto Algebraic Geometry Seminar and has led research on topological cyclic homology, equivariant algebraic K-theory, and motivic infinite loop spaces. Elmanto collaborates widely, contributing to fields like étale motivic spectra, Voevodsky’s convergence conjecture, and the Quillen-Lichtenbaum dimension. His research emphasizes foundational questions in modern algebraic geometry, with applications to arithmetic and geometric contexts.

Mona Merlingمشاهده پروفایل

دانشیار

• Algebraic K-Theory
• Equivariant Stable Homotopy Theory
• Manifold Theory
• +۳ مورد دیگر

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.

• Arithmetic Algebraic Geometry
• Motivic Homotopy Theory

Prof. Dr. Niko Naumann is a faculty member at the University of Regensburg, affiliated with the Department of Mathematics (NWF I - Mathematics). His research focuses on the intersection of Arithmetic Algebraic Geometry and Motivic Homotopy Theory. His work explores stable homotopy theory, equivariant algebraic K-theory, and the application of topological modular forms to arithmetic problems. Notable collaborations include researchers such as Tobias Barthel, Akhil Mathew, and Justin Noel. The 15 most recent publications span topics in homotopy theory, algebraic geometry, and number theory, with a particular emphasis on nilpotence theorems, motivic spectra, and arithmetic invariants. Key journals include Inventiones Mathematicae, Advances in Mathematics, and Geom. Topol. Niko Naumann’s departmental role includes leadership in international academic exchange programs like ERASMUS. Current advisees or students are not explicitly listed in the provided text.

Kevin Coulembierمشاهده پروفایل

استاد

• Representation Theory
• Noncommutative Algebra
• Monoidal Categories
• +۳ مورد دیگر

Kevin Coulembier is a Professor in the Algebra Research Group at the University of Sydney . He has held a continuing position since 2017 and received prestigious awards including the Christopher Heyde Medal (2021), G. de B. Robinson Award (2022), and the Frontiers of Science Award (2024). Research Focus: Representation theory of algebraic groups, Lie (super)algebras, quantum groups, and monoidal categories; tensor ideals; and homological algebra. Grants: ARC Future Fellowship (2023), ARC Discovery Projects (2021, 2018), and DECRA Fellowship (2017). Students: Supervised postdocs and PhD students including Nick Bridger, Joseph Newton, Bregje Pauwels, Alexander Sherman, and Willow Stewart. Editorial Roles: Editor for Annals of Representation Theory and Mathematische Zeitschrift .