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.

Oscar Randal-Williamsمشاهده پروفایل

استاد

• Algebraic Topology
• Geometric Topology
• Mapping Class Groups
• +۸ مورد دیگر

Oscar Randal-Williams is the Sadleirian Professor of Pure Mathematics at the University of Cambridge, where he is affiliated with the Faculty of Mathematics and the Department of Pure Mathematics and Mathematical Statistics (DPMMS). His work is centered in the Differential Geometry & Topology research group, where he contributes to advancing knowledge in geometric and algebraic topology. Professor Randal-Williams specializes in Algebraic and Geometric Topology, with particular expertise in mapping class groups, moduli spaces, cobordism categories, spaces of manifolds, surgery theory, configuration spaces, characteristic classes, and K-theory. His research explores the deep connections between homotopy theory and geometric structures, with applications across various mathematical domains. His work often bridges abstract algebraic structures with concrete geometric problems, creating new frameworks for understanding topological phenomena. An analysis of Professor Randal-Williams' recent publications reveals a strong focus on homological stability phenomena, mapping class groups of high-dimensional manifolds, and the interplay between algebraic structures and geometric topology. His work frequently involves E ∞ -algebras, general linear groups, and the topology of diffeomorphism groups. A significant portion of his research investigates the structure of moduli spaces of manifolds and their connections to algebraic K-theory, with recent work extending to applications in mathematical physics through studies of symmetries in quantum field theories. Professor Randal-Williams maintains active collaborations with leading mathematicians worldwide, including Søren Galatius, Alexander Kupers, and Jeremy Miller, among others. His research has been published in top-tier mathematical journals including the Annals of Mathematics, Inventiones Mathematicae, and the Journal of the American Mathematical Society.

Eric Larsonمشاهده پروفایل

دانشیار

• Algebraic Geometry
• Brill-Noether Theory
• Moduli Spaces
• +۳ مورد دیگر

Eric Larson is an Associate Professor at Brown University's Department of Mathematics, specializing in algebraic geometry. His research focuses on moduli spaces, Brill-Noether theory, and algebraic curves. He collaborates with notable mathematicians such as Isabel Vogt and Izzet Coskun on topics like normal bundles, Chow rings, and stability conditions. Larson actively engages in academic outreach, organizing Putnam competition practices and undergraduate colloquia. He has developed computational tools for studying elliptic curves' Galois representations and contributed to expository works on interpolation problems and LaTeX accessibility.

• 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.

• Algebraic Geometry
• Syzygies of Algebraic Varieties
• Secant Varieties
• +۶ مورد دیگر

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).

Johan Taflinمشاهده پروفایل

مدرس

• Complex Dynamics
• Pluripotential Theory
• Dynamical Systems
• +۲ مورد دیگر

Johan Taflin is a Lecturer at the University of Burgundy, affiliated with the Institute of Mathematics of Burgundy (IMB) under the Faculty of Science. His research focuses on complex dynamics in several variables and pluripotential theory, with significant contributions to attracting sets, equidistribution, and moduli spaces of dynamical systems. He has led the ANR DynAtrois project since 2025 and oversees the new Master of Mathematics program launching in 2025. Research Interests: Complex dynamics in projective spaces and several variables Pluripotential theory and its applications Dynamical systems, attractors, and moduli spaces Interdisciplinary links with mathematical physics and algebraic geometry Publications Trends: His work spans complex dynamics, including studies on blenders, postcritically finite maps, and equidistribution toward Green currents. Key subfields include holomorphic endomorphisms, algebraic geometry, and mathematical physics. Leadership: He directs the ANR DynAtrois project (2025–2030) and manages the Dijon Master of Mathematics program, which emphasizes fundamental and applied mathematics with ties to artificial intelligence.

Brian Lawrenceمشاهده پروفایل

استادیار

• Arithmetic Geometry
• Number Theory
• Diophantine Geometry
• +۲ مورد دیگر

Brian Lawrence is an Assistant Professor in the Department of Mathematics at the University of Wisconsin–Madison, currently on leave as of 2025. Previously, he held positions at UCLA, the University of Chicago, and Columbia University, following doctoral studies at Stanford University under Akshay Venkatesh. His educational background includes: PhD in Mathematics from Stanford University (advisor: Akshay Venkatesh) Lawrence's research centers on arithmetic geometry, specializing in Diophantine problems through p-adic methods. His work develops innovative approaches to Mordell's conjecture, Shafarevich-type results, and rational point distribution using p-adic Hodge theory, étale cohomology, and period mappings. He bridges theoretical number theory with computational frameworks, particularly in algorithmic solutions for Diophantine equations. His publication trends reveal sustained focus on foundational Diophantine geometry problems, with recent work emphasizing conditional algorithms for the Mordell problem and sparsity phenomena in integral points. Collaborations with leading mathematicians like Venkatesh and Sawin demonstrate interdisciplinary engagement across number theory and algebraic geometry. Lawrence actively mentors undergraduate researchers, supervising projects on resultants, Hodge theory, and symmetric polynomials by students including Pramana Saldin, Yuchen Chen, Anuj Sakarda, and Spencer Dembner. His organizational roles include founding the Crystalline Cohomology seminar at Columbia and co-organizing the University of Chicago Number Theory Seminar, fostering collaborative research environments. He contributes extensively through expository notes on schemes, polynomials on lattices, and Fibonacci numbers modulo p, reflecting commitment to mathematical education and knowledge dissemination across multiple institutions.

Sug Woo Shinمشاهده پروفایل

استاد

• Number Theory
• Automorphic Forms
• Algebraic Geometry
• +۶ مورد دیگر

Sug Woo Shin is a Professor of Mathematics at the University of California, Berkeley ( Math Genealogy , MathSciNet Profile ). His research focuses on Number Theory and Automorphic Forms, with significant contributions to the Langlands Program, Shimura varieties, and cohomology of arithmetic spaces. Editorial roles: Astérisque , Manuscripta Mathematica , Journal of the Korean Mathematical Society Recent research explores cohomological properties of locally symmetric spaces, tempered A-packets for classical groups, and modularity of symplectic Galois representations Collaborators include Ana Caraiani, Mark Kisin, Arno Kret, and Peter Scholze He has supervised PhD theses on topics like affine Deligne-Lusztig varieties, specialization maps in Scholze's category of diamonds, and statistical properties of automorphic representations. Teaching includes graduate courses on Number Theory (254A/254B), undergraduate Linear Algebra (110), and Calculus (1A), as well as seminars on global Langlands reciprocity and p-adic cohomology theories. Co-organized conferences include the BIRS workshop on Langlands programs (2025), PRIMA algebraic number theory sessions (2022), and KAST Symposium on automorphic forms (2021). His work appears in journals like Annals of Mathematics, Duke Mathematical Journal, and Compositio Mathematica.

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.

Mark D. Haimanمشاهده پروفایل

استاد

• Algebra
• Combinatorics
• Algebraic Geometry
• +۱۲ مورد دیگر

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 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.

• Algebraic Geometry
• Arithmetic Geometry
• Number Theory
• +۵ مورد دیگر

Prof. Peter Scholze is a leading mathematician at the Max Planck Institute for Mathematics in Bonn, specializing in algebraic geometry and arithmetic geometry. He holds the academic rank of Professor and is part of the Arbeitsgruppe Algebraische Geometrie und Darstellungstheorie. His research focuses on foundational questions in algebraic geometry, number theory, and representation theory, particularly through the lens of the Langlands program, p-adic Hodge theory, and perfectoid spaces. Scholze has pioneered geometric approaches to the local Langlands correspondence and introduced revolutionary concepts like prismatic cohomology and condensed mathematics. He actively contributes to academia through advanced courses on topics such as geometrization of the Langlands program, étale cohomology, and condensed mathematics. His work bridges algebraic geometry with representation theory, addressing fundamental problems in arithmetic geometry and p-adic analysis. Scholze’s research outputs include seminal papers on perfectoid spaces, prismatic cohomology, and the geometrization of local Langlands correspondence. He collaborates extensively with leading mathematicians globally, contributing to collaborative research initiatives like the ARGOS seminar and the Habiro ring project. His teaching engagements include advanced lectures on algebraic geometry, representation theory, and p-adic geometry, reflecting his commitment to training the next generation of researchers. Despite no explicitly listed awards in the provided text, Scholze is widely recognized as a Fields Medalist (2018) and a leading figure in modern mathematics.