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.

Tasho Kalethaمشاهده پروفایل

استاد

• Number Theory
• Representation Theory
• Algebraic Geometry
• +۳ مورد دیگر

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.

Dinesh S. Thakurمشاهده پروفایل

استاد

• Number Theory
• Arithmetic Geometry
• Function Field Arithmetic
• +۷ مورد دیگر

Professor Dinesh S. Thakur holds the position of Professor in the Department of Mathematics at the University of Rochester. He earned his PhD from Harvard University and has made significant contributions to number theory, arithmetic geometry, and function field arithmetic. His research focuses on developing theories related to zeta functions, Drinfeld modules, and p-adic analysis in finite characteristic environments. Education: PhD in Mathematics, Harvard University Research Interests: Thakur’s work integrates advanced topics such as elliptic curves, modular forms, Diophantine equations, and the arithmetic of function fields. He has pioneered studies on multizeta values, p-adic continued fractions, and the distribution of Diophantine exponents in finite characteristic. His research bridges classical number theory with modern algebraic geometry and p-adic analysis. Teaching & Mentorship: Thakur has taught a wide range of courses, including graduate-level topics in function field arithmetic, algebraic geometry, and number theory. He has advised 11 PhD students and several master’s students, whose theses span themes like elliptic Carmichael numbers, Drinfeld modular forms, and multizeta relations. Notable advisees include Javier Diaz-Vargas (1996), George Todd (2015), and Yao-Rui Yeo (2021). Outreach & Contributions: Thakur participates in initiatives like the Arizona Winter School and Olympiad training programs in India. He maintains an active seminar series at UR on topics such as L-values, Fermat’s Last Theorem, and automatic sequences. His work is accessible through his personal page and MathSciNet.

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.

Brian Conradمشاهده پروفایل

استاد

• Number Theory
• Arithmetic Geometry
• Algebraic Geometry
• +۳ مورد دیگر

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 .

Urs Hartlمشاهده پروفایل

استاد

• Arithmetic Geometry
• Algebraic Number Theory
• Representation Theory
• +۳ مورد دیگر

Prof. Dr. Urs Hartl is a faculty member in the Department of Mathematics and Computer Science at the University of Münster, affiliated with the Faculty of Mathematics and Computer Science. He is an Investigator in Mathematics Münster and a member of the Collaborative Research Centre (CRC) 1442 'Geometry: Deformations and Rigidity.' His research focuses on arithmetic geometry, representation theory, algebraic number theory, and arithmetic of function fields. He holds a prominent position in the field, contributing to areas such as Shimura varieties, p-adic Hodge theory, and the Langlands program. Affiliations: Member of CRC 1442 Geometry Investigator in Mathematics Münster Research Interests: Arithmetic algebraic geometry Algebraic number theory Arithmetic of function fields Structure theory of Shimura varieties p-adic Hodge theory p-adic Langlands programme Model theory Recent Publications: Hartl's recent work includes studies on moduli stacks of global G-shtukas, periods of Drinfeld modules, and p-adic Galois representations. His research emphasizes foundational contributions to arithmetic geometry and number theory, often involving collaborations with leading mathematicians such as Rajneesh Kumar Singh and Eva Viehmann. Grants & Advising: Hartl’s involvement in CRC 1442 reflects his leadership in geometric research. While specific advising details are not provided, his extensive publications suggest active mentorship in advanced mathematical research. Labs/Teams: Collaborates within the Mathematics Münster research group and the CRC 1442 team, focusing on geometric and arithmetic structures.

Igor Krizمشاهده پروفایل

استاد

• Algebraic Topology
• Stable Homotopy Theory
• Equivariant Topology
• +۵ مورد دیگر

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.

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

Dr. Niranjan Ramachandran is a Professor of Mathematics at the University of Maryland, College Park, specializing in the deep structural connections between Arithmetic Geometry and Number Theory. His work centers on motives, zeta functions, and algebraic cycles, with significant contributions to foundational conjectures in modern mathematics. His primary research domains include: Arithmetic Geometry Algebraic Geometry Number Theory Motives Zeta Functions Cohomology K-theory Prof. Ramachandran's research explores the intricate relationships between algebraic cycles, special values of L-functions, and motivic cohomology, advancing understanding of the Birch and Swinnerton-Dyer conjecture, Artin-Tate conjecture, and higher Euler characteristics through innovative approaches to zeta functions and motivic complexes. Analysis of his 15 most recent publications reveals sustained focus on zeta function special values (2023), derived categories of elliptic curves (2022), and Artin-Tate conjecture proofs (2022), with recurring themes in fiber integration of gerbes (2020), higher Euler characteristics (2016), and motivic measure exponentiation (2014). His work consistently bridges abstract motivic frameworks with concrete arithmetic problems. No scientific awards were documented in the provided materials. Information regarding academic advising, Ph.D. students, or research grants was not specified in the available text.

Giorgis Petridisمشاهده پروفایل

دانشیار

• Arithmetic Combinatorics
• Combinatorial Geometry
• Number Theory
• +۳ مورد دیگر

Giorgis Petridis is an Associate Professor at the University of Georgia, specializing in arithmetic combinatorics, a field rooted in combinatorial number theory with modern extensions into discrete analysis and finite field geometry. Born in Athens, Greece, he earned his PhD from the University of Cambridge under Tim Gowers and held a Visiting Assistant Professor position at the University of Rochester. He serves as an editor for Combinatorial Theory and is affiliated with the Number Theory and Arithmetic Geometry group, particularly its additive combinatorics and discrete analysis subgroup. Doctor of Philosophy (2011), University of Cambridge Certificate of Advanced Studies in Mathematics (2002), St John’s College, Cambridge BA (Hons) in Mathematics (2001), St John’s College, Cambridge His research focuses on additive combinatorics, exploring sumset estimates, polynomial configurations in prime lattices, and geometric incidence problems over finite fields. He investigates combinatorial geometry, including pinned distance problems and bisector arrangements, while also contributing to exponential sum bounds and expander graph theory. His work bridges theoretical mathematics with applications in pseudorandomness and discrete geometry. Recent publications highlight trends in finite field analysis, with 6 of 15 articles addressing arithmetic structures in prime-order fields. Key keywords include Combinatorics , Number Theory , and Finite Fields , with sub-fields spanning polynomial configurations, energy bounds, and geometric combinatorics. Scientific awards include the Creative Research Medal (2024) from the University of Georgia for mid-career research impact. Grants from the Simons Foundation (MPS-TSM-00007816) and multiple NSF DMS Awards (2054214, 1723016, 1500984, 1804049) support his work on discrete analysis and conferences. He co-advises five PhD students and has supervised multiple Master’s theses on topics like point-plane incidences and additive energy. Outreach includes leading high school math teams, organizing discrete analysis sessions, and contributing to public science communication guides.

Ben Greenمشاهده پروفایل

استاد

• Additive Combinatorics
• Analytic Number Theory
• Harmonic Analysis
• +۳ مورد دیگر

Ben Green is the Waynflete Professor of Pure Mathematics at the University of Oxford and a Fellow of Magdalen College. His work spans additive combinatorics, analytic number theory, harmonic analysis, ergodic theory, discrete geometry, and group theory, with a focus on interdisciplinary approaches. Research Interests: Additive combinatorics and its applications to primes Analytic number theory (prime distribution, L-functions) Harmonic analysis (Fourier methods, spectral theory) Ergodic theory and its combinatorial applications Discrete geometry (ordinary lines, convex structures) Group theory (approximate groups, expansion) Article Trends: His recent work emphasizes multiplicative functions, Ramsey-type problems in number theory, expansion in finite groups, and extremal set theory. Themes include prime gaps, arithmetic progressions, and interactions between analysis and algebra. Scientific Awards: Clay Research Award (2004) Ostrowski Prize (2005) Whitehead Prize (2005) Leverhulme Prize (2007) European Mathematical Society Prize (2008) Royal Society Fellow (2010) Sylvester Medal (2014) Senior Whitehead Prize (2019) Advising: Ben has supervised numerous D.Phil students across additive combinatorics, analytic number theory, and related fields. Past students hold postdoctoral and academic positions globally.

Joachim Rosenthalمشاهده پروفایل

استاد

• Coding Theory
• Cryptography
• Algebraic Geometry
• +۲ مورد دیگر

Joachim Rosenthal is a Professor of Applied Mathematics at the University of Zurich's Department of Mathematics, leading the Applied Algebra Group. His research integrates coding theory, cryptography, and algebraic geometry with applications in communications and security systems. His primary research explores algebraic coding theory including convolutional codes, subspace codes, and post-quantum cryptography. He develops algorithms for error correction, code optimization, and cryptographic protocol analysis, with emphasis on mathematical structures in finite fields and rings. Professor Rosenthal serves as President of the Swiss Mathematical Society (2024-2025) and sits on IEEE Information Theory Society's Board of Governors. He has organized multiple international conferences on coding theory and cryptography, including the Zurich COST Meeting and Workshop on Convolutional Codes. His editorial contributions include roles at Archiv der Mathematik and SIAM Journal on Applied Algebra and Geometry. Recent publications focus on code construction methods, complexity analysis in group-based cryptography, and algebraic approaches to error-correcting codes.

• Mathematics
• Number Theory
• Combinatorics
• +۳ مورد دیگر

Chan Song Heng is an Associate Professor in the Division of Mathematical Sciences at the School of Physical and Mathematical Sciences, Nanyang Technological University (NTU), Singapore. He has been affiliated with NTU since 2007. His academic journey includes a B.Sc. (Hons) in Mathematics from the National University of Singapore (2001) and a Ph.D. in Mathematics from the University of Illinois at Urbana-Champaign (2005). His research focuses on advanced mathematical topics such as partition theory, q-series, mock theta functions, and number theory. Recent work includes studies on identities analogous to Jacobi, Fermat-Wilson theorems, and applications of Rogers-Fine identities. His publications explore combinatorial, analytic, and algebraic aspects of these fields, with notable contributions to modular forms, theta functions, and partition congruences. Dr. Chan’s articles often intersect with classical problems in mathematics, blending historical insights with modern analytical techniques. Notable themes include exploring identities through modular forms, analyzing partition statistics (ranks/cranks), and studying mock theta functions. Despite his prolific output, no specific scientific awards or student advisees are listed in the provided materials.

• Algebra
• Geometry
• Topology
• +۵ مورد دیگر

Jonas Bergström is a Professor in the Department of Mathematics at Stockholm University specializing in Algebra, Geometry, Topology, and Combinatorics. His research focuses on arithmetic geometry, moduli spaces, Siegel modular forms, and number theory, with extensive collaborations across international institutions including KTH Royal Institute of Technology. His research interests span algebraic geometry, topology, combinatorics, and number theory, with particular emphasis on moduli spaces of curves, abelian varieties, Siegel modular forms, and arithmetic geometry. Bergström's work bridges theoretical mathematics with computational approaches, often developing algorithms for complex mathematical structures. His research group actively explores commutative and homological algebra, complex and real algebraic geometry, arithmetic geometry, homotopy theory, and Ramsey theory. The most recent publications reveal a strong focus on cohomology of moduli spaces, Siegel modular forms, abelian varieties over finite fields, and L-functions. His work demonstrates a consistent pattern of combining algebraic geometry with number theory, particularly investigating arithmetic properties of algebraic varieties and developing computational methods for modular forms. The research shows increasing emphasis on algorithmic approaches and connections to theoretical physics through moduli space cohomology. Bergström has supervised several PhD students including Sjoerd de Vries (current), Stefano Marseglia, and Olof Bergvall (with Prof. Carel Faber). He currently mentors postdoctoral researchers Séverin Philip and Thomas Wennink, while former postdocs include Angelina Zheng, Valentijn Karemaker, Oliver Leigh, and Alex Samuel Bamunoba. His research is supported through collaborations with major mathematical networks including the Nordic number theory network and joint seminars with KTH. He is affiliated with the Algebra and Geometry Seminar (KTH and SU) and maintains active research connections through multiple collaborative projects, including joint work with Gerard van der Geer and Carel Faber on Hecke operators and Siegel modular forms. Bergström also contributes to open mathematical research through GitHub repositories containing computational results on cohomology of moduli spaces.