جستجوی استاد راهنمای دانشگاهی

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

• Number Theory
• Arithmetic Geometry
• Automorphic Forms
• +۳ 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.

• Arithmetic Geometry
• Number Theory
• Diophantine Geometry
• +۲ 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.

• Number Theory
• Arithmetic Geometry
• Function Field Arithmetic
• +۷ 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
• Arithmetic Geometry
• Stacks Theory
• +۴ مورد دیگر

Alexander Gorodnik is a Professor of Mathematics at the University of Zurich, focusing on the interplay between dynamical systems and number theory. His work bridges ergodic theory, homogeneous dynamics, and Diophantine approximation, with applications to arithmetic counting problems and geometric distribution of lattice orbits. Current lectures include MAT121: Analysis I and MAT221: Analysis III at the University of Zurich Co-author of the book The ergodic theory of lattice subgroups (Princeton University Press, 2010) Editor of the journal Ergodic Theory and Dynamical Systems His research explores Diophantine approximation through dynamical systems, investigating how orbits of group actions distribute in homogeneous spaces. Key topics include mixing properties , central limit theorems , and metric theorems for multiplicative approximation. Recent publications address automorphic density estimates , discrepancy in intrinsic Diophantine approximation , and effective equidistribution of translated measures. His work often employs tools from representation theory and spectral analysis . Current working group members include Zhiyuan Deng , Zouhair Ouaggag , and Yuval Yifrach . He has taught courses at institutions in Zurich, Bristol, Princeton, and Mumbai, with lecture materials covering topics from ergodic theorems to Každan's property (T) .

• Dynamical Systems
• Analytic Number Theory
• Diophantine Approximation
• +۵ 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 .

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

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

• Extremal Combinatorics
• Ramsey Theory
• Combinatorial Number Theory
• +۳ مورد دیگر

Matthew Emerton is a Professor in the Department of Mathematics at the University of Chicago, part of the Physical Sciences Division. He specializes in number theory, arithmetic geometry, and the Langlands program. His research focuses on automorphic forms, Galois representations, and p-adic methods in arithmetic geometry. Education: BSc (Hons) from the University of Melbourne (1993), PhD in Mathematics from Harvard University (1998), advised by Barry Mazur. Research Highlights: Pioneered work on the p-adic Langlands program, moduli stacks of Galois representations, and prismatic cohomology. Authored over 50 publications, including foundational works on p-adic Hodge theory and local-global compatibility. Awards: Alfred P. Sloan Doctoral Dissertation Fellowship (1997-98), Rackham Summer Faculty Fellowship (1999). Grants: Multiple NSF awards (e.g., DMS-2201242 for 'Arithmetic Aspects of the Langlands Program', DMS-1952705 for geometric aspects of the p-adic Langlands program). Students: Mentored 25+ PhD students and postdocs, many contributing to number theory and representation theory.

• Number Theory
• Arithmetic Geometry
• Automorphic Forms
• +۳ مورد دیگر

Prof. Dr. Philipp Habegger is a faculty member at the University of Basel's Department of Mathematics and Computer Science . His research focuses on Number Theory , specifically Diophantine Geometry, heights on abelian varieties, unlikely intersections, and algebraic number theory. He leads the Research Group in Number Theory and participates in collaborative seminars like the Number Theory Web Seminar with Mike Bennett and Alina Ostafe. Contact : philipp.habegger@unibas.ch | +41 61 207 26 98 Office : Spiegelgasse 1, 4051 Basel, Switzerland Academic Role : Research and teaching in number theory and Diophantine problems Research Overview Habegger's work addresses fundamental questions about the distribution of special points on algebraic varieties and the arithmetic properties of polynomial dynamics. His recent publications analyze degeneracy loci in abelian families, canonical heights, and the geometric Bogomolov conjecture. The 15 most recent articles reflect a focus on number theory, algebraic geometry, and effective bounds in Diophantine problems. Scientific Collaborations Collaborated with Ziyang Gao, Harry Schmidt, Umberto Zannier, and others Contributed to journals: Annals of Mathematics , Forum of Mathematics, Sigma , Compositio Mathematica Key themes: Abelian varieties , Heights , Unlikely intersections , CM jacobians

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

Laura DeMarco is a Professor of Mathematics at Harvard University and holds the Radcliffe Alumnae Professorship at the Radcliffe Institute for Advanced Study. She is affiliated with the Department of Mathematics at Harvard's Science Center (Office 337). Her research focuses on dynamical systems, arithmetic geometry, and complex analysis, with a particular emphasis on algebraic dynamics and the interplay between geometry and number theory. DeMarco earned her Ph.D. in Mathematics from Harvard University in 2002, with a thesis on holomorphic families of rational maps. Her work explores topics such as preperiodic points, moduli spaces of dynamical systems, and arithmetic equidistribution. She has organized events like the Algebraic Dynamics Seminar and participates in conferences worldwide, including the 2025 Diophantine approximation conference in France. Her research publications analyze geometric and arithmetic properties of dynamical systems, such as the geometry of preperiodic points, bifurcation measures, and the classification of polynomial basins of infinity. Her studies often bridge algebraic geometry, complex dynamics, and number theory, contributing to foundational questions in arithmetic dynamics. DeMarco has collaborated extensively with researchers like N. M. Mavraki, H. Krieger, and X. Wang, advancing topics like bounded geometry in dynamical families and uniform results in the Manin-Mumford conjecture. Her work has been published in leading journals such as the Annals of Mathematics, Compositio Mathematica, and the Journal of the European Mathematical Society.

• Dynamical systems
• Arithmetic geometry
• Complex analysis
• +۳ مورد دیگر

Henri Darmon is a Distinguished James McGill Professor in the Department of Mathematics and Statistics at McGill University, affiliated with the Centre Interuniversitaire en Calcul Mathématique Algébrique (CICMA) and the Centre de Recherches Mathématiques (CRM). He holds citizenships of Canada, France, and Switzerland. His research focuses on algebraic number theory, particularly elliptic curves, modular forms, and L-functions, with contributions to the Birch and Swinnerton-Dyer conjecture and Stark conjectures. Education: B.Sc. Mathematics & Computer Science, McGill University (1987) Ph.D. Mathematics, Harvard University (1991) Key Positions: Director of CICMA (1998–2024) Editorial roles at journals like Commentarii Mathematici Helvetici and Transactions of the AMS Organizer of major conferences including CNTA, ICM satellite events, and thematic programs at MSRI and CRM Research Interests: Stark-Heegner points and Euler systems p-adic L-functions and Iwasawa theory Arithmetic of modular curves and Shimura varieties His work bridges analytic and algebraic approaches to number theory, emphasizing computational and geometric methods.

• Number Theory
• Algebraic Geometry
• Elliptic Curves
• +۳ مورد دیگر

Patrick Allen is an Associate Professor in the Department of Mathematics and Statistics at McGill University, where he contributes to research in number theory and related fields. He is affiliated with the Montreal Number Theory Group and the Centre Interuniversitaire en Calcul Mathématique Algébrique (CICMA), focusing on areas such as Galois representations, automorphic forms, and algebraic number theory. His work bridges algebraic geometry and arithmetic, with a particular emphasis on modularity lifting theorems and deformation theory. Allen's research interests include the study of CM fields, modular forms, and elliptic curves, alongside investigations into the Langlands program and p-adic methods. He has published extensively on topics such as potential automorphy, monodromy, and adjoint Selmer groups. His contributions address questions in arithmetic algebraic geometry and cohomological automorphic forms, often intersecting with representation theory. While his articles span over 20 years, recent work (2020–2023) emphasizes the modularity of Galois representations over CM fields and the application of automorphic techniques to solve problems in number theory. Allen’s research often involves collaboration with international experts in algebraic number theory and arithmetic geometry. Scientific Awards: None explicitly listed in the provided materials. Advising & Grants: No formal advisees or grant details are listed in the text. His affiliations with CICMA suggest participation in collaborative research initiatives, though specific grants are not mentioned. Labs/Teams: Active member of the Montreal Number Theory Group and CICMA, contributing to inter-university collaborative projects in algebraic number theory.

• Number Theory
• Galois Representations
• Automorphic Forms
• +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.

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

Manfred Einsiedler is a Professor in the Department of Mathematics at ETH Zurich, Switzerland, with office HG G 64.2 at Rämistrasse 101, 8092 Zurich. He teaches undergraduate and graduate courses including Linear Algebra (HS 2019), Analysis I/II, and Functional Analysis I/II, using his co-authored textbook Functional Analysis, Spectral Theory, and Applications . His research centers on dynamical and equidistribution problems in homogeneous spaces, with focus on closed horocycle orbits, geodesic orbits on the modular surface, and measure rigidity. Key contributions include work on effective equidistribution, entropy methods, and connections between ergodic theory and number theory. He has co-authored foundational texts: Ergodic Theory with a view towards Number Theory and Functional Analysis, Spectral Theory, and Applications in Springer's Graduate Texts in Mathematics series, alongside multiple in-progress volumes on entropy, homogeneous dynamics, and unitary representations. Recent publications explore integer points on spheres, rigidity of invariant measures, and Diophantine approximation on fractals, emphasizing collaborations with Lindenstrauss, Ward, Margulis, and Venkatesh. His work demonstrates consistent focus on homogeneous dynamics with applications to arithmetic problems, particularly through effective methods and measure classification theorems. While no specific awards or student lists are documented in the source, his extensive publication record and textbook authorship establish significant scholarly impact.

• Dynamical systems
• Ergodic theory
• Homogeneous spaces
• +۴ مورد دیگر

Christoph Kehle is an Assistant Professor in the Department of Mathematics at the Massachusetts Institute of Technology (MIT) since 2024. He works at the intersection of General Relativity, Partial Differential Equations, and Mathematical Physics, focusing on black hole stability, cosmic censorship, and gravitational collapse phenomena. Education: PhD in Mathematics (2020) from the University of Cambridge under Mihalis Dafermos, MASt (2015) at Cambridge, and BS/MS (2016) from LMU Munich. Research: His work addresses fundamental questions about black hole interiors, extremal black hole formation, and nonlinear wave dynamics on curved spacetimes. He investigates connections between Diophantine approximation and spacetime stability, as well as turbulence in AdS black hole systems. Scientific Awards: Recipient of the Research Scholar at Trinity College (Cambridge), EPSRC PhD Scholarship, Senior Scholarship Exam Prize, and scholarships from the German Academic Foundation and Max Weber-Program. Publications: 15 most recent articles span nonlinear stability of extremal black holes, critical collapse phenomena, and geometric PDEs. Collaborators include Y. Angelopoulos, R. Unger, A. Figalli, and M. Van de Moortel.

• Analysis
• Partial Differential Equations
• General Relativity
• +۳ مورد دیگر