جستجوی استاد راهنمای دانشگاهی

• Dynamical systems
• Arithmetic geometry
• Complex analysis
• +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.

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.

Paata Ivanisviliمشاهده پروفایل

دانشیار

• Analysis
• Partial Differential Equations
• Probability
• +۵ مورد دیگر

Paata Ivanisvili is an Associate Professor at the University of California, Irvine (UCI), Department of Mathematics, School of Physical Sciences. His research focuses on Analysis, Probability, Harmonic Analysis, and Functional Analysis, with a particular emphasis on isoperimetric inequalities, functional inequalities, and discrete structures such as the Hamming cube. He has held visiting positions at institutions including the Hausdorff Research Institute for Mathematics and Princeton University. Ivanisvili has organized conferences such as the Dual Trimester Program at the Hausdorff Institute on Boolean Analysis in Computer Science (2024) and annual Summer/Fall Schools since 2021. He earned his PhD in Mathematics from Michigan State University (2015) and a BS from Saint Petersburg State University (2011). His research interests include sharp inequalities in analysis (e.g., Poincaré, Beckner, Ehrhard), hypercontractivity, and applications to discrete mathematics and probability. He has collaborated with prominent mathematicians such as Fedor Nazarov, Alexander Volberg, and Roman Vershynin. Notable awards include the NSF CAREER Award (2021–2025) and Simons Fellowship in Mathematics (2025–2026). Ivanisvili’s recent work explores the interface between harmonic analysis and discrete mathematics, including studies on additive energies, convex hulls of space curves, and learning theory. His articles frequently address foundational questions in geometric functional analysis, often using tools like Bellman functions and optimal control theory. He actively advises PhD students and has mentored visiting researchers at UCI.

Sugata Mondalمشاهده پروفایل

مدرس

• Spectral Geometry
• Analysis of PDE
• Geometric Analysis
• +۳ مورد دیگر

Dr. Sugata Mondal is a Lecturer in Pure Mathematics at the University of Reading's Department of Mathematics and Statistics, part of the School of Mathematical, Physical and Computational Sciences. He serves as the School Director of Postgraduate Research Studies. His research focuses on spectral geometry, analysis of partial differential equations (PDEs), geometric analysis, and hyperbolic geometry. He obtained his PhD from Université Paul Sabatier in Toulouse, followed by postdoctoral positions at the Max-Planck Institute in Bonn and Indiana University. Previously, he held a Reader position at TIFR, Mumbai until 2022. His academic qualifications include a BSc (Honors) in Mathematics from Ramakrishna Mission Vidyamandira (University of Calcutta) and an M.Math from ISI, Kolkata. His research explores geometric properties of Laplace eigenfunctions on domains and manifolds, with recent work addressing spectral instability, Schiffer's conjecture, and critical points on polygons. His publications span topics in spectral geometry, hyperbolic surfaces, and eigenvalue analysis. Dr. Mondal’s work bridges pure mathematics with geometric analysis, emphasizing the interplay between spectral theory and geometric structures. He teaches Real Analysis I (MA1RA1) and contributes to the Pure Mathematics and Analysis research groups at Reading.

• Number Theory
• Modular Forms
• Galois Representations
• +۵ مورد دیگر

Haruzo HIDA is a Distinguished Research Professor of Mathematics at the University of California, Los Angeles (UCLA). His work spans advanced topics in Number Theory, Modular Forms, Galois Representations, and Arithmetic Geometry. HIDA has held significant positions globally, including lectures and research visits at institutions in India, China, Japan, and Europe. University: University of California, Los Angeles Department: Mathematics Academic Rank: Research Professor Research Interests: HIDA’s research focuses on complex and p-adic Number Theory, Modular Forms, and their connections to Galois Representations, Iwasawa Theory, L-functions, and Automorphic Forms. His recent work addresses adjoint L-values, Selmer groups, and the interplay between arithmetic invariants and geometric structures. Publications: HIDA’s recent articles (2014-2025) explore themes like Hecke algebras, anticyclotomic Iwasawa theory, Tate-Shafarevich groups, and p-adic rigidity. His work often bridges modular forms with arithmetic geometry and automorphic representations. Students: He has supervised numerous PhD students, including Koji Kitagawa, Chandrashekhar Khare, Eknath Ghate, Ashay Burungale, and Jaclyn Lang, contributing to their research in topics like modular forms and arithmetic geometry. Grants: His research has been partially supported by NSF grants, documented across multiple publications and lecture notes.

Ana Caraianiمشاهده پروفایل

استاد

• Number Theory
• Arithmetic Geometry
• Langlands Program
• +۳ مورد دیگر

Ana Caraiani is a Royal Society University Research Fellow and Professor in the Department of Mathematics at Imperial College London, specializing in Number Theory and Arithmetic Geometry. She is a member of the Number Theory group, focusing on the Langlands program, Shimura varieties, and p-adic Galois representations. Her work bridges arithmetic geometry and representation theory, with contributions to modularity lifting theorems, cohomology of Shimura varieties, and local-global compatibility in the Langlands program. Education: She earned a Ph.D. in Mathematics from Harvard University in 2012. She held positions as a Veblen Research Instructor (2013–2015) and Veblen Fellow (2015–2016) at the Institute for Advanced Study's School of Mathematics. Research Interests: Her research emphasizes the classical and p-adic Langlands programs, Shimura varieties, arithmetic geometry, and moduli stacks of Galois representations. Specific topics include vanishing theorems for cohomology, modularity of elliptic curves over CM fields, and applications of perfectoid spaces. Key Contributions: Caraiani has advanced the proof of modularity of elliptic curves over imaginary quadratic fields, established vanishing theorems for Shimura varieties with torsion coefficients, and contributed to the potential automorphy of Galois representations over CM fields. Her work links geometric approaches to arithmetic conjectures, such as the Sato-Tate and Ramanujan conjectures. Awards and Recognition: Royal Society University Research Fellowship (202?), Veblen Research Instructor/Fellowships (2013–2016), and contributions to major collaborative projects like the Potential Automorphy over CM Fields paper in the Annals of Mathematics.

• 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.

Henri Darmonمشاهده پروفایل

استاد

• Number Theory
• Algebraic Geometry
• Elliptic Curves
• +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.

Sanjay Jainمشاهده پروفایل

استاد

• Inductive Inference
• Recursion Theory
• Complexity Theory
• +۳ مورد دیگر

Sanjay Jain is a Provost's Chair Professor in the Department of Computer Science at the School of Computing, National University of Singapore (NUS). His research focuses on theoretical computer science with particular emphasis on inductive inference, recursion theory, complexity theory, and computational learning theory. Education: B.Tech. in Computer Science from Indian Institute of Technology Kharagpur, India (1986) M.S. in Computer Science from University of Rochester, USA (1988) Ph.D. in Computer Science from University of Rochester, USA (1990) Professor Jain's research spans multiple areas of theoretical computer science. His primary contributions are in computational learning theory, where he has made significant advances in understanding the intrinsic complexity of language identification and the limits of inductive inference. His work on recursion theory explores fundamental questions about computability and complexity, while his research in complexity theory addresses structural aspects of computational problems. A notable achievement was his work on "Deciding Parity Games in Quasipolynomial Time," which won the prestigious STOC 2017 best paper award and later the EATCS-IPEC Nerode Prize. Professor Jain's publication record shows a consistent focus on theoretical foundations of computer science, particularly in learning theory and computational complexity. His recent work has expanded into automatic structures, semiautomatic models, and connections between computational learning and algebraic structures. There is a clear progression from foundational work on language identification to more complex models involving automatic functions, transducers, and connections to mathematical logic. Scientific Awards: STOC 2017 Best Paper Award for "Deciding Parity Games in Quasipolynomial Time" EATCS-IPEC Nerode Prize (2021) Professor Jain has served on the editorial board of Information and Computation and has been actively involved in the academic community through program committee memberships for major conferences including COLT, ALT, LATA, TAMC, and PRICAI. He has held leadership roles as program co-chair for ALT 2000 and ALT 2013, and conference chair for ALT 2005. His work has been supported by various research grants, though specific details are not provided in the available materials. Professor Jain leads research in theoretical computer science at NUS, where he has built a strong research group focused on computational learning theory and related areas. His work often involves collaborations with researchers from around the world, particularly with Frank Stephan, with whom he has co-authored numerous papers. His research group has made significant contributions to understanding the fundamental limits and possibilities of computational learning models.

Markus Landمشاهده پروفایل

دانشگاهی

• Algebraic Topology
• Homotopy Theory
• K-Theory
• +۳ مورد دیگر

Markus Land is a Tenure Track Professor at the Department for Mathematics, Ludwig Maximilian University of Munich, affiliated with the Algebraic Geometry Working Group. His research bridges algebraic topology, homotopy theory, and K-theory, focusing on their interplay with L-theory and manifold topology. He has held postdoctoral positions at the University of Copenhagen (supported by an EU Marie Curie Fellowship and DFG Grant) and the University of Regensburg, and earned his PhD at the University of Bonn under Wolfgang Lück. Education : PhD in Mathematics (University of Bonn, 2016) Positions : Postdoctoral (University of Copenhagen, 2019–2022; University of Regensburg, 2016–2019) Research Interests : Markus Land explores algebraic topology and homotopy theory , particularly algebraic K-theory , hermitian K-theory , and their connections to L-theory and manifold topology . His work often applies infinity-categories to foundational problems in operator K-theory and geometric topology. Recent Publications : His research includes groundbreaking studies on chromatic localization in K-theory, Grothendieck-Witt groups in ring theory, and additivity in cobordism categories . Collaborations with leading mathematicians like Georg Tamme and Ulrich Bunke highlight interdisciplinary approaches to algebraic and geometric problems. Awards & Grants : EU Marie Curie Individual Fellowship (2020–2022) DFG Individual Research Grant (2019–2020) Teaching & Academic Leadership : He has designed advanced courses including Topology I–V , Algebraic K-Theory , and Condensed Mathematics , emphasizing homotopy theory and infinity-categories . Future initiatives include student seminars on arithmetic and algebraic geometry to foster academic collaboration. Working Group : As part of the Algebraic Geometry Working Group at LMU Munich, he contributes to seminars and research projects on arithmetic geometry , manifold classification , and spectral algebra .

David Rohrlichمشاهده پروفایل

استاد

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

David Rohrlich is a Professor of Mathematics and Statistics at Boston University, serving as Director of Graduate Studies. His primary affiliation is with the Department of Mathematics and Statistics. He specializes in Number Theory, focusing on topics such as Artin representations, arithmetic statistics, and Galois theory. His research explores areas including algebraic number theory, arithmetic geometry, and representation theory. Notable contributions include studies on self-dual Artin representations, quaternionic structures in arithmetic statistics, and the interplay between Galois representations and L-functions. Rohrlich has published extensively on topics such as Mordell-Weil groups, average multiplicities, and dihedral Artin representations. His work often involves intricate connections between algebraic structures and number-theoretic phenomena. He holds a PhD and has advised numerous graduate students (though specific names are not listed here). His office is located in CDS 433, with regular in-person and virtual office hours.

Franziska Jahnkeمشاهده پروفایل

استاد

• Model Theory
• Set Theory
• Algebra
• +۳ مورد دیگر

Prof. Dr. Franziska Jahnke is a Professor in the Faculty of Mathematics and Computer Science at the University of Münster, affiliated with the Institute for Mathematical Logic and Foundational Research. She specializes in model theory and its applications to algebra, particularly valued fields, set theory, and arithmetic definability. Her research bridges foundational mathematics and algebraic structures, with a focus on henselian valuations, NIP fields, and combinatorial aspects of valued fields. Education: Diplom in Mathematics from Albert-Ludwigs-Universität Freiburg (2009), DPhil in Mathematics from the University of Oxford (2013). Academic roles include Junior Professor at Münster (2017–2024), and a visiting position at the University of Amsterdam (2023–2024). Research Interests: Model theory of fields, arithmetic definability of valuations, perfectoid fields, and connections to infinite combinatorics. Key contributions include work on Ax-Kochen-Ershov principles, NIP fields, and classification conjectures in strongly dependent fields. Recent Activities: Organized workshops on non-archimedean geometry and model theory of valued fields. Recipient of the Teaching Prize 2022 and a fellow of the Daimler und Benz Stiftung. Deputy Equal Opportunity Representative in her department. Supervision: Advised multiple PhD students (e.g., Blaise Boissonneau, Simone Ramello) and postdocs. Taught courses on algebra, logic, and model theory, including lectures on valued fields and stability theory.

David Savittمشاهده پروفایل

استاد

• Algebraic Number Theory
• Galois Representations
• Modular Forms
• +۳ مورد دیگر

David Savitt is a Professor and Chair of the Department of Mathematics at Johns Hopkins University, affiliated with the Krieger School of Arts & Sciences. His research focuses on algebraic number theory, with emphasis on Galois representations, modular forms, and p-adic Hodge theory. He holds a PhD from Harvard University and has served on the board of directors for Canada/USA Mathcamp, a summer program for high school students. His work spans theoretical contributions to arithmetic geometry, including studies on moduli stacks of Galois representations and geometric aspects of the p-adic Langlands program. Education: PhD in Mathematics from Harvard University. Research interests include the interplay between Galois representations and modular forms, p-adic Hodge theory, and moduli spaces. His recent work explores geometric structures in the Emerton-Gee stack and the Breuil-Mézard conjecture. Over 20 years of research has produced influential papers on topics like Serre weight conjectures and crystalline lifts of Galois representations. Professional contributions include editorial roles for journals and books, such as co-editing p-adic Geometry: Lectures from the 2007 Arizona Winter School . His involvement with Mathcamp highlights his dedication to nurturing young talent in mathematics.

Patrick Allenمشاهده پروفایل

دانشیار

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

Chris De Saمشاهده پروفایل

دانشیار

• Machine Learning
• Distributed Systems
• Optimization Algorithms
• +۵ مورد دیگر

Chris De Sa is an Associate Professor in the Department of Computer Science at Cornell University, affiliated with the Cornell Machine Learning Group and leading the Relax ML Lab. His research focuses on algorithmic, software, and hardware techniques for high-performance machine learning, particularly relaxed-consistency stochastic algorithms like asynchronous and low-precision stochastic gradient descent (SGD). He earned his Ph.D. from Stanford University under advisors Kunle Olukotun and Chris Ré. His work emphasizes constructing efficient, parallel, and distributed machine learning frameworks for deep learning and data analytics. Education: Ph.D. in Computer Science, Stanford University (2017) Research Interests: Algorithmic techniques for scalable ML, quantization, distributed optimization, hyperbolic geometry in ML, and reliable measurement of ML systems. His group develops frameworks for efficient inference/training and explores the intersection of ML with domains like agriculture and plant science through courses like PLSCI 7202. Recent Highlights: DARPA YFA Grant (2024), NSF CAREER Award, Google Research Scholar Award, and multiple best paper recognitions. Key contributions include QuIP quantization methods, Coneheads attention mechanisms, and theoretical advances in decentralized training. Awards: NSF CAREER Award DARPA YFA Grant (2024) Google Research Scholar Award Mr. & Mrs. Richard F. Tucker Teaching Award Grants & Advising: Advises 8 Ph.D. students (including Ruqi Zhang, Yucheng Lu, A. Feder Cooper) and holds leadership roles in MLSys conferences. Active in grant-funded research (e.g., NSF Robust Intelligence). Labs/Teams: Leads the Relax ML Lab and participates in Cornell’s Institute for Digital Agriculture (CIDA).