جستجوی استاد راهنمای دانشگاهی

Ricky Ini Liuمشاهده پروفایل

دانشیار

• Algebraic Combinatorics
• Algebraic Geometry
• Combinatorial Geometry
• +۵ مورد دیگر

Ricky Ini Liu is an Associate Professor in the Department of Mathematics at the University of Washington. Previously, he held positions at North Carolina State University, the University of Michigan, and the University of Minnesota. He earned his Ph.D. in Mathematics from MIT in 2010 under Alexander Postnikov. His research focuses on algebraic combinatorics, particularly its intersections with algebraic geometry, combinatorial geometry, and representation theory. Key interests include Schubert polynomials, polytopes, Hopf algebras, and Kronecker coefficients. He has contributed to foundational work on birational rowmotion, Gelfand-Tsetlin polytopes, and Fomin-Kirillov algebras. Liu has taught a wide range of courses at UW, including special topics in dynamical algebraic combinatorics, combinatorial theory, and problem-solving. He has also been a key instructor at the Mathematical Olympiad Summer Program since 2007 and mentored undergraduates in research programs at the University of Minnesota, Duluth. His publications span high-impact journals like Selecta Mathematica and Journal of Combinatorial Theory , with recent work addressing topics such as determinantal formulas for Schubert polynomials and applications of flow polytopes to diagonal harmonics. Though no specific awards are listed, his extensive publication record and academic roles reflect significant contributions to combinatorial mathematics.

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.

Alexander Gorodnikمشاهده پروفایل

استاد

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

Imre Leaderمشاهده پروفایل

استاد

• Extremal Combinatorics
• Ramsey Theory
• Combinatorial Number Theory
• +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

• Nonlinear partial differential equations
• Singularity formation
• Mathematical analysis
• +۲ مورد دیگر

Manuel Del Pino is Professor at the University of Bath's Department of Mathematical Sciences and Royal Society Professor specializing in nonlinear partial differential equations. His research focuses on singularity formation, geometric evolution equations, and asymptotic analysis in fluid dynamics and mathematical physics. His investigations encompass blow-up phenomena in heat equations, vortex dynamics in Euler flows, and minimal surface theory. Current projects examine infinite-time singularity formation in parabolic equations and asymptotic properties of vortex configurations. Del Pino has received the Royal Society Professorship and leads multiple grants including 'Asymptotic patterns in nonlinear evolution problems' (EPSRC). He maintains collaborations with researchers globally through projects on singularity formation in PDEs.

David Jerisonمشاهده پروفایل

استاد

• Fourier analysis
• partial differential equations
• free boundary problems
• +۲ مورد دیگر

David Jerison is a Professor of Mathematics at the Massachusetts Institute of Technology (MIT), where he conducts research in Fourier analysis and partial differential equations. His work focuses primarily on free boundary problems and, more recently, on internal Diffusion Limited Aggregation (internal DLA), a stochastic growth model. He maintains an active research program with numerous publications in leading mathematical journals. Professor Jerison's research spans several interconnected areas of mathematical analysis. His primary interests include Fourier analysis and partial differential equations, with particular emphasis on free boundary problems. In recent years, he has expanded his research to include internal Diffusion Limited Aggregation, a stochastic growth model that has connections to probability theory and mathematical physics. His work often bridges geometric analysis, spectral theory, and probabilistic methods, demonstrating the deep connections between different branches of mathematics. Analysis of Professor Jerison's recent publications reveals a consistent focus on geometric aspects of partial differential equations, particularly free boundary problems. His research shows progression from classical PDE theory toward more stochastic and probabilistic approaches, as evidenced by his work on internal DLA. The publications demonstrate interdisciplinary connections between mathematical analysis, probability theory, and mathematical physics, with applications ranging from geometric measure theory to quantum mechanics. Professor Jerison is actively involved in teaching and mentoring at MIT. He has taught courses including Differential Equations (18.03), Fourier Analysis and Applications (18.103), and Differential Analysis (18.155). He also directs the Summer Program for Undergraduate Research (SPUR), which is exclusively for MIT undergraduates, and organizes the mathematics section of the Research Science Institute (RSI) for high school students. His teaching materials are available through MIT's Open Courseware platform, indicating his commitment to educational outreach and accessibility.

David Eppsteinمشاهده پروفایل

استاد

• Graph Algorithms
• Computational Geometry
• Graph Theory
• +۳ مورد دیگر

David Eppstein is a Distinguished Professor of Computer Science at the University of California, Irvine (UCI), affiliated with the Donald Bren School of Information & Computer Sciences. He holds academic leadership roles as director of the Center for Algorithms and Theory of Computation and associate director of the Center for Algorithms, Combinatorics, and Optimization. His research focuses on graph algorithms, computational geometry, discrete mathematics, and geometric graph theory. Eppstein earned a B.S. in Mathematics from Stanford University (1984) and a Ph.D. in Computer Science from Columbia University (1989). Research Interests: Graph drawing, information visualization, dynamic graph algorithms, mesh generation, optimal triangulation, K-shortest paths, subgraph isomorphism, data depth, exponential-time algorithms for NP-hard problems. Awards: ACM Fellow (2012), AAAS Fellow (2017), Distinguished Professor (2020), Best Paper Awards (2023, 2022), and SIAM recognition. Grants: Co-PI on a $1.2M NSF grant (2022) for geometric graph research, and previous NSF grants for algorithm studies (2016). His work bridges theoretical computer science and practical applications, including contributions to graph visualization, geometric algorithms, and combinatorial optimization. Notable recent achievements include resolving open questions in graph biplanarity and authoring the book Forbidden Configurations in Discrete Geometry (2018).

• Algebraic Geometry
• Symplectic Geometry
• Mathematical Physics
• +۱ مورد دیگر

Kazushi Ueda is an Associate Professor at the Graduate School of Mathematical Sciences, The University of Tokyo, where he has been since April 2015. His research spans algebraic geometry, symplectic geometry, and mathematical physics, with a focus on homological mirror symmetry and its applications to moduli spaces, Calabi-Yau manifolds, and singularities. He previously held academic positions at Osaka University from 2006 to 2015, including roles as Assistant Professor and Associate Professor. Ueda has also had visiting appointments at institutions such as the University of Oxford, Max Planck Institute for Mathematics, and Korea Institute for Advanced Study. Bachelor of Science, Kyoto University (1997-2001) Master of Science, Kyoto University (2001-2003) Doctor of Science, Kyoto University (2003-2006) Ueda's research explores the deep interplay between complex and symplectic geometry through mirror symmetry, particularly in the context of Calabi-Yau varieties, toric degenerations, and dimer models. His work addresses derived categories, stability conditions, and moduli problems, with recent contributions to noncommutative algebraic geometry and applications in mathematical physics. He has collaborated extensively with researchers like Akira Ishii, Masahiro Futaki, and Shinnosuke Okawa. His publications highlight homological mirror symmetry for K3 surfaces, Grassmannians, and singularities, as well as studies on modular forms, cluster transformations, and the Grothendieck ring. Ueda is a member of the Mathematical Society of Japan and has contributed to educational programs, including graduate lectures on mirror symmetry and symplectic geometry.

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.

Alan Hammondمشاهده پروفایل

استاد

• Statistical Mechanics
• Mathematical Probability
• Probability Theory
• +۵ مورد دیگر

Alan Hammond is a Professor in the Department of Statistics at the University of California, Berkeley. His research focuses on rigorous mathematical probability techniques applied to problems in statistical mechanics, including percolation theory, polymer models, and random growth processes. He has contributed to understanding critical phenomena, phase transitions, and universality classes in stochastic systems. Hammond's work spans topics such as KPZ universality, Brownian motion, and the geometry of random media. He has investigated models like last passage percolation, self-avoiding walks, and tug-of-war games, often uncovering deep connections between stochastic processes and nonlinear PDEs. His teaching includes courses on stochastic processes and statistical theory at both graduate and undergraduate levels. Notable research highlights include studies on fractal properties of Airy processes, stability in dynamical last passage percolation, and the behavior of geodesics in random environments. His contributions bridge probability theory with applications in physics and combinatorics.

• Dynamical systems
• Ergodic theory
• Homogeneous spaces
• +۴ 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.

Josef Dickمشاهده پروفایل

استاد

• Numerical Integration
• Quasi-Monte Carlo Rules
• Number Theory
• +۵ مورد دیگر

Professor Josef Dick serves as a Professor and Deputy Head in the School of Mathematics & Statistics at the University of New South Wales (UNSW). With a distinguished career in computational mathematics, he has established himself as a leading researcher in numerical integration methods and quasi-Monte Carlo theory. His work bridges theoretical mathematics with practical computational applications across various scientific domains. Dr. Dick earned his PhD in Mathematics from UNSW in 2004 and his MSc in Mathematics from the University of Salzburg in 2001. His academic journey reflects a strong foundation in both theoretical and applied mathematics, which has informed his subsequent research contributions. Professor Dick's research primarily focuses on numerical integration and quasi-Monte Carlo rules , employing techniques from number theory , abstract algebra (particularly finite fields), discrepancy theory , wavelet theory , and statistics . His work provides rigorous analysis of practical algorithms for computational problems, with implementations often provided in Matlab to bridge theory and application. His research has successfully addressed point distributions on the unit cube for numerical integration, completely uniformly distributed sequences for Markov chain quasi-Monte Carlo algorithms, and explicit constructions of uniformly distributed points on the sphere. Analysis of his recent publications (2022-2025) reveals a consistent focus on advancing quasi-Monte Carlo methods, with increasing integration of machine learning techniques and applications to complex computational problems. His work demonstrates strong interdisciplinary connections between pure mathematics, computational science, and practical engineering applications, particularly in uncertainty quantification and high-dimensional numerical integration. Discovery project from Australian Research Council (2012-2014): "Mathematics in the round - the challenge of computational analysis on spheres" Queen Elizabeth II Fellowship from Australian Research Council (2010-2014): "Algebraic methods for Markov Chain Monte Carlo and quasi-Monte Carlo" UNSW Vice Chancellor Fellowship (2006-2009) Professor Dick has supervised numerous PhD and Honours students working on topics including Quasi-Monte Carlo methods, Discrepancy Theory, Markov chain Monte Carlo, and Uncertainty Quantification. His research has been supported by significant grants from the Australian Research Council, including serving as Chief Investigator on multiple projects. Beyond his research, he serves as an Editor for the Journal of Complexity and Journal of Approximation Theory, demonstrating his leadership in the mathematical community. He teaches courses in Algebra and Mathematical Computing for Finance at UNSW.

Nathan Kaplanمشاهده پروفایل

استاد

• Number Theory
• Algebraic Geometry
• Combinatorics
• +۶ مورد دیگر

Nathan Kaplan is a Professor in the Department of Mathematics at the University of California, Irvine, where he conducts research in number theory, algebraic geometry, and combinatorics. His work spans rational points on varieties over finite fields, arithmetic statistics, coding theory, and the study of numerical semigroups. He is actively involved in the mathematical community, organizing seminars and conferences including the UC Irvine Number Theory Seminar and the Southern California Number Theory Day. Dr. Kaplan received his PhD from Harvard University in 2013 under the direction of Noam Elkies. Following his doctorate, he was a postdoctoral researcher at Yale University from 2013-2015 before joining the faculty at UC Irvine. His research interests focus on the intersection of number theory and algebraic geometry, with particular attention to problems involving rational points on varieties over finite fields, arithmetic statistics, and coding theory. He has made significant contributions to the study of numerical semigroups, cokernels of random p-adic and integer matrices, and quadratic forms and lattices. His work often bridges theoretical mathematics with applications in coding theory and cryptography. Analysis of his recent publications shows a strong trend toward combinatorial aspects of number theory, particularly in the study of numerical semigroups and their properties. He frequently collaborates with researchers across institutions, with recent work spanning algebraic geometry, combinatorics, and coding theory. His publications demonstrate expertise in both theoretical developments and computational aspects of number theory. Dr. Kaplan is deeply committed to undergraduate research and mentoring. He has experience as a mentor for undergraduate research projects through programs including SUMRY (a research program for Yale undergraduates), the University of Minnesota-Duluth REU program, and the Trinity University REU program. He actively encourages undergraduates to apply for summer research opportunities and has organized numerous outreach activities. He is an organizer of the UC Irvine Number Theory Seminar and the Southern California Number Theory Day conference series. In 2018, he co-organized the Conference on Open Questions in Cryptography and Number Theory in honor of Alice Silverberg's 60th Birthday. Dr. Kaplan has given numerous talks at mathematical venues including the Museum of Mathematics' Math Encounters series, where he presented "Error-Correcting Codes: The Mathematics of Communication" in July 2022. He has also spoken at the Yale Undergraduate Math Society, the UCI Math Circle, and various other outreach events.

Jörn Steudingمشاهده پروفایل

استاد

• Zeta and L-Functions
• Diophantine Analysis
• Modular Forms and Elliptic Curves
• +۱۲ مورد دیگر

Professor Jörn Steuding holds the Professorship for Number Theory at the University of Würzburg since 2006, where he is affiliated with the Institute of Mathematics within the Faculty of Mathematics and Computer Science. His academic career includes a Ramon y Cajal research position at Universidad Autónoma de Madrid (2004-2006), postdoctoral work at the University of Frankfurt under Professors W. Schwarz and J. Wolfart (1999-2004), and completion of his habilitation at Frankfurt in 2004. His educational background includes a PhD from the University of Hannover in 1999 under Prof. G.J. Rieger, where he also served as an assistant from 1996-1999, and undergraduate studies in mathematics at Hannover from 1991-1995. Professor Steuding's research spans multiple areas of number theory, with particular focus on Zeta and L-functions (including zero distribution, universality properties, and connections to Random Matrix Theory), Diophantine analysis (covering approximation theory, equations, and the abc conjecture), elliptic curves and modular forms , algebraic number theory (including arithmetically equivalent fields), and elementary number theory with applications to primality testing and factorization. His work often bridges theoretical foundations with historical perspectives, as evidenced by his research on the Hurwitz brothers' contributions to complex continued fractions. His publication record demonstrates consistent contributions to leading journals in number theory, with research trends showing evolution from foundational work on Riemann zeta function zeros to broader investigations of L-functions in the Selberg class, Diophantine problems over quadratic fields, and historical aspects of number theory. His publications appear in prestigious journals including Mathematische Annalen, Acta Arithmetica, and the Bulletin of the American Mathematical Society. Professor Steuding has authored significant monographs including Diophantine Analysis (CRC Press/Chapman-Hall, 2005), Value distribution of L-functions (Springer Lecture Notes in Mathematics 1877, 2007), and Elementary Number Theory: A Gentle Introduction to Higher Mathematics (Springer Spektrum, 2015, co-authored with N. Oswald). He serves as the Erasmus Coordinator for his department alongside Dr. Jens Jordan, facilitating international academic exchanges. His research collaborations span multiple institutions, with notable co-authors including N. Oswald, M. Technau, H. Nagoshi, and L. Pankowski. Professor Steuding leads the Number Theory team at the University of Würzburg, maintaining an active research group focused on contemporary problems in analytic and algebraic number theory. His work continues to explore connections between classical number theory and modern mathematical physics through Random Matrix Theory applications.

• Analytic Number Theory
• Number Theory
• Mathematics

Dr. Jiseong Kim serves as a Visiting Assistant Professor in the Department of Mathematics at the University of Mississippi, affiliated with the College of Liberal Arts. His research focuses on Analytic Number Theory , exploring advanced topics such as divisor functions, Hecke eigenvalues, and Goldbach conjectures. He teaches core courses including Unified Calculus & Analytic Geometry I, III, IV, and Elementary Differential Equations. His recent work emphasizes applications of zero-free regions, shifted sums, and ergodic averages in number-theoretic contexts. Research Interests: Analytic Number Theory with specializations in additive problems, distribution of arithmetic functions, and L-functions. His studies often involve advanced techniques from modular forms and automorphic representations. His publications (2021–2024) reveal a focus on primes in short intervals, divisor function behavior, and Hecke eigenvalue distributions. While no awards are explicitly listed, his active publication record indicates strong scholarly engagement. Teaching responsibilities include foundational calculus and differential equations courses. No grants or student advisees are currently documented.