Find Academic Supervisors

• Algebra
• Combinatorics
• Number Theory
• +3 more

Gábor Somlai is a mathematics researcher at Eötvös Loránd University's Faculty of Science, affiliated with the Department of Algebra and Number Theory since 2006. He is a core member of the HUN-REN-ELTE Geometric and Algebraic Combinatorics Research Group (previously MTA-ELTE until 2023) and participates in the Asymptotic Group Theory ERC project. His institutional roles include contributions to the Mathematics Doctoral School and the Institute of Mathematics. His research spans Algebra , Combinatorics , and Number Theory , with emphasis on spectral sets, tiling problems, group theory, and finite geometry. Recent work explores cyclotomic polynomials, the generalized trifference problem, and connections between tiling and spectral properties in finite abelian groups. His publications reveal a strong focus on combinatorial number theory and algebraic methods in discrete geometry. Somlai's publication trends show sustained contributions to theoretical foundations of tiling and spectral sets (testing Fuglede's conjecture in cyclic groups) Cayley graph properties and CI-group classifications polynomial methods in finite geometry and direction problems His work bridges pure algebra with combinatorial applications, often resolving long-standing conjectures in specialized domains. As part of the HUN-REN-ELTE research group, he collaborates on geometric and algebraic combinatorics projects, leveraging ERC funding for asymptotic group theory investigations. His research infrastructure includes access to the Alfréd Rényi Institute of Mathematics (http://www.renyi.hu) resources.

Julie BergnerView profile

Professor

• Homotopy Theory
• Algebraic Topology
• Algebraic K-Theory
• +3 more

Julie Bergner is a Professor in the Department of Mathematics at the University of Virginia. She is currently on sabbatical during 2024-25 as a Visiting Fellow at Clare Hall, University of Cambridge. Her research focuses on Homotopy Theory, Algebraic Topology, Algebraic K-Theory, and Category Theory, with a particular emphasis on higher category theory and homotopical algebraic structures. University of Virginia (Professor, Department of Mathematics) University of Cambridge (Visiting Fellow at Clare Hall, 2024-25) Her work spans 2-Segal objects, model categories, Waldhausen constructions, and applications to topological field theories. She has received NSF CAREER awards for her research on equivariant topological field theories and higher cluster categories. Her recent publications explore combinatorial models, enriched categories, and homotopy limits in the context of functor calculus and higher structures. Julie Bergner contributes to mathematical exposition through articles on writing papers in the mathematical sciences and homotopy theory applications. She is actively involved in the department's topology seminar and supports collaborative learning initiatives. Her research has implications in algebraic topology, category theory, and their interdisciplinary applications.

Max AlekseyevView profile

Associate Professor

• Computational Graph Theory
• Enumerative Combinatorics
• Computational/Algorithmic Biology
• +1 more

Max Alekseyev is an Associate Professor in the Mathematics Department and Computational Biology Institute. His research spans computational graph theory, enumerative combinatorics, computational/algorithmic biology, and comparative genomics. He focuses on interdisciplinary problems, blending mathematics with biological applications, particularly in genome assembly and analysis. His work includes advancements in genome scaffolding algorithms, combinatorial sequence analysis, and mathematical biology. Notable contributions involve genome assembly tools like CAMSA and studies on ancestral genome reconstruction. He also explores theoretical topics such as Bernoulli series generalizations and modular data classification. His research trends highlight a blend of pure mathematics (e.g., number theory, graph theory) and applied computational methods, addressing challenges in genomics and evolutionary biology. He secured an NSF Student Travel Grant in 2018 for computational molecular biology.

Nathan KaplanView profile

Professor

• Number Theory
• Algebraic Geometry
• Combinatorics
• +6 more

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.

Xiaochun LiView profile

Professor

• Harmonic Analysis
• Functional Analysis
• Differential Equations
• +3 more

Xiaochun Li is a Professor of Mathematics at the University of Illinois at Urbana-Champaign, affiliated with the Department of Mathematics within the College of Liberal Arts & Sciences. His research focuses on Harmonic Analysis, with expertise in multilinear oscillatory integrals, Hilbert transforms along vector fields, and multilinear Carleson theorems. He earned his Ph.D. from the University of Missouri at Columbia in 2001. His recent work explores topics such as pointwise convergence of cone multipliers, Stein-Tomas restriction theorems, and polynomial Roth theorems. These studies bridge functional analysis, Fourier analysis, and operator theory, contributing to foundational advancements in mathematical analysis. No scientific awards or grants are explicitly listed in the provided materials. His research is supported through his academic appointment, and he maintains an active publication record in prestigious journals such as the Journal of Functional Analysis and Mathematische Annalen.

Leo GoldmakherView profile

Associate Professor

• Number Theory
• Cryptography
• Topology
• +7 more

Leo Goldmakher is an Associate Professor of Mathematics at Williams College, where he teaches courses in cryptography, topology, Fourier analysis, measure theory, and analytic number theory. He holds a B.A. in Mathematics from Princeton University (2004) and a Ph.D. in Mathematics from the University of Michigan (2009). Research interests Teaching areas Publications His research focuses on number theory, including topics such as Gauss sums, character sums, multiplicative functions, and analytic methods. He has contributed to refinements of classical theorems like Lagrange’s four-square theorem and Artin’s primitive root conjecture. His recent publications explore bounds on character sums, spectral properties of random graphs, and algebraic structures in number theory. The work demonstrates a strong emphasis on analytic and algebraic techniques. Leo has been affiliated with Williams College’s Department of Mathematics and Statistics, which received the 2014 Exemplary Department Award from the American Mathematical Society. He has taught advanced courses such as Cryptography, Topology, and Analytic Number Theory, though these were not offered in the 2025/26 academic year.

Steven BradlowView profile

Professor

• Differential Geometry
• Gauge Theory
• Algebraic Geometry
• +3 more

Steven Bradlow is a Professor in the Department of Mathematics at the University of Illinois at Urbana-Champaign (UIUC), affiliated with the College of Liberal Arts & Sciences. His research focuses on differential geometry, gauge theory, algebraic geometry, and topology, with particular emphasis on Higgs bundles, moduli spaces, and geometric structures. He holds a PhD from the University of Chicago (1988) and has held additional campus roles as a Professor of Mathematics. Research Interests: Bradlow’s work explores advanced topics such as holomorphic vector bundles, stability conditions, and geometric invariant theory. His studies of Higgs bundles integrate techniques from algebraic geometry, differential geometry, and mathematical physics, addressing questions related to moduli spaces, spectral curves, and representation varieties. He investigates exotic components of surface group representations and their connections to Teichmüller theory, contributing to the broader understanding of geometric structures and their topological properties. Recent Work Trends: Recent publications highlight his focus on Cayley correspondences, higher rank Teichmüller spaces, and uniformization techniques for branched surfaces. His collaborative projects often bridge algebraic and differential geometry, with applications to gauge theories and geometric analysis. He has also contributed to editorial work honoring peers like Karen Uhlenbeck and Oscar García-Prada. Grants & Advising: While specific grant details are not listed, Bradlow has been involved in NSF-funded initiatives (e.g., EMSW21-MCTP, RNMS: Geometric Structures). His advising contributions are reflected in co-authored works with students/postdocs such as Brian Collier and Oscar García-Prada. He is associated with research networks exploring geometric representation theory and mathematical collaborations. Labs/Teams: Active within UIUC’s Department of Mathematics, Bradlow collaborates with researchers in geometry and topology. His work often intersects with interdisciplinary groups studying geometric structures, though specific lab affiliations are not detailed here.

Alireza Salehi GolsefidyView profile

Professor

• Algebra
• Number Theory
• Combinatorics
• +4 more

Alireza Salehi Golsefidy is a Professor in the Department of Mathematics at the University of California, San Diego (UCSD). He received his Ph.D. from Yale University under Gregory Margulis, a Fields Medalist. His research focuses on algebraic, arithmetic, and analytic properties of linear groups, homogeneous dynamical systems, and expander graphs. He has held positions at Princeton University and the Institute for Advanced Study as a Veblen Research Instructor before joining UCSD in 2011. Education: Ph.D. in Mathematics, Yale University (2006). Research Interests: His work bridges discrete subgroups of Lie groups, homogeneous dynamics, and number theory. Recent contributions include studies on super-approximation, spectral independence, and geometric group theory. He has organized workshops on thin groups, arithmetic groups, and homogeneous dynamics at MSRI and Oberwolfach. Grants & Awards: Alfred P. Sloan Research Fellowship (2012), Clay Liftoff Award (2006), NSF grants 1602137, 1902090, and 2302519. His research explores applications of expander graphs and random walks in algebraic structures. Teaching: Currently teaching Algebra (Math 200C) in Spring 2025. Past courses include advanced algebraic topology, representation theory, and graduate-level number theory. Labs/Teams: Co-organizes UCSD's Algebra Seminar and contributed to the 2013 Lie Theory Workshop. Active in collaborative projects on group actions and automorphic forms.

Nathan NgView profile

Professor

• Analytic Number Theory
• Riemann Zeta Function
• L-functions
• +2 more

Nathan Ng is a Professor in the Department of Mathematics and Computer Science at the University of Lethbridge , Canada, and has served as the PIMS Site Director since 2019. His research lies at the intersection of analytic number theory and L-functions, with a particular focus on the Riemann zeta function, prime number distribution, and multiplicative number theory. Education: He earned a B.Sc. from the University of British Columbia (1994), an M.Sc. from the University of Toronto (1995), and a Ph.D. from UBC (2000). His doctoral thesis, Limiting Distributions and Zeros of Artin L-functions , laid the groundwork for his subsequent research. Research Interests: His work spans a wide range of topics in analytic number theory, including: Mean values and moments of L-functions Non-vanishing of L-functions Distribution of zeros of the Riemann zeta function Prime number races and comparative prime number theory Chebotarev density theorem and applications Convolution sums of arithmetic functions Publications: He has published extensively in leading journals such as Proceedings of the London Mathematical Society , Duke Mathematical Journal , and Advances in Mathematics . His recent work includes studies on the sixth and eighth moments of the Riemann zeta function, subconvexity bounds for L-functions, and effective versions of Chebotarev's density theorem. Awards and Honors: He received the Canadian Mathematical Society Doctoral Prize in 2001 for his outstanding doctoral dissertation. Student Supervision: He has supervised or co-supervised numerous graduate students and postdocs, including: Ph.D. Students: Farzad Aryan (2016), Sourabhashis Das (ongoing), Quanli Shen (ongoing) M.Sc. Students: Allysa Lumley (2014), Majid Shahabi (2012) Postdocs: Lee Troupe, Peng-Jie Wong, Alia Hamieh, Timothy Trudgian, Brandon Fodden Seminar and Conference Organization: He is an active organizer of the Lethbridge Number Theory and Combinatorics Seminar and has co-organized major conferences such as the Canadian Number Theory Association (CNTA XII) meeting in 2012 and the Analytic Number Theory and Diophantine Approximation Summer School in Ottawa (2008). Labs and Teams: He is affiliated with the Lethbridge Number Theory Group , a vibrant research collective within the department that fosters collaboration and supports graduate training in number theory.

• graph algorithms
• optimization
• high-dimensional geometry
• +3 more

Yang P. Liu is an Assistant Professor in the Computer Science Department at Carnegie Mellon University's School of Computer Science. Previously, he was a Postdoctoral Member at the Institute for Advanced Study and earned his PhD from Stanford University under the supervision of Aaron Sidford. He completed his undergraduate studies at MIT, graduating in May 2018. His educational background includes: PhD in Computer Science, Stanford University (Advisor: Aaron Sidford) Bachelor's degree, Massachusetts Institute of Technology (graduated May 2018) Dr. Liu's research spans the intersection of mathematics and computer science, with particular focus on graph algorithms , optimization , high-dimensional geometry , and additive combinatorics . His work often develops novel algorithmic techniques that bridge theoretical insights with practical applications. He has made significant contributions to areas such as convex optimization, linear programming, and combinatorial problems. His teaching includes courses like "A Principled Approach to Optimization" (CS 15-759), which covers rigorous treatments of convex optimization topics including gradient descent, interior point methods, linear regression, linear programming, and sparsification. His extensive publication record in top-tier conferences (FOCS, STOC, SODA) demonstrates a consistent focus on developing almost-linear time algorithms for fundamental graph problems, optimization techniques, and combinatorial theorems. Recent work shows increasing emphasis on combinatorial lines, corners theorem, and k-CSP approximability, while maintaining strong connections to optimization theory and graph algorithms. Dr. Liu has received notable recognition for his work: National Defense Science and Engineering Graduate (NDSEG) Fellowship (2018-2021) Google PhD Fellowship (2022-2023) Best Paper award at FOCS 2022 for "Maximum Flow and Minimum-Cost Flow in Almost Linear Time" Best Student Paper at STOC 2021 for "Discrepancy Minimization via a Self-Balancing Walk" His research has been supported by prestigious fellowships including the NDSEG Fellowship and Google PhD Fellowship. His work on graph algorithms, optimization, and combinatorics involves collaborations with researchers across theoretical computer science and mathematics. His publications often involve co-authors from multiple institutions, suggesting active research collaborations across the field. Dr. Liu maintains an active research program with a focus on developing efficient algorithms for fundamental computational problems. His recent work continues to push the boundaries of what's computationally feasible in graph algorithms, optimization, and combinatorial mathematics, with particular emphasis on achieving almost-linear time complexity for challenging problems.

Elon LindenstraussView profile

Professor

• Ergodic theory
• Topological dynamics
• Flows on homogeneous spaces
• +6 more

Elon Lindenstrauss is a Professor at Hebrew University since 2008 and previously held faculty positions at Princeton University (2004-2010) and Stanford University (2001-2003). He is a member of the Academia Europaea (elected 2012) and has been affiliated with prestigious institutions including the Institute for Advanced Study (Princeton) and Courant Institute (NYU). Fields Medal recipient (2010) ERC Advanced Grant awardee (2011) Recipient of multiple fellowships including Clay Mathematics Institute (2003-2005) and Clore Fellowship (1998-1999) His research focuses span multiple mathematical disciplines: Ergodic theory and dynamical systems Homogeneous spaces and equidistribution Connections between number theory and quantum chaos Additive combinatorics and random walks As a leading mathematician, he has organized major conferences, including: 2013-14 Semester program at Hebrew University 2010 Oberwolfach workshop on Homogeneous Dynamics 2007 Clay Summer School on Homogeneous Flows

• Ergodic Theory
• Combinatorics
• Ergodic Ramsey Theory
• +3 more

Vitaly Bergelson is a Professor of Mathematics and Physical Sciences at The Ohio State University, affiliated with the Department of Mathematics within the College of Arts and Sciences. His work focuses on Ergodic Theory , Combinatorics , Ergodic Ramsey Theory , Polynomial Szemerédi Theorems , and Number Theory . He holds a PhD from the Hebrew University of Jerusalem (1984). His research explores the interplay between ergodic systems, combinatorial structures, and number-theoretic phenomena. Notable contributions include polynomial extensions of Szemerédi's theorem and foundational work on ergodic Ramsey theory. Recent articles address topics like multiplicative functions, Diophantine approximations, and quasirandom group structures. His work often bridges abstract mathematical frameworks with concrete combinatorial problems, yielding applications in additive combinatorics and symbolic dynamics. Publications highlight advancements in recurrence properties, uniform distribution, and the structure of algebraic dynamical systems. Collaborations with scholars like A. Leibman, N. Hindman, and J. Moreira underscore his interdisciplinary approach. His research is disseminated through top-tier journals such as Inventiones Mathematicae and Journal d'Analyse Mathématique .

Tim BrowningView profile

Professor

• Number Theory
• Analytic Number Theory
• Diophantine Geometry
• +4 more

Tim Browning is a Professor of Number Theory at the Institute of Science and Technology Austria (IST Austria). He leads the Browning Group, focusing on analytic number theory and its interfaces with algebraic geometry. His research addresses Diophantine equations, rational points on algebraic varieties, and the distribution of arithmetic objects. He organizes the Algebraic Geometry & Number Theory Seminar and the Women in Math Day. Previously, he held roles at the University of Bristol and University of Oxford. He has authored over 100 publications and received accolades including the Ferran Sunyer i Balaguer Prize and an ERC Starting Grant. His group includes PhD students and postdocs working on topics like rational points, sieve methods, and arithmetic statistics. Education: PhD in Mathematics, University of Oxford (2002) Postdoctoral Fellowships at University of Oxford and Université de Paris-Sud Research Interests: Analytic and arithmetic methods in number theory, Diophantine geometry, rational points on varieties, circle method, sieve theory, and arithmetic statistics. His work often combines geometric and analytic techniques, such as the circle method and algebraic geometry to solve problems like Manin's conjecture and the distribution of solutions to polynomial equations. Grants & Leadership: ERC Starting Grant (2012) Serves on editorial boards of journals like Compositio Mathematica and Commentarii Mathematici Helvetici Organizes international conferences and workshops Labs/Teams: Leads the Browning Group at IST Austria, which includes postdocs and PhD students working on number theory and algebraic geometry. Collaborates with researchers globally on topics like the arithmetic of Fano varieties and rational curves.

Asaf ShapiraView profile

Professor

• Extremal Combinatorics
• Graph Theory
• Property Testing
• +4 more

Professor Asaf Shapira is a faculty member in the Department of Theoretical Mathematics at Tel Aviv University's School of Mathematical Sciences. He has been actively contributing to combinatorics and graph theory research for over a decade, with numerous publications in top journals including Journal of the ACM, Advances in Mathematics, and Geometric and Functional Analysis. Professor Shapira's research focuses on extremal combinatorics, graph theory, and property testing. His work explores fundamental questions in Ramsey theory, hypergraph theory, and probabilistic methods in combinatorics. He has made significant contributions to the study of graph regularity, removal lemmas, and extremal problems in dense and sparse graphs. His recent publications demonstrate a consistent focus on theoretical aspects of combinatorics with connections to theoretical computer science. A notable trend is his work on developing polynomial bounds for various combinatorial theorems and exploring connections between combinatorial structures and computational complexity. His research often bridges pure mathematics with theoretical computer science applications. Professor Shapira teaches advanced courses at Tel Aviv University including Extremal Graph Theory, Basic Combinatorics, and seminars on specialized topics in combinatorics. His teaching spans undergraduate and graduate levels, reflecting his commitment to educating the next generation of mathematicians.

Tibor SzabóView profile

Professor

• Combinatorics
• Extremal Graph Theory
• Random Structures and Algorithms
• +5 more

Tibor Szabó is a Professor in the Combinatorics and Graph Theory group at the Department of Mathematics, Freie Universität Berlin. He holds a PhD from The Ohio State University, advised by Ákos Seress. Prior to his current position, he held roles at McGill University, ETH Zürich, the Institute for Advanced Study (Princeton), and the University of Illinois (UIUC) as a J.L. Doob Research Assistant Professor. Research Interests: His work focuses on combinatorics and combinatorial optimization, including extremal problems, random structures and algorithms, pseudorandom graphs, positional games, and the combinatorics of linear programming. He explores tools from algebra, probability theory, and topology applied to combinatorics. Teaching: He teaches courses such as Algorithmic Combinatorics, Extremal Combinatorics, and runs the Combinatorics Seminar. His lecture notes include works on positional games and explicit constructions in extremal combinatorics. Students & Postdocs: Notable PhD advisees include Yamaan Attwa, Silas Rathke, Simona Boyadzhiyska, and Patrick Morris. Postdoctoral fellows include Olaf Parczyk and Anurag Bishnoi. His research has involved collaborations with over 50 co-authors. Funding & Grants: Supported by grants from the Swiss National Science Foundation (SNF) and German Research Foundation (DFG), focusing on topics like positional games and extremal graph theory.