Find Academic Supervisors

Ricky Ini LiuView profile

Associate Professor

• Algebraic Combinatorics
• Algebraic Geometry
• Combinatorial Geometry
• +5 more

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.

• Applied Topology
• Dynamical Systems
• Algebraic Topology
• +5 more

Robert Ghrist is the Andrea Mitchell University Professor at the University of Pennsylvania with dual appointments in the Department of Mathematics and the Department of Electrical and Systems Engineering. He serves as Associate Dean for Undergraduate Education for Penn Engineering. His educational background includes a B.S. in Mechanical Engineering from the University of Toledo (1991), and M.S. and Ph.D. degrees in Applied Mathematics from Cornell University (1994, 1995). Ghrist's research bridges pure and applied mathematics, focusing on applied algebraic topology , dynamical systems , and geometric methods in data science. His work extends to network theory, topological data analysis, and computational geometry, with applications spanning robotics, neuroscience, and social dynamics. Key innovations include developing sheaf-theoretic approaches for networked systems and persistence homology techniques for high-dimensional data. Analysis of his recent publications reveals a strong emphasis on lattice-theoretic frameworks , topological robotics , and network dynamics , with emerging applications in neural data interpretation and geometric computing. His research consistently integrates category theory with real-world engineering challenges. Significant scientific recognition includes: Presidential Early Career Award (PECASE, 2004) Scientific American 'Top 50' Research Leader (2007) Mathematical Association of America's Chauvenet Prize (2013) University of Pennsylvania Lindback Award for Distinguished Teaching (2015) DoD National Security Science and Engineering Faculty Fellowship (NSSEFF, 2015) Ghrist leads multiple federally funded research initiatives supported by AFOSR, DARPA, NSF, and ONR. He directs the development of educational tools including the Calculus BLUE/GREEN Project video series and custom GPTs for mathematical pedagogy. His open online courses have reached over 100,000 learners globally.

• Graph Algorithms
• Optimization
• High-Dimensional Geometry
• +3 more

Yang P. Liu is an Assistant Professor at Carnegie Mellon University 's Department of Computer Science . He received his PhD from Stanford University under the supervision of Aaron Sidford and previously studied at MIT . Fields of Interest : Graph Algorithms, Optimization, High-Dimensional Geometry, Additive Combinatorics, Theoretical Computer Science. His research focuses on algorithmic design and analysis for graph problems, optimization, and combinatorics, with applications in machine learning and complexity theory. Recent work includes advancements in parallel repetition games , combinatorial lines , and dynamic graph algorithms . In 2024, his research spanned FOCS , STOC , and RANDOM conferences, addressing problems in k-CSPs , min-cost flow , and hypergraph sparsification . Earlier contributions (2023) included deterministic flow algorithms and spectral hypergraph techniques. Scientific Awards : NDSEG Fellowship (2018-2021), Google PhD Fellowship (2022-2023), FOCS Best Paper (2022), STOC Best Student Paper (2022), FOCS Best Student Paper (2021). He teaches CS 15-759 , a graduate course on convex optimization theory and applications, covering gradient descent, interior point methods, and algorithmic sparsification techniques.

Jacob FoxView profile

Professor

• Combinatorics
• Probability
• Graph Theory
• +3 more

Jacob Fox is a Professor at Stanford University, specializing in Combinatorics and Probability. His research focuses on extremal combinatorics, Ramsey theory, graph theory, and additive combinatorics. He advises students like Maya Sankar. His work explores structural and enumerative aspects of graphs, hypergraphs, and combinatorial configurations. Recent studies include advancements in Ramsey numbers, sumset theory, and probabilistic methods in discrete mathematics. Key research areas include Ramsey numbers for sparse structures, hypergraph properties, and applications of combinatorial geometry. His publications often bridge theoretical insights with algorithmic applications. No scientific awards are listed in the provided text. His advising includes Maya Sankar, with research aligned to combinatorial problems. Collaborative projects involve extremal graph theory and probabilistic combinatorics. No labs or dedicated research groups are explicitly mentioned.

Mark D. HaimanView profile

Professor

• Algebra
• Combinatorics
• Algebraic Geometry
• +12 more

Mark D. Haiman is a Professor at the University of California, Berkeley, Department of Mathematics, with research interests spanning algebra, combinatorics, and algebraic geometry. His work connects symmetric function theory with geometric objects like Hilbert schemes and algebraic structures such as Cherednik algebras and Hecke algebras. Appointed: 2001 Contact: mhaiman@math.berkeley.edu Teaching: Math 256B—Algebraic Geometry (Spring 2025), Math 249—Algebraic Combinatorics (Spring 2024), and others in calculus and Lie groups. Research Interests : Haiman's research focuses on Macdonald polynomials, LLT polynomials, Hilbert schemes of points in the plane, and their combinatorial and geometric implications. His work includes resolving the Macdonald positivity conjecture and the n! conjecture through algebraic geometry. Publications : Haiman has contributed to foundational papers in combinatorial and algebraic structures, including generalizations of the shuffle theorem and positivity results for LLT polynomials. His articles often bridge representation theory, symmetric functions, and geometric methods. Students : He has supervised numerous PhD students, including Magda Hlavacek (2023), Foster Tom (2022), Jeremy Meza (2021), Maryam Farahmand-Asil (2018), Maria Monks Gillespie (2016), and others working on combinatorial algebraic geometry and related fields.

• Commutative Algebra
• Algebraic Geometry
• Hyperplane Arrangements
• +4 more

Ştefan Tohăneanu is a Professor in the Department of Mathematics and Statistical Science at the University of Idaho , affiliated with the College of Science. His academic journey includes a Ph.D. in Mathematics from Texas A&M University (2007), and M.S. degrees in Algebra (2001) and Analysis (2001) from the University of Bucharest, where he also earned a B.S. in Mathematics (1997). Research Focus: Commutative Algebra, Hyperplane Arrangements, Matroid Theory, and applications to Coding Theory, including generalized Hamming weights, Orlik-Terao algebras, and homological properties of ideals. Publications: Recent work explores Betti numbers, Jacobian ideals, logarithmic derivations, and connections between algebraic invariants and coding theory problems like minimum distance computation and error correction. Collaborations: Engages with global research networks through affiliations with institutions such as Texas A&M University, University of Bucharest, and University of Idaho.

Afonso S. BandeiraView profile

Professor

• High Dimensional Probability
• Random Matrices
• Mathematical Statistics
• +3 more

Afonso S. Bandeira is a Professor in the Department of Mathematics (D-MATH) at ETH Zurich, where he conducts research at the intersection of mathematics, statistics, and computer science. He maintains strong affiliations with several interdisciplinary research centers including the Institute For Operations Research (IFOR), the Max Planck ETH Center for Learning Systems, the ETH Foundations of Data Science, and the ETH AI Center, with a courtesy appointment at D-ITET. Bandeira actively teaches courses including Mathematics of Signals, Networks, and Learning, and Mathematics of Data Science. His research focuses on High Dimensional Probability, Random Matrices, Mathematical Statistics, Theoretical Computer Science, Combinatorics, and Mathematical Optimization. Bandeira's work often explores the theoretical foundations of data science, examining phase transitions in statistical problems, computational barriers, and the geometry of high-dimensional spaces. He maintains a research group blog called Randomstrasse101 that emphasizes open problems in his field. Analysis of his recent publications reveals a strong focus on matrix and tensor concentration inequalities, synchronization problems, nonconvex optimization landscapes, and computational-statistical tradeoffs in high-dimensional inference. His work bridges theoretical mathematics with practical applications in machine learning and data analysis, particularly examining where computational limitations arise in statistical problems. Bandeira actively mentors students and researchers, currently supervising several doctoral candidates including Daniil Dmitriev, Konstantin Donhauser, Anastasia Kireeva, Kevin Lucca, Chiara Meroni, Gil Kur, Petar Nizic-Nikolac, and Almut Roedder. He emphasizes that students working with him should participate in the DACO seminar and group meetings, and encourages prospective students to have completed his Mathematics of Signals, Networks, and Learning or Mathematics of Data Science courses. He leads a research group focused on the mathematics of data science, with regular group meetings and seminars. Bandeira has developed comprehensive lecture notes including 'A Tour Through the Mathematics of Signals, Learning, and Networks' (2025) and 'Mathematics of Machine Learning' (2021), and previously authored 'Ten Lectures and Forty-Two Open Problems in the Mathematics of Data Science' (2015).

Jelena GrbicView profile

Professor

• Topology
• Algebra
• Combinatorics
• +6 more

Professor Jelena Grbic is a distinguished mathematician serving as Professor of Mathematics within the School of Mathematical Sciences at the University of Southampton since 2012. Her academic journey began with a B.Sc. in Mathematics from the University of Belgrade, Serbia in 1997, followed by a Ph.D. in Algebraic Topology from the University of Aberdeen in 2004. Prior to her current position, she held academic appointments at the University of Manchester (2007-2012) as Lecturer and Senior Lecturer, and at the University of Aberdeen (2004-2006) as Lecturer. Professor Grbic's research spans multiple interconnected domains of pure mathematics, with a primary focus on modern homotopy theory, particularly unstable homotopy theory, and its applications across topology, algebra, and geometry. Her work centers on decompositions and exponent problems in homotopy theory, homotopy aspects of Toric Topology, Hopf algebras, and geometric problems related to cobordisms and string topology. This research bridges abstract mathematical theory with potential applications in data science and computational topology. Analysis of her recent publications (2020-2025) reveals a consistent research trajectory in algebraic topology with increasing interdisciplinary connections. Her work demonstrates sophisticated mathematical techniques applied to complex topological structures, particularly moment-angle complexes and polyhedral products. Notably, her 2022 paper 'Aspects of topological approaches for data science' indicates growing interest in applying topological methods to contemporary data analysis problems, suggesting an expanding research horizon beyond pure mathematics. Professor Grbic actively supervises PhD students, including current student Salvatore Elia in Mathematical Sciences, and teaches modules covering algebraic topology and homotopy theory. She serves as a reviewer for prestigious journals including Homology, Homotopy and Application (2019), Transactions of the London Mathematical Society (2021), and The LMS Newsletter (2017), contributing to the scholarly community through peer review and academic service.

Anush TserunyanView profile

Professor

• Mathematics
• Ergodic Theory
• Combinatorics
• +3 more

Anush Tserunyan is a Professor of Mathematics at McGill University, Canada, and a Visiting Professor at the Unit of Pure and Applied Mathematics (UMPA) at École normale supérieure de Lyon from December 1, 2024, to January 31, 2025. She holds a bachelor's and master's in computer science and applied mathematics from Yerevan State University (2005–2007) and a Ph.D. in Mathematics from UCLA (2013), focusing on finite generators for group actions, equivalence relations, and recursive program complexity. Research Interests: Anush Tserunyan specializes in Ergodic Theory , Combinatorics , and Group Actions , with notable contributions to graph theory, hypergraphs, and Ramsey theory. Her work bridges combinatorial structures with analytic methods, particularly in dynamical systems and descriptive set theory. Collaborations: During her visit to UMPA, she collaborates with teams in Geometry, Groups and Dynamics , and Number Theory , alongside researchers like Benjamin Schraen and Sophie Morel. Her stay includes seminars on GGD, Number Theory, and the 'Actions!' working group. Publications: Her research spans topics like ergodic theorems, disjoint matchings in graphs, and algebraic hypergraphs, reflecting a focus on foundational mathematical structures and their applications.

Imre LeaderView profile

Professor

• Extremal Combinatorics
• Ramsey Theory
• Combinatorial Number Theory
• +3 more

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

• Geometric Topology
• Geometric Group Theory
• Low-Dimensional Topology
• +6 more

Prof. Harry Hyungryul Baik is a Tenured Associate Professor at KAIST's Department of Mathematical Sciences since 2017. He holds a PhD from Cornell University (2014) and a B.S. from KAIST (2009), advised by William Thurston, John Hubbard, and Dylan Thurston. His research focuses on geometric topology, geometric group theory, and low-dimensional topology, with notable contributions to mapping class groups, Kleinian groups, and Teichmüller theory. Education: PhD in Mathematics (Cornell, 2014), B.S. in Mathematics (KAIST, 2009). Key research areas include asymptotic translation lengths, laminar groups, and circular orders of groups. He co-leads the KAIST-KIAS joint research group 2K-GATE as Director, emphasizing collaboration between topologists. Research highlights: Characterization of Fuchsian groups via laminations, unsmoothability of mapping class group actions on 1-manifolds, and exponential torsion growth in random 3-manifolds. His work bridges topology with dynamical systems and geometric group theory, often involving collaborations with institutions like KIAS and MPIM. Awards include the Sangsan Prize (2018), Young-KAST membership (2020–2023), and multiple grants from Samsung and POSCO. He advises 7 PhD students and has mentored 15+ alumni, many of whom hold postdoc positions globally. His lab actively hosts conferences like the KAIST Geometric Topology Fair. Labs/Teams: Director of 2K-GATE (KAIST-KIAS), core member of the KAIST Topology Research Group, collaborator with international networks including the Harvard-MIT-Princeton topology axis.

Paul LarsonView profile

Professor

• Set Theory
• Topology
• Model Theory
• +3 more

Paul Larson is a Professor of Mathematics at Miami University. His research focuses on set theory, topology, and model theory, with particular expertise in forcing axioms, descriptive set theory, and infinitary logic. He holds a Ph.D. in Mathematics from the University of California, Berkeley. His work bridges foundational mathematical logic with applications in topology and combinatorics. Key contributions include studies on canonical models under fragments of the Axiom of Choice, polar forcings, and cardinal characteristics. Larson has collaborated extensively with leading researchers such as Saharon Shelah and Jindřich Zapletal. His publications span prestigious journals like the Annals of Pure and Applied Logic and Transactions of the American Mathematical Society. Beyond research, he contributes to the academic community through editorial work and expository writings on historical developments in determinacy theory. Education: Ph.D., Mathematics, University of California, Berkeley Research interests emphasize foundational questions in set theory with applications to topology and model theory. His recent work explores advanced forcing techniques, square principles in Pmax extensions, and combinatorial properties of cardinal invariants. Publications reflect interdisciplinary engagement, including crystal structure prediction in high-pressure chemistry and operator theory in functional analysis. Despite an extensive publication record, no specific scientific awards are documented here. His advising and grant activities remain unspecified in the provided texts. Collaborations span international institutions, reflecting his role as a central figure in contemporary set theory research.

Brett KolesnikView profile

Research Fellow

• Probability Theory
• Random Structures
• Bootstrap Percolation
• +4 more

Brett Kolesnik is a Research Fellow in the Department of Statistics at the University of Warwick. His research focuses on probability theory, random structures, bootstrap percolation, and interactions with combinatorics. He has held postdoctoral fellowships at UC Berkeley, San Diego, and the University of Oxford, and was a Senior Demy at Magdalen College. His work includes organizing workshops on bootstrap percolation and collaborating with leading researchers in probability and combinatorics. Education: PhD in Mathematics from the University of British Columbia (advised by Omer Angel). Notable awards include the NSERC Postdoctoral Fellowship and the Florence Nightingale Bicentennial Fellowship in Statistics. Research interests span bootstrap percolation models, random graph dynamics, and stochastic processes. Recent work includes studies on Brownian map geometry, tournament score sequences, and Coxeter group structures. Selected articles explore topics such as critical beta-splitting processes, Catalan percolation, and random walks on algebraic structures. His publications appear in top journals like Electronic Journal of Probability and Annals of Applied Probability . Awards include the Florence Nightingale Fellowship and NSERC Postdoctoral Fellowship. Professional involvement includes organizing the 2024 BIRS workshop on Bootstrap Percolation and contributing to interdisciplinary collaborations in probability and combinatorics.

David NadlerView profile

Professor

• Geometric Representation Theory
• Symplectic Geometry
• Langlands Duality
• +3 more

David Nadler is a Professor in the Department of Mathematics at the University of California, Berkeley, appointed in 2012. His research centers on geometric representation theory and symplectic geometry, with significant contributions to the Langlands program, microlocal sheaf theory, and symplectic topology. He maintains an active research group and teaches courses ranging from undergraduate linear algebra to graduate algebraic topology and geometry. Nadler's research explores the interface of algebraic geometry, topology, and representation theory. His work in geometric representation theory focuses on Langlands duality, Springer theory, and Betti geometric Langlands. In symplectic geometry, he investigates microlocal sheaves, Fukaya categories, and Weinstein structures. His recent publications demonstrate a consistent focus on categorical methods in geometric Langlands correspondence and symplectic arborealization. His publications consistently emphasize categorical and geometric approaches to representation theory. Recent works cluster in three areas: (1) extensions of the geometric Langlands program to Betti cohomology settings, (2) microlocal analysis of sheaves on symplectic manifolds, and (3) combinatorial models in symplectic topology. This reflects sustained development of 'Betti geometric Langlands' as a distinct research program bridging topology and automorphic forms. Nadler has advised over a dozen PhD students since 2012, with dissertations spanning geometric representation theory, symplectic geometry, and algebraic topology. Student projects frequently investigate categorical aspects of geometric Langlands, microlocal sheaves, and combinatorial models in symplectic topology.

Primoz SkrabaView profile

Professor

• Applied Topology
• Geometry
• Algebra
• +5 more

Dr. Primoz Skraba is a Professor in Applied and Computational Topology at the School of Mathematical Sciences, Queen Mary University of London. As Deputy Head of the Centre for Probability, Statistics and Data Science, he bridges theoretical topology with practical applications in data analysis, machine learning, and optimization. Education : PhD in Electrical Engineering from Stanford University (2009) Prior Roles : Positions at INRIA, France; Jozef Stefan Institute, Slovenia; University of Primorska; University of Nova Gorica His research focuses on applying topological methods to analyze complex data. Key areas include: Stability of persistence diagrams for quantitative control in finite sampling Variants of persistence (zig-zag, robustness, multiparameter) Algorithmic Complexity in computational topology Stochastic Topology for random geometric models (Poisson, Boolean) Recent publications emphasize persistent homology in random geometric complexes, universality theorems, and integrating topological methods into machine learning. He received grants from the Leverhulme Trust, EPSRC, and Alan Turing Institute for projects on topological universality and AI foundations. His advisee Gabryel Mason-Williams explores wireless sensor network applications of homology.