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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.

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.

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 PerkinsonView profile

Professor

• Combinatorics
• Graph Theory
• Algebraic Geometry
• +5 more

David Perkinson is a Professor of Mathematics at Reed College, where he holds a position in the Department of Mathematics. His research focuses on combinatorics, algebraic geometry, and discrete mathematics, with a particular emphasis on sandpile models, graph theory, and matroid theory. He is the author of the textbook *Divisors and Sandpiles: An Introduction to Chip-Firing*, which explores the combinatorial theory of chip-firing on graphs. Perkinson has also developed software tools like the Sandpile Java App, which visualizes and analyzes the Abelian Sandpile Model. He organizes the Cascade Lectures in Combinatorics (CALICO), a series of conferences funded by the National Science Foundation, aimed at fostering collaboration among researchers in combinatorics. His work bridges discrete mathematics with algebraic geometry, emphasizing connections between graph theory and geometric structures. Perkinson teaches advanced courses in analysis and contributes to the academic community through his research on topics such as divisor theory on graphs, sandpile groups, and combinatorial game theory. His recent publications (2015–2024) address matroid theory, sandpile dynamics, and applications of algebraic methods to discrete systems.

Thomas LamView profile

Professor

• Algebraic Combinatorics
• Total Positivity
• Cluster Algebras
• +5 more

Thomas Lam is a professor of mathematics at the University of Michigan , specializing in algebraic combinatorics, total positivity, and connections to mathematical physics. His work bridges cluster algebras, positive geometry, and integrable systems, with applications to scattering amplitudes in quantum field theory. Lam has collaborated extensively with physicists such as Nima Arkani-Hamed and mathematicians like Pavlo Pylyavskyy and Mark Shimozono. Key research areas: Cluster algebras, total positivity, electrical networks, positroid varieties, and quantum cohomology. Notable contributions: Defining polypositroids, proving regularity theorems for totally nonnegative flag varieties, and establishing cluster structures in braid varieties. Recent work focuses on positive geometries , including the amplituhedron and moduli spaces of points on projective lines, with implications for particle physics. His articles often explore dual graded graphs, K-theoretic Schubert calculus, and the interplay between combinatorics and algebraic structures. Lam's research has been supported by NSF grants, including DMS-0748636 and DMS-1249708 .

Tobias DyckerhoffView profile

Professor

• Higher Structures in Algebra and Geometry
• Algebraic Topology
• Homological Algebra
• +3 more

Prof. Dr. Tobias Dyckerhoff is a Professor of Mathematics at the University of Hamburg , specializing in Higher Structures in Algebra and Geometry . He is affiliated with the Cluster of Excellence "Quantum Universe" and the Center for Mathematical Physics . His academic career includes positions at the University of Bonn, University of Oxford, Yale University, and the University of Pennsylvania. Research Interests : Higher category theory, homological algebra, perverse sheaves, Fukaya categories, and applications to symplectic geometry and quantum topology. Editorial Roles : Managing Editor of Abhandlungen aus dem mathematischen Seminar der Universität Hamburg (since 2023) and Editor of Applied Categorical Structures (since 2023). Publications & Articles focus on advanced topics like stable ∞-categories, spherical functors, and Calabi-Yau structures. Notable trends include interconnections between algebraic topology, category theory, and symplectic geometry. Scientific Awards : Bonn Junior Fellow (2014–2018) Titchmarsh Postdoctoral Fellow (2013–2014) Simons Postdoctoral Fellow (2010–2013) Students & Collaborations : Mentors active researchers like Angus Rush, Till Heine, and Jonte Gödicke. Collaborates with institutions such as MPI Bonn and international experts in higher structures.

Yulan QingView profile

Assistant Professor

• Low-Dimensional Topology
• Geometric Group Theory
• Asymptotic Properties of Groups
• +4 more

Yulan Qing is an Assistant Professor in the Department of Mathematics at the University of Tennessee, Knoxville (UTK), part of the College of Arts and Sciences. She holds a Ph.D. in Mathematics from Tufts University. Her research focuses on low-dimensional topology, geometric group theory, asymptotic properties of groups, and big mapping class groups. Notable projects include studies on Gromov boundaries, genericity in groups, and curve graphs. She has published extensively in journals like Geometry & Topology and the Journal of the London Mathematical Society. Dr. Qing has organized conferences such as the 53rd Barrett Memorial Lectures and the GGTea Webinar, fostering collaboration in geometric group theory. She has taught courses like Honors Topology at UTK and supervised graduate students including Sagnik Jana and Alex Squires. Her work bridges theoretical foundations with applications in topology and geometry. Recent invited talks include presentations at the University of Virginia, Caltech, and the 2nd China-Russia Conference on Topology. She actively mentors undergraduate and graduate students, contributing to initiatives like the Math Circle programs at Tufts and MIT's RSI Summer Program.

Nathan ReadingView profile

Professor

• Algebraic Combinatorics
• Geometric Combinatorics
• Coxeter Groups
• +3 more

Nathan Reading is a Professor in the Department of Mathematics at North Carolina State University (NCSU). He holds a Ph.D. in Mathematics from the University of Minnesota (2002) and a B.S. in Physics from Stanford University (1995). His research focuses on algebraic and geometric combinatorics, particularly in Coxeter groups, cluster algebras, and lattice-theoretic approaches. He has been actively involved in organizing the Triangle Lectures in Combinatorics, a biannual research conference. His research interests include noncrossing partitions, cluster scattering diagrams, and the lattice theory of torsion classes. Recent work explores connections between Coxeter groups and combinatorial structures on surfaces. Reading has authored numerous papers on topics such as semidistributive lattices, scattering diagrams, and Cambrian frameworks. He teaches advanced combinatorics courses (e.g., MA 724: Combinatorics II) and has advised graduate students. His work has been supported by grants from the National Science Foundation (NSF), including DMS-1500949. Reading maintains an active presence in the mathematics community through publications, conference organization, and pedagogical contributions.

• Mapping Class Groups
• Geometric Group Theory
• Low-Dimensional Topology
• +3 more

Tara Brendle is Professor of Mathematics at the University of Glasgow within the School of Mathematics and Statistics, specializing in the interplay between algebra and topology. Her research centers on mapping class groups of surfaces and their profound connections to braid groups, Coxeter groups, arithmetic groups, and automorphism groups of free groups. Her primary research explores how these algebraic structures determine the topology of 3- and 4-manifolds through constructions like Heegaard splittings and Lefschetz fibrations. She investigates cohomological properties, subgroup structures, and representation-theoretic aspects of mapping class groups, with significant contributions to understanding the Johnson kernel and hyperelliptic Torelli groups. Over the past two decades, Brendle's publications reveal a consistent focus on geometric and algebraic properties of surface automorphism groups, evolving from foundational work on generators and relations to cutting-edge research on high-dimensional cohomology of moduli spaces and stability phenomena. Her collaborations with leading mathematicians like Dan Margalit and Andrew Putman have produced influential results across geometric group theory. She actively supervises doctoral research on mapping class groups, braid groups, and low-dimensional topology, guiding students including Bader, Philipp; Corrigan, Gabriel; Giannini, Riccardo; and Pietrzak, Alicja on advanced topics at the intersection of algebra and geometry.

• Algebraic Combinatorics
• Quasisymmetric Functions
• Schubert Calculus
• +4 more

Vasu Tewari is an Assistant Professor (CLTA) at the University of Toronto, working across both the Downtown Toronto (St. George) and Mississauga (UTM) campuses. Their office is located at HU1015 (215 Huron), and they can be reached at vasu.tewari@utoronto.ca. As a member of the Department of Mathematics within the Faculty of Arts and Science, Professor Tewari contributes to both teaching and research activities at the university. Professor Tewari's research focuses on advanced topics in algebraic combinatorics, with particular expertise in: Quasisymmetric functions and their geometric interpretations Schubert polynomial theory and related structures Representation theory of symmetric groups and related algebras Combinatorial aspects of algebraic geometry Enumerative combinatorics with connections to symmetric functions Algebraic structures arising from combinatorial objects Analysis of Professor Tewari's recent publications reveals a consistent focus on the interplay between combinatorial structures and algebraic frameworks. Their work often explores generalizations of classical symmetric function theory through the lens of quasisymmetric functions, providing new insights into Schubert calculus, permutation statistics, and geometric combinatorics. A notable trend in their research is the investigation of stability phenomena in combinatorial structures and the development of new algebraic tools for studying these phenomena. Professor Tewari has made significant contributions to understanding the geometry of combinatorial objects through algebraic methods, particularly in the areas of permutahedral varieties, zonotopal algebras, and quiver representations. Their work bridges pure mathematics with potential applications in theoretical physics and computer science.

• Tropical Geometry
• Cluster Algebras
• Combinatorics
• +5 more

David E Speyer is a Professor in the Department of Mathematics at the University of Michigan . His research focuses on algebraic problems with combinatorial flavors , particularly in tropical geometry , cluster algebras , and geometry of Lie groups . He has supervised multiple PhD students, including Shelby Cox, Will Dana, and John Wiltshire-Gordon, and collaborated on projects with undergraduates like Grant Barkley and Benjamin Branman. Education: PhD in Mathematics from UC Berkeley under Bernd Sturmfels; undergraduate at Harvard. Research: Key areas include tropical geometry , cluster algebras , and flag manifolds . His work often bridges combinatorics, algebraic geometry, and representation theory. Publications: Over 40 papers, including breakthroughs in cluster algebras , affine weak order , and braid variety cluster structures . Awards: Clay Research Fellow (2005-2010). Teaching: Coordinates courses like Math 593 (graduate algebra) and Math 214 , with a focus on inquiry-based learning .

• Discrete subgroups of Lie groups
• Pseudo-Riemannian geometry
• Projective geometry
• +3 more

Fanny Kassel is a CNRS Research Director at the Institute of Advanced Scientific Studies (IHES), focusing on geometric, dynamical, and spectral aspects of discrete subgroups of Lie groups. Her work connects discrete group actions on homogeneous spaces with geometric structures on manifolds, such as pseudo-Riemannian and projective geometries, and higher Teichmüller-Thurston theory. Her research spans topics like convex projective geometry, Anosov representations, and pseudo-Riemannian hyperbolic spaces. She has been recognized with the CNRS Bronze Medal (2015), an ERC Starting Grant (2016), and the Mathematics Medal of the French Academy of Sciences (2024). She actively organizes workshops and contributes to editorial boards, including Mathematics of the IHES and Gazette de la SMF . Her recent publications highlight advancements in convex projective geometry, spectral theory, and discrete group dynamics. Awards and grants underscore her influence in geometric group theory and related fields.

Christopher ManonView profile

Associate Professor

• Algebraic Geometry
• Tropical Geometry
• Combinatorial Geometry
• +5 more

Christopher Manon is an Associate Professor in the Department of Mathematics at the University of Kentucky, within the College of Arts & Sciences. His research focuses on algebraic geometry, tropical geometry, and their connections to combinatorics, representation theory, and phylogenetics. He explores topics such as toric varieties, vector bundles, Bruhat-Tits buildings, and geometric compactifications. Manon's work frequently intersects with combinatorial structures like matroids, polytopes, and phylogenetic networks. His studies on toric vector bundles and tropical geometry have advanced understanding of degenerations and moduli spaces. He has contributed to the theory of Fano varieties and Gorenstein polytopes, linking algebraic geometry with lattice theory and mirror symmetry. His recent research trends emphasize geometric families of degenerations via polytope mutations, invariants in phylogenetic models, and equivariant cohomology in arithmetic contexts. Collaborative projects include work on frame theory and conformal blocks in representation theory. Manon's research has been supported through collaborative grants, including projects on combinatorial buildings and tropical geometry. His work bridges pure mathematics disciplines such as algebraic geometry, combinatorics, and representation theory, often with applications to geometric modeling and theoretical biology.

Ravi VakilView profile

Professor

• Algebraic Geometry
• Enumerative Geometry
• Moduli Spaces
• +3 more

Ravi Vakil is the Robert Grimmett Professor of Mathematics at Stanford University and the President of the American Mathematical Society (AMS). He specializes in algebraic geometry, with contributions to enumerative geometry, moduli spaces, intersection theory, and Schubert calculus. His research interests also extend to mathematics education and public outreach. He earned his Ph.D. from Harvard University under Joe Harris. Vakil is renowned for his book The Rising Sea: Foundations of Algebraic Geometry , set for publication by Princeton University Press in 2025. He co-founded MathOverflow and Proof School, and serves on editorial boards of journals like Algebra and Number Theory and Involve . His awards include the AMS Centennial Fellowship, Coxeter-James Prize, Sloan Fellowship, and the Chauvenet Prize for mathematical exposition. He has advised numerous Ph.D. students and is known for his dedication to teaching, receiving the Dean’s Award for Distinguished Teaching. Vakil actively participates in academic service, including roles on the AMS Board and the National Math Stars advisory board. His research explores foundational questions in algebraic geometry, often with connections to combinatorics and representation theory.

Richard M. GreenView profile

Professor

• Algebraic Combinatorics
• Representation Theory
• Coxeter Groups
• +7 more

Dr. Richard M. Green is a Professor of Mathematics at the University of Colorado Boulder, where he has been teaching since at least 2001. He holds a Ph.D. from the University of Warwick (1995) and specializes in algebraic combinatorics and representation theory. His teaching portfolio includes undergraduate courses like Calculus 3 and Number Theory, as well as graduate courses in Algebra and Ring Theory. Education: Ph.D. in Mathematics, University of Warwick, 1995 Dr. Green's research focuses on the intersection of algebra and combinatorics, with particular emphasis on Coxeter groups, Hecke algebras, and diagram algebras. His work explores the combinatorial structures underlying representation theory, including Kazhdan-Lusztig theory, heaps of pieces, and minuscule representations. He has made significant contributions to understanding the structure of cellular algebras and their connections to Lie theory. His 2013 book "Combinatorics of Minuscule Representations" (Cambridge University Press) is a major reference in the field. Analysis of Dr. Green's recent publications reveals a continued focus on Coxeter groups and their generalizations, with increasing attention to 2-roots, orthogonal structures, and connections to Weyl groups. His work demonstrates a consistent thread connecting combinatorial structures with representation-theoretic phenomena, particularly in the context of Kazhdan-Lusztig theory and cellular algebras. The research shows progression from foundational work on Temperley-Lieb algebras to more sophisticated analyses of Coxeter group structures and their applications. Dr. Green has authored numerous scholarly publications and his book "Combinatorics of Minuscule Representations," which has established him as a leading researcher in algebraic combinatorics. His Erdős number is 3, indicating significant connections to the broader mathematical community. As an educator, Dr. Green has supervised numerous undergraduate and graduate students through coursework and independent studies. His teaching spans the mathematics curriculum from introductory calculus to advanced graduate algebra. He has taught a wide range of courses including MATH 2400 (Calculus 3), MATH 3110 (Number Theory), MATH 3170 (Combinatorics 1), and graduate courses MATH 6130/6140 (Algebra 1/2) and MATH 6250 (Theory of Rings). His teaching philosophy emphasizes clear exposition of complex mathematical concepts. Dr. Green maintains active research collaborations and contributes to the academic community through publications and participation in the Rocky Mountain Algebraic Combinatorics Seminar. His work continues to influence both theoretical developments in algebraic combinatorics and pedagogical approaches to advanced mathematics.