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.
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
Vadim Lozin is a Professor of Mathematics at the University of Warwick, affiliated with the Department of Mathematics within the School of Mathematics. His research interests span graph theory, combinatorics, and discrete mathematics, focusing on areas such as clique-width, Ramsey numbers, and structural graph theory. He has held visiting positions at institutions including the Université Paris-Dauphine, EPFL, and KAUST. Lozin has received several accolades, including the Best Paper Award for 'Linear Ramsey numbers' in 2018 and a 2024 award at the International Symposium on Algorithms and Computation. His work involves collaborations with global researchers and contributions to conferences like IWOCA and WG. Lozin serves on editorial boards for journals such as Discrete Applied Mathematics and Electronic Notes in Discrete Mathematics . His research explores foundational problems in graph theory, with applications in algorithm design and complexity analysis. Lozin’s publications include studies on union-closed sets, functional graph properties, and algorithmic approaches to graph parameters. He has also contributed to books like Words and Graphs , bridging formal language theory with graph structures. His grants focus on clique-width and stability in graphs, reflecting his commitment to advancing theoretical and applied discrete mathematics.
Ben Green is the Waynflete Professor of Pure Mathematics at the University of Oxford and a Fellow of Magdalen College. His work spans additive combinatorics, analytic number theory, harmonic analysis, ergodic theory, discrete geometry, and group theory, with a focus on interdisciplinary approaches. Research Interests: Additive combinatorics and its applications to primes Analytic number theory (prime distribution, L-functions) Harmonic analysis (Fourier methods, spectral theory) Ergodic theory and its combinatorial applications Discrete geometry (ordinary lines, convex structures) Group theory (approximate groups, expansion) Article Trends: His recent work emphasizes multiplicative functions, Ramsey-type problems in number theory, expansion in finite groups, and extremal set theory. Themes include prime gaps, arithmetic progressions, and interactions between analysis and algebra. Scientific Awards: Clay Research Award (2004) Ostrowski Prize (2005) Whitehead Prize (2005) Leverhulme Prize (2007) European Mathematical Society Prize (2008) Royal Society Fellow (2010) Sylvester Medal (2014) Senior Whitehead Prize (2019) Advising: Ben has supervised numerous D.Phil students across additive combinatorics, analytic number theory, and related fields. Past students hold postdoctoral and academic positions globally.
Nathan (Nati) Linial is a Professor at the School of Computer Science and Engineering at the Hebrew University of Jerusalem, where he has been a faculty member since completing his postdoctoral period at UCLA. He earned his undergraduate degree in mathematics from the Technion and his PhD in graph theory from the Hebrew University. His research spans multiple areas of theoretical computer science and mathematics, with primary focus on combinatorics, theoretical computer science, and bioinformatics. Linial's work has made significant contributions to high-dimensional combinatorics, expander graphs, metric embeddings, and computational molecular biology. His research often bridges geometry, analysis, and combinatorial structures, demonstrating deep connections between seemingly disparate mathematical fields. Linial's recent publications reveal a strong trend toward high-dimensional combinatorial structures, including simplicial complexes, hypertrees, and high-dimensional permutations. His work frequently employs probabilistic methods, linear programming techniques, and geometric approaches to solve fundamental combinatorial problems. The breadth of his research is evident in both pure mathematical contributions and applications to computational biology. Fellow of the American Mathematical Society ISI Highly Cited Researcher Conant Prize (2008) for the influential survey paper "Expander graphs and their applications" Linial has served on the editorial boards of several prestigious journals including the Israel Journal of Mathematics (as Chief Editor 2013-2017), Random Structures and Algorithms, and Combinatorica. His academic leadership extends to organizing conferences and workshops in combinatorics and theoretical computer science. He has mentored numerous students whose work spans theoretical computer science, combinatorics, and computational biology. Linial is associated with research projects including ProtoNet (for protein sequence classification) and EVEREST (for evolutionary conserved protein domains), demonstrating his commitment to interdisciplinary research that bridges computer science with molecular biology.
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.
Prof. Michael Krivelevich holds the Baumritter Chair in Combinatorics at the School of Mathematical Sciences, Tel Aviv University. His research focuses on probabilistic methods in combinatorics, random graphs, and positional games. He has authored influential books such as Positional Games and contributed to foundational work in random graph theory. Currently teaching Introduction to Combinatorics and Graph Theory (Spring 2025), he has extensive experience in courses like Graph Theory and Hypergraph Coloring. His work bridges theoretical computer science, coding theory, and combinatorics, with over 150 publications. Recent research explores game-theoretic thresholds, random graph evolution, and equitable coloring algorithms. Education: Ph.D. in Mathematics, Tel Aviv University (not explicitly stated, inferred from career trajectory). Research Interests Krivelevich's work emphasizes random structures , extremal graph theory , and probabilistic combinatorics . He investigates phase transitions in random graphs, positional game strategies, and algorithmic challenges in graph coloring. His contributions include proving sharp thresholds for Hamilton cycle games and analyzing WalkSAT performance on smoothed k-CNF formulas. Collaborations span theoretical computer science and discrete mathematics. Publications Recent articles address Hamiltonicity in Maker-Breaker games, equitable coloring of random graphs, and smoothed analysis of satisfiability processes. His work often combines rigorous proofs with algorithmic insights. Teaching & Mentorship Guides students through advanced combinatorial topics and has taught foundational courses since 2002. No explicit student listings available in provided texts.
Jim Geelen is a Professor in the Department of Combinatorics and Optimization at the University of Waterloo, Faculty of Mathematics. His research focuses on matroid theory, particularly the Matroid Minors Project, which extends the Graph Minors Theory of Robertson and Seymour to matroids. Notably, he, Bert Gerards, and Geoff Whittle proved Rota's Conjecture, characterizing matroids representable over finite fields. His work also addresses extremal matroid theory, growth rates of minor-closed classes, and algorithmic applications. He has advised doctoral students including Kerri Webb, Tony Huynh, Peter Nelson, Rohan Kapadia, and Benson Joeris. Geelen teaches advanced courses like CO749 on Graph Minors, offering video lectures. His research collaborations span matroid minors, excluded minors, and representation theory, with contributions to fields like combinatorics, Ramsey theory, and geometric density theorems. His recent work explores the Erdős-Posa property in matroids, density Hales-Jewett theorems, and the structure of exponentially dense matroid classes. Geelen's publications include foundational papers on matroid connectivity, branch-width, and inequivalent representations, reflecting his deep engagement with foundational and applied aspects of combinatorial mathematics.
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.
John Gimbel is a Professor of Mathematics at Western Michigan University since 1987. He holds a PhD from 1984 and has made significant contributions to graph theory, particularly in Ramsey Theory and graph coloring. Research Interests: His work focuses on the inevitability of order in disordered graphs (Ramsey Theory) and graph coloring methods, including fractional coloring and constraints on bounded genus/triangle-free graphs. Key themes include structural analysis, extremal properties, and surface embeddings. Selected Publications: Spanning 1991–2025, his research covers H-free subgraphs in random graphs, genus/girth coloring bounds, triangle-free coloring, convexity numbers, and defective Ramsey numbers in degenerate graphs. Contact: Email: jggimbel@alaska.edu . Office: CH 304C, Phone: 907-474-6102.
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.
Lutz Warnke is a Professor of Mathematics at the University of California, San Diego, with prior affiliations at Georgia Institute of Technology (where he received tenure in 2021) and Peterhouse, Cambridge University (Junior Research Fellow until 2016). His research focuses on probabilistic combinatorics, random graphs, phase transitions, and combinatorial probability, with applications to extremal combinatorics and Ramsey theory. Education : Ph.D. in Mathematics from the University of Oxford (2012), supervised by Oliver Riordan. Dr. Warnke's research explores the structure and evolution of random graphs and processes, including Achlioptas processes, Ramsey numbers, and extremal problems. His work often bridges probabilistic methods with algorithmic applications and theoretical computer science. His publications from 2022–2025 reveal trends in random graph isomorphisms, clique coloring thresholds, extremal subgraph counts, and hardness of online algorithms. Key subfields include percolation, phase transitions, and probabilistic methods applied to combinatorial structures. Scientific Awards : Dénes König Prize (2016), Alfred P. Sloan Research Fellowship (2018), NSF CAREER Award (2020), Richard Rado Prize (2014). Dr. Warnke actively supervises PhD students and postdocs, including Matthew Cho (PhD ongoing), Erlang Surya (PhD 2025), Emily Zhu (PhD 2025), and He Guo (PhD 2021). He has received teaching accolades at Georgia Tech and contributes to graduate courses in probabilistic combinatorics, random graph theory, and stochastic processes.
Benny Sudakov is a Professor of Mathematics at ETH Zurich, where he conducts research in combinatorics. He has previously held positions at UCLA, Princeton University, and the Institute for Advanced Study. His work is supported by the SNSF grant 200021_196965. Research Interests: His primary research areas include Extremal Graph and Hypergraph Theory, Ramsey Theory, Random Structures, and the application of Algebraic and Probabilistic Methods in Combinatorics, with strong connections to Theoretical Computer Science. He investigates fundamental structural properties of discrete systems, such as the existence of regular subgraphs, extremal configurations, and the behavior of random combinatorial objects. The recent popular science articles on his work highlight a consistent trend of solving long-standing open problems in extremal combinatorics using sophisticated probabilistic and algebraic techniques. His research spans topics like equiangular lines, graph decompositions, and the emergence of cycles in sparse graphs, demonstrating a deep focus on the interplay between structure and randomness. Scientific Awards: No specific awards are mentioned in the provided text. Advising and Grants: He has advised numerous Ph.D. students, many of whom have gone on to become professors at top universities (e.g., Oxford, Stanford, CMU, ETH, Princeton). His research is currently funded by the Swiss National Science Foundation (SNSF). He has organized workshops and seminars, such as the Theory of Combinatorial Algorithms Mittagsseminar at ETH and a workshop at UCLA on Extremal and Probabilistic Combinatorics. Labs and Teams: He is a key member of the combinatorics group at ETH Zurich and co-organizes the Theory of Combinatorial Algorithms Mittagsseminar, a central forum for research discussions in discrete mathematics at the institution.
Professor Stefan Glock is an Assistant Professor of Discrete Mathematics at the University of Passau's Faculty of Computer Science and Mathematics, a position he has held since September 2022. Prior to this appointment, he spent three years as a Junior Fellow at the Institute for Theoretical Studies at ETH Zurich, following the completion of his doctorate at the University of Birmingham. Stefan Glock received his mathematics education at Technische Universität Ilmenau from 2009 to 2014, then pursued his PhD at the University of Birmingham, which he completed in 2018. His doctoral dissertation, "Decompositions of Graphs and Hypergraphs," was the runner-up for the Richard-Rado-Preis 2018. Professor Glock's research focuses on discrete mathematical structures, with particular emphasis on their asymptotic properties. His work spans several interconnected fields of combinatorics: Extremal Combinatorics : Investigating the maximum or minimum possible size of mathematical structures satisfying certain properties Probabilistic Combinatorics : Applying probability theory to solve combinatorial problems Graph Theory : Studying properties of graphs and networks Ramsey Theory : Examining conditions under which order must appear in large structures Design Theory : Creating arrangements of elements satisfying specific balance properties Discrete Geometry : Analyzing geometric problems with discrete structures Analysis of Professor Glock's recent publications reveals a consistent focus on solving long-standing open problems in combinatorics using innovative methods that combine probabilistic techniques with structural insights. His work often bridges theoretical mathematics with applications in theoretical computer science, particularly in the analysis of algorithms and network structures. A significant portion of his research addresses fundamental questions about graph and hypergraph decompositions, which have implications for coding theory, cryptography, and network design. Professor Glock has received notable recognition for his contributions to mathematics: Runner-up for the Richard-Rado-Preis 2018 for his dissertation "Decompositions of Graphs and Hypergraphs" Awarded funding through the prestigious DFG Emmy Noether Programme in 2024 for his research group on "the interplay of structure and randomness in mathematics" As a faculty member at the University of Passau, Professor Glock leads the Discrete Mathematics research group and actively collaborates with mathematicians worldwide. He has established a strong research program that has attracted funding for academic visitors and supports multiple research projects. His approach to mathematical problems emphasizes developing new methods that have far-reaching implications beyond the specific problems being solved. Professor Glock's research group at the University of Passau focuses on the interplay between structure and randomness in discrete mathematics. The group maintains active collaborations with leading institutions including ETH Zurich, University of Birmingham, and various research centers across Europe. Through the DFG Emmy Noether Programme funding, his group is expanding its research on combinatorial structures and their applications.
Xiaoyu He is a tenure-track Assistant Professor at the School of Mathematics, Georgia Institute of Technology. Starting Fall 2025, he will teach Math 8803, a graduate-level topics course on Ramsey and Turán problems for graphs and hypergraphs. His research spans extremal, probabilistic, and algebraic combinatorics , focusing on Ramsey theory, graph coloring, additive combinatorics, discrete geometry, and coding theory with applications to computer science. Education: PhD in Mathematics from Stanford University (2021), advised by Jacob Fox. Prior Roles: NSF Postdoctoral Research Fellow at Princeton University (mentored by Noga Alon). Current Group: Collaborates with Visiting Assistant Professor Jiaxi Nie and PhD students Ruben Ascoli, Winston Stucki, and Logan Post. Awards: NSF Postdoctoral Research Fellowship. Contact: xhe399@gatech.edu , Office: Skiles 260.
