A Borel Local Lemma for Finite Asymptotic Separation Index
Explore a Borel version of the Lovász Local Lemma for graphs with finite asymptotic separation index, improving measurable local lemma exponents and extending to exponential growth groups.
Canonical Colourings in Random Graphs
Explore canonical colourings in random graphs with Nina Kamčev, delving into extremal combinatorics, Ramsey theory, and asymptotic enumeration.
Recent Progress on the Erdos-Hajnal Conjecture
Explore recent advancements in the Erdos-Hajnal Conjecture with Oxford mathematician Alexander Scott, delving into extremal and probabilistic combinatorics and structural graph theory.
Hypergraph Decompositions and Their Applications
Explore hypergraph decompositions and their applications in combinatorics with Oxford Professor Peter Keevash, known for solving the Existence Conjecture for Combinatorial Designs.
Rainbow Thresholds in Graph Theory
Explore extremal combinatorics, graph theory, and theoretical computer science with Prof. Jie Han's insights on rainbow thresholds in mathematics.
A Random Hall-Paige Conjecture
Explore extremal combinatorics, focusing on Ramsey theory, Latin squares, and positional games. Delve into problems bridging combinatorics and algebra with an expert in the field.
Partitioning a Tournament into Sub-Tournaments of High Connectivity
Explore tournament partitioning techniques to create highly connected sub-tournaments, delving into extremal and probabilistic combinatorics, Ramsey theory, and random graphs.
Finite Hypergraph Families with Rich Extremal Turan Constructions via Mixing Patterns
Explore finite hypergraph families and their extremal Turán constructions through mixing patterns. Gain insights into combinatorics and discrete structures from a renowned expert.
A Solution to Erdős and Hajnal's Odd Cycle Problem
Explore a solution to Erdős and Hajnal's odd cycle problem in extremal and probabilistic combinatorics with Associate Professor Richard Montgomery.
Simonovits's Theorem in Random Graphs
Explore Simonovits's theorem in random graphs with Wojciech Samotij. Gain insights into extremal and probabilistic combinatorics from an award-winning mathematician.
Hypertrees in Combinatorics and Graph Theory
Explore hypertrees with Professor Nati Linial, delving into combinatorics, algorithms, and their applications in computer science and mathematics.
New Ramsey Multiplicity Bounds and Search Heuristics
Explore new Ramsey multiplicity bounds and search heuristics in combinatorics and graph theory with Professor Tibor Szabó's insightful lecture.
Decomposing Cubic Graphs into Isomorphic Linear Forests
Explore cubic graph decomposition into isomorphic linear forests with Shoham Letzter, delving into extremal and probabilistic combinatorics.
Exponentially Many Graphs Are Determined by Their Spectrum
Explore discrete analogues of Kac's question on "hearing the shape of a drum" and learn about graphs determined by their spectrum in this mathematical seminar.
Learning Causal Models via Algebraic Constraints
Explorez les modèles causaux linéaires et leurs graphes dirigés. Découvrez des méthodes algébriques pour identifier les relations causales à partir de données observationnelles, même avec des cycles ou variables cachées.
Combinatorial Testing Problems - Lecture 1
Explore combinatorial testing problems, including hidden clique and high-dimensional random geometric graphs, with insights on statistical challenges and estimation techniques.
Analytic and Reidemeister Torsions of Digraphs and Path Complexes
Explore Reidemeister and analytic torsions on finite digraphs using path homology theory. Learn about Hodge Laplace operators, torsion identities, and formulas for Cartesian products and joins.
A Proof of the Erdos-Faber-Lovasz Conjecture
Explore the recent proof of the Erdos-Faber-Lovasz conjecture and its generalization, delving into linear hypergraphs and chromatic index concepts.
Hypergraph Bipartite Turan Problems
Explore recent findings on hypergraph bipartite Turan problems, including solutions to challenges posed by prominent researchers in the field.
Recent Progress in Ramsey Theory
Explore recent advancements in Ramsey Theory, focusing on new techniques and proofs related to Ramsey numbers and graph coloring. Gain insights into geometric, algebraic, probabilistic, and combinatorial methods.
Structures Robust Under Randomness - Probabilistic Combinatorics and Thresholds
Explore robustness of discrete system substructures under random subsampling, examining thresholds in random graphs and key conjectures in probabilistic combinatorics.