K-tilings of the Aztec Diamond
Explore K-tilings of the Aztec diamond, a fascinating mathematical concept in integrable systems and exactly solvable models.
Crystal Bases in Statistical Mechanics, Representation Theory and Combinatorics - Part II
Explore crystal base theory applications in symmetric functions and cyclic sieving through combinatorial crystal definitions in statistical mechanics and representation theory.
Crystal Bases in Statistical Mechanics, Representation Theory and Combinatorics - Part I
Explore crystal base theory applications in symmetric functions and cyclic sieving through combinatorial definitions, enhancing understanding of statistical mechanics and representation theory.
Introduction to Circular Orderings - Lecture 2
Explore algebraic and combinatorial aspects of circularly-orderable groups, focusing on cohomology, central extensions, and obstruction spectra. Gain insights through exercises and open problems.
Introduction to Circular Orderings - Lecture 3
Explore algebraic and combinatorial aspects of circularly-orderable groups, focusing on cohomology, left-ordered central extensions, and obstruction spectra. Gain insights through exercises and open problems.
Introduction to Circular Orderings - Lecture 1
Explore algebraic and combinatorial aspects of circularly-orderable groups, covering definitions, group operations, cohomology, and obstruction spectra. Gain insights through exercises and open problems.
Introduction to Circular Orderings - Lecture 4
Explore algebraic and combinatorial aspects of circularly-orderable groups, focusing on cohomology, left-ordered central extensions, and obstruction spectra. Gain insights through exercises and open problems.
The Loop Hecke Algebra and Charge Conserving Yang-Baxter Operators
Explore Loop Braid Group, Loop Hecke Algebras, and charge conserving Yang-Baxter operators. Gain insights into recent mathematical developments in quantum symmetries and topological quantum field theories.
Polynomial Inequalities and Combinatorial Interpretations
Explore polynomial inequalities and their combinatorial interpretations, focusing on explicit injections and challenges in proving inequalities when naive approaches fail.
Free Resolutions of Powers of Square-Free Monomial Ideals
Explore free resolutions of square-free monomial ideals and their powers, focusing on combinatorial methods and discrete topology. Gain insights into this central problem in commutative algebra.
Degeneracy Loci in Geometry and Combinatorics
Explore degeneracy loci in geometry, tracing their history and examining modern formulas connecting geometric concepts with Schubert polynomial combinatorics.
New Frontiers in Structure vs Randomness with Applications to Combinatorics, Complexity, and Algorithms
Explore new frontiers in structure vs randomness, delving into applications in combinatorics, complexity, and algorithms. Gain insights on Erdos-Turan problem and recent advancements in additive combinatorics.
Around the Alexandrov-Fenchel Inequality - Convex Geometry and Its Applications
Explore the history and recent progress in convex geometry, focusing on Minkowski's theory and its connections to various mathematical disciplines.
The Chromatic Number of Random Graphs
Explore the chromatic number of random graphs, focusing on lower bounds for G(n,1/2) and its limiting distribution. Discover recent advancements in graph theory and probabilistic methods.
Hamiltonicity of Expanders: Optimal Bounds and Applications
Explore optimal bounds and applications of Hamiltonicity in expanders with Nemanja Draganić, delving into extremal and probabilistic combinatorics, Ramsey theory, and theoretical computer science.
Hausdorff Dimension of Three-Dimensional Kakeya Sets
Explore groundbreaking research on Kakeya sets in R^3, uncovering a new lower bound for Hausdorff dimension and its implications in geometric measure theory.
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.
Sharp Stability for the Brunn-Minkowski Inequality for Arbitrary Sets
Explore sharp stability in the Brunn-Minkowski inequality for arbitrary sets, delving into combinatorics and its connections with metric geometry and analysis.
Resolution of the Quadratic Littlewood-Offord Problem
Explore the resolution of the Quadratic Littlewood-Offord problem with expert Mathew Kwan, delving into combinatorics and its probabilistic connections.