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A symmetric monoidal category is a category equipped with a monoidal product that is uniquely commutative up to isomorphism. In this way the iterated monoidal product has an action from the symmetric groups. We can generalize this notion by allowing...

The Schensted correspondence is a bijection between permutations in Sn and pairs of standard Young tableaux (P,Q) with n boxes which have the same shape. This bijection has remarkable properties in algebraic and enumerative combinatorics. Motivated...

The KPZ (Kardar-Parisi-Zhang) universality class is a loose term for a collection of random interface growth models and random planar metrics that exhibit the same behaviour under rescaling. Examples of models in this class include TASEP, last...

The KPZ (Kardar-Parisi-Zhang) universality class is a loose term for a collection of random interface growth models and random planar metrics that exhibit the same behaviour under rescaling. Examples of models in this class include TASEP, last...

A core challenge for modern biology is how to infer the trajectories of individual cells from population-level time courses of high-dimensional gene expression data. Birth and death of cells present a particular difficulty: existing trajectory...

The wavefunction of a particle describes everything that could be known about a quantum mechanical system. One of the key insights over the past few decades is that a wavefunction, despite its name, is not an ordinary function, but should be regarded...

A set S in the Euclidean plane is an integer distance set if the distance between any pair of its points is an integer. Interestingly, all the so-far-known integer distance sets have all but up to four of their points on a single line or circle. And...

Feynman’s path integral expresses the probability amplitude of a quantum mechanical system as a “sum of trajectories” of the classical system. Since this integral has not been given a satisfactory mathematical meaning, a widely accepted treatment is...

Every curve has an abelian variety associated to it, called the Jacobian. Poincaré's total reducibility theorem states that any abelian variety is isogenuous to a product of simple abelian varieties. We are interested to know this decomposition for...

Given two graphs H and G, the homomorphism density t(H,G) represents the likelihood that a random mapping from V(H) to V(G) is a homomorphism. Sidorenko Conjecture states that for any bipartite graph H, t(H,G) is greater or equal to t(K_2,G)^{e(H)}...