Dating back to the 1600s modeling has been used to study cardiovascular dynamics enabling scientist to answer essential questions. In fact, todays knowledge that the cardiovascular system is circulating was…
In this talk I'll explain a surprising relationship between the objects in the title. Two n-dimensional polytopes, $P$, $Q$ are said to be scissors congruent if one can cut $P$…
A fundamental problem in Bayesian inference and statistical machine learning is to efficiently sample from probability distributions. Standard Markov chain Monte Carlo methods could be prohibitively expensive due to various complexities of…
The Robinson-Schensted-Knuth (RSK) correspondence is an important combinatorial bijection that associates to any permutation a pair of objects called standard Young tableaux. We will describe this correspondence in detail and…
Rooted binary trees are used in evolutionary biology to represent the evolution of a set of species where the leaves denote the existing species and the internal nodes denote the…
Motivated by modeling borrowing and lending between banks, we start by illustrating systemic risk with a toy model of diffusions processes coupled through their drifts. We then show that such…
All of the math department staff relevant for graduate students will be here to tell you what they do and answer your pressing questions.
he emergence of vascular networks is a long-standing problem which has been the subject of intense research in the past decades. One of the main reasons being the widespread applications that it has in tissue regeneration, wound…
Polytopes (also known in dimensions zero through three as "points", "line segments", “polygons", and “polyhedra") have been objects of interest to mathematicians throughout the recorded history of mathematics. Most notably,…
Let be a free associative algebra over generated by for in some indexing set and let be a poset. For and we define an action of on (the complex vector space with basis ) in a way such that either annihilates or…
Let Q be an orientation of a type A Dynkin diagram. An eta map corresponding to Q is a surjection from the weak order on permutations to a Cambrian lattice…
The Penrose triangle, also known as the impossible tribar is an icon for cohomology. It is literally the icon for Cech cohomology on Wikipedia. The idea goes back to a…
Much of the literature on the design and analysis of supersaturated designs (SSDs), in which the number of factors exceeds the number of runs, rests on design principles assuming a least-squares analysis. More…