Past Events

We study the existence of powers of Hamiltonian cycles in graphs with large minimum degree to which some additional edges have been added in a random manner. It follows from

For a (multi)graph G=(V,E), we denote by χ'(G) the minimum number of colors needed to color the edges of G properly. Clearly, Δ≤χ'(G). Vizing proved that χ'(G)≤ Δ(G)+μ(G), where μ(G)

Christie Nelson and students in the Professional Masters program in Business and Science have partnered with the NJ State Police Forensics Lab on a ballistics data analysis project, utilizing machine

I might actually talk about the method of containers. This is a powerful technique that was only developed in the last decade and has been used to prove some long

In the online bipartite matching problem with replacements, all the vertices on one side of the bipartition are given, and the vertices on the other side arrive one by one

What is the probability that a random graph has exactly the average number of copies of $K_5$? We will discuss a new technique developed since our last talk at Rutgers

Can you factor a random polynomial with integer coefficients into smaller factors also with integer coefficients? Work on this simple question goes back more than 80 years, and there is

Earlier this semester, Aditya showed a construction of "important graphs." In this talk, we will see these graphs are indeed important. Based on Noga Alon's talk at https://www.renyi.hu/conferences/ll70/ .

In many cases, a group action on a manifold can be associated with a map called a moment map. Surprisingly, the image of the manifold under this map is always

Let X denote the number of triangles in the random graph G(n, p). The problem of determining the asymptotics of the rate of the upper tail of X, that is,

We build schemes to count the number of words avoiding a certain (finite) set of patterns. We can handle (at least in principle) infinitely many such sets of patterns.

Introduction to Noncommutative Birational Geometry I will discuss several phenomena related to noncommutative triangulations of surfaces.

Bootstrap percolation is a process defined on a graph, which starts with a set S of initially infected vertices. Afterward, at each step, an uninfected vertex with at least r

Using Number Theory and Combinatorial Optimization to Solve a Problem in Statistics

Combinatorial optimization is important because it captures many natural problems, e.g., spanning tree, bipartite matching, set cover, network design, clustering, and submodular/subadditive optimization. Classically, these problems have been studied in

The stable marriage problem is a classic one in the library of discrete math. The best-known results on the problem stem from the work of David Gale and Lloyd Shapley,

A non-backtracking random walk on a graph is a directed walk with the constraint that the last edge crossed may not be immediately crossed again in the opposite direction. This

We'll talk about how representation theory can be used to determine fundamental questions about the rate of convergence of random walks on groups, and how the approach benefits from computer

WZ Theory is a powerful method to automatically conjecture and prove identities involving hypergeometric series. I will give an overview of the method and important results