Past Events

Conolly's sequence (A046699) is defined by the nested recurrence relation C(n)=C(n-C(n-1))+C(n-1-C(n-2)) and the initial conditions C(1)=C(2)=1. This sequence is monotone increasing with each positive integer appearing at least once, a

The Alon-Jaeger-Tarsi conjecture states that for any field F with |F|geq 4 and any non-singular matrix A over F, there is a vector x such that both x and Ax

Demand for resources that are collectively controlled or regulated by society, like social services or organs for transplantation, typically far outstrips supply. How should these scarce resources be allocated? Any

Every k entries in a permutation can have one of k! different relative orders, called patterns. How many times does each pattern occur in a large random permutation of size

A partition of a positive integer n is a finite nonincreasing sequence of positive integers \lambda_1, \lambda_2 . . . \lambda_k whose sum is equal to n. We will start

We take a geometric perspective to study networks that come from the physical world, such as the wireless and sensor networks, as well as mobile and social networks. I will

The main question we will discuss is, how number of terms of a polynomial(a.k.a Sparsity) relates to number of terms of its factors. This is a fundamental problem which lies

The study of permutation patterns began with Knuth's analysis of a certain "stack-sorting algorithm" in 1968. In his 1990 PhD. thesis, West investigated a deterministic variant of Knuth's algorithm, which

When a large set is stored remotely, membership queries (that is, checking if an element is present in the set) can be expensive. Instead of querying the remote set each

The orchard problem asks for the maximum number of collinear triples in a finite set of points in the plane. Very recently, Green and Tao gave an upper bound on

We prove a number of tight graph homomorphism inequalities, where, for a fixed H, we wish to maximize the number of homomorphism from G to H (after exponentially normalizing by

Fermat and Pascal's two different methods for solving the problem of division lead to two different mathematical foundations for probability theory: a measure-theoretic foundation that generalizes the method of counting

A wagering mechanism is a zero-sum competition among forecasters. Many wagering mechanisms exist, starting with parimutuel wagering in 1867, and today handle billions of dollars in trade. Recently, we invented

Call a subset A of an abelian group G unique sum free (USF) if every sum s in A+A is not uniquely represented. That is, for every a and b

We consider a random nxn matrix, M_n, whose entries are independent and identically distributed (i.i.d.) Rademacher random variables (taking values {-1,1} with probability 1/2) and prove 2^{-(0.5+o(1))n^2} <=P (M_n is

An s,t-core partition is a partition with no hook length equal to s or t. Recently Ekhad-Zeilberger used experimental methods to prove that the asymptotic distribution size among s,t-cores (with

We investigate whether the standard dimensionality reduction technique of PCA inadvertently produces data representations with different fidelity for two different populations. We show on several real-world data sets, PCA has