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Given a finite transitive group G ≤ Sym(Ω), a set F ⊂ G is intersecting if for any g, h ∈ G, there exists ω ∈ Ω such that ω g = ω h . The intersection den- sity ρ(G) is the maximum ratio of |F| |Gω| , where F runs through all intersecting sets of G...

A classical problem in signal recovery is to determine whether a finite signal can be recovered from its Fourier transform with missing values. This problem has been studied by many authors starting with the seminal papers by Matolsci and Szuks in...

Abstract TBA

The Rudin-Shapiro polynomials $p_{m}$ were first studied by Rudin, Shapiro, and Golay independently nearly 80 years ago and are defined recursively by $p_{0}(x) = q_{0}(x) = 1$ and $$ p_{m}(x) = p_{m-1}(x) + x^{2^{m-1}} q_{m-1}(x), $$ $$ q_{m}(x) = p...

Abstract: A new frontier for the modeling and analysis of reaction-diffusion PDE systems is where the diffusing species are nonlinearly coupled through dynamic interactions on the domain boundaries. Some specific examples of such systems, including...

A set $A\subset\mathbb{Z}$ tiles the integers by translations if there is a set $T\subset\mathbb{Z}$ such that every integer $n\in\mathbb{Z}$ has a unique representation $n=a+t$ with $a\in A$ and $t\in T$. It is well known that the translation set in...

Students of grades 5 to 7 are invited to challenge and develop their thinking and creativity skills at the Math Circle Workshops. This is an enrichment program for students organized by the faculty members of the Department of Mathematics at the...

Abstract: In this talk we will introduce the modular method, the approach followed by Wiles to prove Fermat’s Last Theorem. We will explain the role of elliptic curves, modular forms, and Galois representations in this framework, and discuss how the...

An n-by-n matrix A=[a_{ij}] is said to be a pairwise comparison matrix (PC matrix) or a reciprocal matrix if it is positive and a_ij=1/a_ji, for all i,j=1,...,n. If, in addition, a_ika_kj=a_ij for all i,j,k, the matrix is said to be consistent. There...

The first regularity results for maps optimizing an open class of cost were proved by Ma-Trudinger-Wang (2005) using a key inequality which they introduced (based on a classical strategy of Pogorelov). Away from the boundary, this inequality controls...