In examining the relationship between the number of points over Fp on certain Calabi-Yau manifolds and hypergeometric series which correspond to a particular period of the manifold, Rodriguez-Villegas identified numerically 22 possible supercongruences. We prove one of the outstanding supercongruence conjectures between a special value of a truncated generalized hypergeometric series and the p-...

In Stanley [16], the author introduces expressions for the normalized characters of the symmetric group and states some positivity conjectures for these expressions. Here, we give an affirmative partial answer to Stanley’s positivity conjectures about the expressions using results on Kerov polynomials. In particular, we use new positivity results in Goulden and Rattan [7]. We shall see that the...

A homeomorphism f : X → X of a compactum X with metric d is expansive if there is c > 0 such that if x, y ∈ X and x 6= y, then there is an integer n ∈ Z such that d(f(x), f(y)) > c. In this paper, we prove that if a homeomorphism f : X → X of a continuum X can be lifted to an onto map h : P → P of the pseudoarc P , then f is not expansive. As a corollary, we prove that there are no expansive ho...

Taylor, Dewey Terese. Fine Bruhat Intersections for Reductive Monoids. (Under the direction of Mohan S. Putcha.) Fine Bruhat intersections for reductive groups have been studied by several authors in connection with Kazhdan-Lusztig theory, canonical bases and Lie Theory. The purpose of this thesis is to study the analogous intersections for reductive monoids. We determine the conditions under w...

We define an affine Jacquet functor and use it to describe the structure of induced affine Harish-Chandra modules at noncritical levels, extending the theorem of Kac and Kazhdan [10] on the structure of Verma modules in the Bernstein–Gelfand–Gelfand categories O for Kac–Moody algebras. This is combined with a vanishing result for certain extension groups to construct a block decomposition of th...