Dept. of Mathematics
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(2019-02-19)The sum-product problem of Erdos and Szemeredi asserts that any subset of the integers has many products or many sums. We explore quantitative aspects of the problem over both the real numbers and finite fields of prime order.
(2019-04-12)We investigate properties of prime numbers and L-functions, and interactions between these two topics. First, we discuss the problem of primes in thin sequences, expanding on work of Maynard and Friedlander-Iwaniec. Next, ...
(2019-04-10)Although the hierarchically hyperbolic space boundary is a generalization of the Gromov boundary, we will show there are fundamental differences between the two. First, we provide negative answers to questions posed by ...
(2019-04-17)This thesis consists of two parts. In the first half, we define, so called, generalized Artin-Schreier cover of a scheme X over k. After defining Artin-Schreier group scheme Γ over X, a generalized Artin-Schreier cover ...
(2019-04-02)In this thesis, we consider nonlinear Schrödinger equations with double well potentials with attractive and repelling nonlinearities. We discuss bifurcations along bound states, especially ground states and the first excited ...