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Visual Processing in the SCN2A Heterozygous Rat Model of Autism Spectrum Disorder

One-Back Perceptual Memory Task: Psychophysics, Computational Model, and EEG Correlates

To yield generalizable insights, models of cognitive function must explain behavioral and brain data across diverse experimental paradigms. In the domain of sensory-perceptual memory, however, most models are tailored to specific tasks, raising the question: are perceptual memories governed by paradigm-specific mechanisms, or can broader, unified principles be identified? A general framework in which different forms of perceptual memory arise from the interaction of multiple memory buffers w...

Fourier Optimization, de Branges Spaces, and Zeros of L-functions

This thesis deals with a few topics at the intersection of Fourier analysis, number theory, and complex analysis. Using the framework of Fourier optimization we obtain new bounds related to the following questions in number theory: the least quadratic non-residue, the least prime in an arithmetic progression, and Montgomery's pair correlation conjecture. We also make contributions related to Hilbert spaces of entire functions, namely, studying norms of embeddings between weighted Paley--Wiene...

On Realizations of Hypergeometric Motives

In this thesis, we investigate some of the arithmetic and geometry underlying hypergeometric functions and their finite field analogues. Motivated by their appearance as periods of families of varieties and as traces of Frobenius in étale cohomology, we study the interplay between hypergeometric functions, and point-counting over finite fields. In Chapter 1, we prove that under mild assumptions, the complex hypergeometric local system coincides with the top weight variation of a family o...