About Natanael Alpay

Corrently I am a Ph.D. Candidate at UCI , and my main areas of interest are Harmonic analysis, functional analysis, probability theory, applied mathematics, and mathematical physics.

I am working on several research projects across both pure and applied mathematics. One of my primary focuses is finding sharp lower bounds for the square function of indicator functions of sets, a problem with connections to harmonic analysis and probability theory. Alongside this theoretical work, I also have project in applied mathematics that investigates weighted stochastic gradient descent methods applied to the solution of the representer theorem which bridges optimization theory and machine learning. In parallel, also studying the stochastic gradient descent with respect to special cases of the T-tensor product, a still young area of study.

Additionally, in quantum theory I studied the thermal states within the Mittag-Leffler Fock space, a reproducing kernel Hilbert space. This work coincides with my research on generalized and fractional reproducing kernel Hilbert spaces, which play a central role in functional analysis, learning theory, and operator theory.

These diverse areas are united by my broader interest in mathematics, physics, and computer science. My interdisciplinary approach reflects a commitment to advancing both theory and its applications.

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