About Natanael Alpay

I was born in Israel to a father of French origin and a mother of Russian origin. Two cultures and viewpoints which emphasize education as a cornerstone of one’s personal identity. From a very young age, mathematics had a strong presence in my family. Throughout my childhood, I used to go with my dad and listen to his lectures at the university where he worked in Beer Sheva, Israel, in the Mathematics Department. From there, my curiosity for math was born.

When starting my undergraduate at Chapman University I was thrilled to take many courses in numerous subjects; with each mathematics, physics, and computer science class I mastered, my passion for learning grew and enrolling in more and more advanced courses became the norm. I graduated with three B.S. degrees in Mathematics, Physics, and Computer Science and a B.A. degree in French.

Upon graduation I awarded the Ronald M. Huntington Outstanding Scholarship Award which is given to a graduating senior judged to have exhibited the most distinguished record of scholarly accomplishments while a student at Chapman University.

Corrently I am a Ph.D. sduent 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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