Fourier Coefficients of Modular Forms and Arithmetic

Abstract: Classical modular forms are highly symmetric, holomorphic functions on the complex upper half plane, of which the simplest were already known to Gauss. Since the insights of Ramanujan on the arithmetic significance of their Fourier coefficients, in the early 20th century, they have been deeply studied and generalized. In this talk, I will begin with some historical examples and explain how these ideas have been generalized to higher dimensions. I will present some new relations between Fourier coefficients and Hecke eigenvalues for certain Siegel modular forms. Along the way, we will encounter some geometry, representation theory, and even a bit of physics.

commutative algebraalgebraic geometrygeneral mathematicsnumber theoryrings and algebras

Audience: undergraduates

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PRiME: Pomona Research in Mathematics Experience

Series comments: PRiME is hosting a series of talks which will take place on Fridays in July. All are welcome to join us either in person at Pomona College or virtually over Zoom. There will be two types of series.

PROFESSIONAL DEVELOPMENT WORKSHOPS

We will have a series of 2-hour workshops geared for undergraduate students, graduate students, and faculty. The Morning Sessions will take place from 10:00 AM - 12:00 PM Pacific, while the Afternoon Sessions will take place from 2:00 PM - 4:00 PM Pacific. The Student Professional Development Series (geared for undergraduates) will meet at Pomona College in Estella 1051 (Argue Auditorium); while the Faculty Professional Development Series (geared for graduate students and junior faculty) will meet in Estella 1021 (Noether Auditorium).

COLLOQUIUM SERIES

We will have outside speakers to visit with us on Fridays from 4:30 PM - 6:00 PM Pacific. We will meet in person at Pomona College in Estella 1051 (Argue Auditorium).

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