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Seminar
FIELD Math: CMC
DATE February 04 (Thu), 2021
TIME 10:00-11:00
PLACE Online
SPEAKER Robert Pollack
HOST Kim, Chan-Ho
INSTITUTE Boston University
TITLE [Number Theory] Slopes of modular forms and the ghost conjecture
ABSTRACT Modular forms are mathematical objects born in complex analysis but in fact have become central objects in number theory. In particular, special modular forms, called eigenforms, have Fourier coefficients which are algebraic integers and these integers contain loads of number theoretic data. In this talk, we will focus on one slice of this data, namely, the highest power of p dividing the pth Fourier coefficient (called the slope of the form). Through many numerical examples, we will discuss the properties of these slopes and ultimately state the so-called "ghost conjecture" which predicts them in a combinatorial way.
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