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Department of Mathematics

Algebra and Number Theory Seminars

Tiling

Group theory is the formal mathematical study of symmetry. Groups are among the foundational objects composing abstract algebra, yet they also pervade nearly every discipline in pure mathematics as well as many areas of science and engineering. One striking result of group theory shows that there are exactly 17 different types of planar symmetry. This image illustrates one of these types of symmetry in a section of tilework at the Alhambra Palace in Granada, Spain. This particular symmetry is characterized by 3-fold rotational symmetry with no reflections (Photo credit The_Alhambra_and_The_Alcazar).

The Algebra and Number Theory Seminar is structured to include talks on a broad range of mathematical areas that are of interest to algebraists and number theorists, including analytic and algebraic number theory, algebra, combinatorics, algebraic and arithmetic geometry, cryptography, representation theory, and more. Talks are given by a variety of local, national, and international speakers in number theory and related areas.

See below for upcoming seminars or access the seminar archive.

Organizers

Mary Flahive, Clayton Petsche, Thomas Schmidt and Holly Swisher

Timing

We traditionally meet every Tuesday at 11:00 a.m.

The Arithmetic of Laurent Coefficients of Meromorphic Modular Forms

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Speaker: Eleanor McSpirit

The arithmetic study of Taylor coefficients of modular forms at CM points has its roots in the classical theory of complex multiplication, beginning with the algebraicity the values of the j-function at CM points. The study of Taylor expansions of modular forms at CM points has since developed through work of Shimura on nearly holomorphic modular forms and became more explicit in later work of e.g. Rodriguez-Villegas and Zagier. Recently, Bogo, Li, and Schwagenscheidt studied Laurent expansions of meromorphic modular forms with poles at CM points and observed arithmetic patterns in examples. In this talk, I will discuss ongoing joint work with Rolen aimed at explaining and characterizing the arithmetic behavior of these Laurent coefficients. Read more.