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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.

Torsion and exceptional units

Online

Speaker: Dino Lorenzini

Associated with an elliptic curve E/K over a number field K is a finite set of integers greater than 1 called the local Tamagawa numbers of E/K. The ratio (product of the Tamagawa numbers)/|Torsion in E(K)| appears in the conjectural leading term of the L-function of E in the Birch and Swinnerton-Dyer conjecture, and we are interested in understanding whether there are cancellations in this ratio when E(K) has a non-trivial torsion subgroup. When N is prime, let us call N-special an elliptic curve E/K with a K-rational torsion point of order N and such that N does not divide the product of the Tamagawa numbers. We will show that the existence of an N-special elliptic curve E/K is intimately linked to the existence of exceptional units in the ring of integers of K. When N > 2d+1, we suggest that there exist only finitely fields K/Q of degree d having (finitely many) N-special elliptic curves E/K. The list of known N-special elliptic curves is surprisingly short when d is at most 7. Read more.

Interpolating Classical Schur Algebras

Strand Agricultural (Stag) Hall 212

Speaker: Addison Day

Classical Schur algebras are a family of finite-dimensional algebras discovered by Issai Schur in 1901. They are intimately related to general linear and symmetric groups, and possess combinatorial structure enabling one to concretely study their representation theory. In this talk we will discuss the construction and representation theory of a new family of algebras which in a certain sense interpolate between the classical Schur algebras. Read more.

TBA

Online

Speaker: Nils Bruin

Read more.

TBA

online

Speaker: Katherine (Katy) Woo

Read more.

TBA

Online

Speaker: Anton Lukyanenko

Read more.