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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.

On a question of WunderNatur

STAG 263

Speaker: Jon Kujawa

The symmetric group has been the object of study since forever. Nevertheless, there are still new things to say. Using the commutator, you can view the group algebra of the symmetric group as a Lie algebra. In 2003, Marin described this Lie algebra as well as the subalgebra generated by the transpositions. Since the symmetric group naturally splits into even and odd permutations, you can also ask about the graded version of the commutator. This makes the group algebra into a Lie superalgebra. In 2023, Chris Drupieski and I obtained the super analogue of Marin’s results. I’ll aim to give a high-level overview of the questions, techniques, and answers that show up. Read more.