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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 10:00 a.m.


Abelian dynamical Galois groups associated to postcritically finite rational functions

On line

Speaker: Chifan Leung

Andrews and Petsche formulated a conjecture that an arboreal Galois extension is abelian if and only if the polynomial is conjugate to a powering map or a Chebyshev map and the base point is a root of unity in a number field. In this talk, we will discuss if a rational function is postcritically finite, and the base point is not preperiodic, then the arboreal Galois tower is not abelian. This uses two deep theorems, a result by Benedetto-Ingram-Jones-Levy on attracting cycles, as well as an equidistribution result by Baker-Rumely, Favre-Rivera-Letelier and Chambert Loir. This work is jointly by me and my advisor Clayton Petsche. Read more.


TBA

Weniger Hall 201

Speaker: TBA

Read more.