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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 11:00 a.m.


Hecke continued fractions and connection points on Veech surfaces

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Speaker: Julian Boulanger

Given a billiard trajectory on a regular polygon starting from thecenter of the polygon and eventually ending at a vertex, is it true thatthe trajectory starting from the center but in the opposite direction also ends eventually at a vertex ? By symmetry, this is certainly true if the number of sides is even. In the odd case, we will see that the answer is 'yes' for the equilateral triangle and the regular pentagon, but 'no' if the polygon has 7 sides or more! The question is closely related to determining the real numbers (in some algebraic field) having a finite Hecke continued fraction expansion, or equivalently cusp representative of the Hecke modular surface. We will also encounter so-called translation surfaces and their Veech groups, and we will discuss the notion of connection points on such surfaces. Read more.


TBA

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Speaker: Thomas Garrity

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TBA

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Speaker: Slade Sanderson

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TBA

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Speaker: Charlene Kalle

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TBA

Bexell 328

Speaker: Emily McGovern

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TBA

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Speaker: Karl Winsor

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TBA

Bexell 328

Speaker: Tom Schmidt

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TBA

TBA

Speaker: Derek Garton

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