Department of

# Mathematics

Seminar Calendar
for events the day of Friday, February 28, 2020.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, February 28, 2020

3:00 pm in 347 Altgeld Hall,Friday, February 28, 2020

#### Eigenvalues on Forms

###### Xiaolong Han (UIUC Math)

Abstract: Recently there has been a growing interest in eigenvalues on forms. It is much more complicated than eigenvalues on functions but can detect finer geometry. It has applications in detecting length of axes of John ellipsoid of convex body, relating Monopole Floer homology to hyperbolic geometry, and commutator length in hyperbolic geometry. In this talk we will show some basic theory and definitions for eigenvalues on forms, and then provide some intuition for the geometry and applications.

4:00 pm in 141 Altgeld Hall,Friday, February 28, 2020

#### Arnold-Liouville Theorem

###### Jungsoo (Ben) Park (UIUC)

Abstract: This talk will be an introduction to fundamental concepts of symplectic geometry. Furthermore, we will delve into the proof of Arnold-Liouville theorem: https://en.wikipedia.org/wiki/Liouville–Arnold_theorem.

4:00 pm in 143 Altgeld Hall,Friday, February 28, 2020

#### Re: Mathematical art and sculpture in connection with the Altgeld/Illini building project

Abstract: Meeting is scheduled for 4-5 p.m.

4:00 pm in 341 Altgeld Hall,Friday, February 28, 2020

#### How to Tile Your Bathroom: An Extremely Impractical Guide from a Mathematician

###### Prof. Sean English   [email] (UIUC Math)

Abstract: Tilings have been considered by mathematicians for centuries and by artists for millennia. The main question for tiling problems involves asking if a small number of shapes can be used to cover an entire geometric region without gaps or overlaps. We will briefly talk about some of the history behind tilings, then we will explore many interesting different directions these sorts of problems can take. We will explore some questions as simple as "which regular polygons can tile the plane?" to questions as obscure as "do chickens give rise to a periodic tiling?". Disclaimer: Unless your bathroom is infinite in size, follows spherical or hyperbolic geometry, or has a floor that is more than two dimensional, this talk may not actually be helpful for tiling your bathroom.