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The Undergraduate Friday Seminar (UFS) is a weekly event aimed at showing undergraduate mathematics students a taste of what they can experience from the professional world of mathematics research. Every Friday, we sit down with a different speaker as they tell us all about the interesting work they do and some of the neat results from their field!

Unlike many seminars, we make it a point to have material presented at a level that even the youngest of mathematicians can grasp. We also include undergraduates as our presenters; all of which is done in an effort to cultivate a generation of mathematicians who can accurately and engagingly present their work and interests to others.

**Interested in Presenting?**

If you are an undergraduate and wish to be added to the list of speakers scheduled for the semester, we ask that you fill out the following form: https://forms.illinois.edu/sec/8588924

Once we have your application, we’ll get in contact with you about how to proceed.

**Schedule for Spring 2020 Semester**

**February 28, 2020**

**4 p.m.
341 Altgeld Hall**

**Speaker:**Sean English, J.L. Doob Research Assistant Professor

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

**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

**February 21, 2020**

**4 p.m.
341 Altgeld Hall**

**Title:**Julia Robinson and Hilbert's Tenth Problem (film)

**Abstract:**Julia Robinson was the first woman elected to the mathematical section of the National Academy of Sciences, and the first woman to become president of the American Mathematical Society. While tracing Robinson's contribution to the solution of Hilbert's tenth problem, the film illuminates how her work led to an unusual friendship between Russian and American colleagues at the height of the Cold War.

**February 14, 2020**

**4 p.m.
341 Altgeld Hall**

**Speaker:**Raghavendra Bhat, Freshman Mathematics Major, UIUC

**Title:**Prime Number Conjectures

**Abstract:**Freshman math major and author (

*Math -- A Subtle Language of the Universe*) Raghavendra Bhat will present some of his prime number conjectures, which he has presented on many platforms across the world. His talk will focus on his recent conjectures and thoughts on number theory research and math in general.

**4 p.m.
341 Altgeld Hall**

**Speaker:**David Altizio, University of Illinois at Urbana-Champaign

**Title:**A Brief Introduction to Problem Writing

**Abstract:**Many of the best mathematics competition problems push the boundaries of pre-calculus math in unexpected ways. While these questions fuel the popularity of contests among middle and high school students, they also make competitions seem inherently unsustainable; constructing these questions appears to be a Herculean task. In this talk, I will shed some insight into how problems are made by exploring my eight-year-long journey through problem writing. In particular, I will discuss common writing philosophies, sources of inspiration, and the stories behind some of my favorite creations.

**January 31, 2020**

**4 p.m.
341 Altgeld Hall**

**Speaker: Robert Joseph Rennie,**University of Illinois at Urbana-Champaign

**Title:**What Is A Mathematics?

**Abstract:**In this talk, I will begin with a mathematization of the process of mathematization. We will then see how category theory and type theory provide a nice general framework for constructing and comparing systems of math. This discussion will motivate, without ever mentioning topological spaces, the study of higher toposes to anyone who cares about theoretical physics (not necessarily just those who study it). This talk requires only an interest in thinking about how math works.

**Contact**

If you have any questions or concerns, feel free to email us: **undergradseminar@math.illinois.edu**** **