**Thursday April 21**TITLE: Fighting infections with mathematics

**SPEAKER: Judy Day, UT**TIME: 3:40pm – 4:35pm

ROOM: Ayres 405

Chances are you have gotten sick from some kind of infection before, but have thankfully recovered enough to read this abstract! In some cases, unfortunately, infections can be fatal – a reality that clinicians working in intensive care units face every day. What is going on inside when we are sick? In more serious infections, why might recovery not be a possibility? How can we understand this process better so we can properly intervene? We will see how combining mathematics with biology can provide a deeper understanding of the dynamics of an infection and reveal possible strategies for successfully controlling the response.

Pizza in A 408 @3:15

**Thursday, April 7**Title: You can count on power series

**Speaker: Jochen Denzler, UT**Time: 3:40pm – 4:35pm

Room: Ayres 405

Power Series have long been known to be useful not only in analysis, but also as an (ac)counting tool for discrete mathematics.

I will give and explain a few examples, in particular one whose 80th anniversary is approaching and which I will take license to name “Polya’s Breathalizer”. The material is classical, but rarely finds entry into the hustling undergraduate math experience.

Pizza in A 408 @ 3:15

**Thursday, March 3**Title: Exploring Complex Functions Using Phase Plots

**Speaker: Elias Wegert, TU Bergakademie Freiberg**Time: 3:40pm – 4:35pm

Room: Ayres 405

Graphical visualization of functions is one of the most powerful tools in (applied) mathematics. While pictorial representations of real functions are widely used for centuries, representations of complex (analytic) functions are not so common. As a counterpart of the traditional “analytic landscapes”, the talk promotes special color-representations, so-called “phase plots”, depicting a function f directly on its domain by color-coding the argument (or phase) of f.

Phase plots are like fingerprints: though part of the information (the modulus) is neglected, meromorphic functions can be uniquely reconstructed from their phase plots up to a positive constant factor. Moreover, several modifications allow one to incorporate additional information.

In the talk we explain how basic properties of a function can be recovered from its phase plot, show images of special functions, and present applications in teaching and research: the argument principle and its extension, universality of the Riemann zeta function, and the discovery of a stochastic periodicity in its phase plot.

Pizza in A 408 at 3:15.

**Thursday, February 11**TITLE: Proofs (not) from the Book

**SPEAKER: Sergei Tabachnikov, Penn State University**TIME: 3:40pm – 4:35pm

ROOM: Ayres 405

The eminent mathematician of the 20th century, Paul Erdos, often mention “The Book” in which God keeps the most elegant proof of every mathematical theorem. So, attending a mathematical talk, he would say: “This is a proof from The Book”, or “This is a correct proof, but not from The Book”. M. Aigner and G. Ziegler authored the highly successful “Proofs from THE BOOK” (translated into 13 languages). In this talk, I shall present several proofs that are not included in the Aigner-Ziegler book but that, in my opinion, could belong to “The Book”.

**Thursday, January 28**TITLE: Panel on UG Research Opportunities in Math

TIME: 3:00pm – 4:00pm (Note: Regular time (3:40p – 4:35p) will resume at next Junior Colloquium)

ROOM: Ayres 405

In this JC, a panel of students and professors will be available to discuss research opportunities in mathematics. Students with research experience in various fields including mathematical biology, algebra, and topology will take part in the panel, as well as faculty members with experience mentoring undergraduate research projects. Members of the panel include Dr. Lenhart, Virgina Parkman, Chris Loa, and Adam LaClair. If you have any questions about undergraduate research and REU opportunities in mathematics, then this is a great place to get started.