**Seminars and Colloquiums**

for the week of January 21, 2019

for the week of January 21, 2019

*SPEAKERS*

**Tuesday**

Oleg Ivrii, California Institute of Technology

**Thursday**

Armin Schikorra, University of Pittsburgh

**Friday**

Danielle Burton and Athma Senthilnathan

**TEA TIME**

3:00 PM – 3:30 PM

Tuesday & Wednesday

Room: Ayres 408 (kitchen)

Hosted by: Maggie Wieczorek

Topics: Teaching support/development resources on campus, outside of Mathematics Department; weekly check-in (a time for students and faculty to discuss current happenings of the Mathematics Department and share any concerns or ideas).

**Tuesday, 1/22**

** SACNAS STUDENT CHAPTER MEETING **

TITLE: SACNAS Student Chapter Meet and Greet

TIME: 11:45 AM-12:30 PM

ROOM: Ayres 401

Come to this "Meet and Greet" with pizza for our chapter representing the Society for Advancement of Chicano/Hispanics and Native Americans in Science. Our chapter wants to connect a diverse group of students and faculty interested in science.

**SPECIAL COLLOQUIUM**

TITLE: Describing Blaschke products by their critical points

SPEAKER: Oleg Ivrii, California Institute of Technology

TIME: 3:30 PM-4:30 PM

ROOM: Ayres 405

In this talk, I will discuss a question which originates in complex analysis but is really a problem in non-linear elliptic PDE. A finite Blaschke product is a proper holomorphic self-map of the unit disk, just like a polynomial is a proper holomorphic self-map of the complex plane. A celebrated theorem of Heins says that up to post-composition with a M\"obius transformation, a finite Blaschke product is uniquely determined by the set of its critical points. Konstantin Dyakonov suggested that it may interesting to extend this result to infinite degree, however, one must be careful since infinite Blaschke products may have identical critical sets. I will show that an infinite Blaschke product is uniquely determined by its "critical structure” and describe all possible critical structures which can occur. By Liouville’s correspondence, this question is equivalent to studying nearly-maximal solutions of the Gauss curvature equation $\Delta u = e^{2u}$. This problem can then be solved using PDE techniques, using the method of sub- and super- solutions.

**Wednesday, 1/23**

**ANALYSIS SEMINAR**

In view of Analysis faculty candidate colloquia during January, the Analysis Seminar is suspended until February. Graduate students working or thinking of working in analysis are STRONGLY encouraged to attend the talks and the open sessions scheduled for the analysis candidates.

**Thursday, 1/24**

**DIFFERENTIAL EQUATIONS SEMINAR**

TITLE: Self-repulsive curvature energies for curves and surfaces: regularity theory and relation to harmonic maps

SPEAKER: Armin Schikorra, University of Pittsburgh

TIME: 2:10 PM-3:10 PM

ROOM: Ayres 114

I will talk about a class of curvature energies for curves, the O'Hara energies, that are nonlocal in nature. In particular, I will present an approach for regularity theory of minimizers and critical points for these curves which is based on a relation to (fractional) harmonic maps. Then I will present some results towards attempts of generalizing this idea to surfaces.

**Friday, 1/25**

**MATH BIOLOGY SEMINAR**

SPEAKER: Danielle Burton and Athma Senthilnathan

TIME: 11:15 AM-12:05 PM

ROOM: Ayres 401

We will begin the semester by discussing the paper by Paul Hurtado and Adam Kirosingh titled "Generalizations of the `Linear Chain Trick': Incorporating more flexible dwell time distributions into mean field ODE models." The discussion on this paper will be led by Danielle Burton and Athma Senthilnathan and will be followed up by a future visit (TBD) by one of the co-authors, Paul Hurtado to discuss the work in person. If you are interested in being added the Math Biology Seminar 'BaseCamp' site to receive notices and seminar materials directly, please contact Judy Day at judyday@utk.edu.

*If you are interested in giving or arranging a talk
for one of our seminars or colloquiums, please review our
calendar. *

*If you have questions, or a date you would like to confirm,
please contact mlangfo5@utk.edu *

**Past notices:**

Winter Break