**Seminars and Colloquiums**

for the week of March 25, 2019

for the week of March 25, 2019

*SPEAKERS*

**Monday**

Thomas Weighill, University of Tennessee

**Tuesday**

David Talmy, University of Tennessee (Microbiology)

**Wednesday**

Joan Lind, University of Tennessee

**Thursday**

Mahir Demir, University of Tennessee

Ram Iyer, Texas Tech University

Suzanne Lenhart, University of Tennessee and National Institute for Mathematical and Biological Synthesis (NIMBioS)

**Friday**

Nathan Pollesch (U.S. Environmental Protection Agency) and Megan Rua (Wright State University)

June Huh, Princeton University

**Monday, 3/25**

**DOCTORAL DEFENSE
**TITLE: On some coarse geometric notions inspired by topology and category theory

SPEAKER: Thomas Weighill, University of Tennessee

TIME: 3:30 PM

ROOM: Ayres 123

His committee consists of Professors: Dydak (chair), Brodskiy, Thistlethwaite, Berry (EECS).

**Tuesday, 3/26**

**SIAM STUDENT CHAPTER TALK**

TITLE: What are the origins of sub-linear predator-prey biomass power-law relationships?

SPEAKER: David Talmy, University of Tennessee (Microbiology)

TIME: 11:10 AM-12:00 PM

ROOM: Ayres 406

This talk will be short (about 25 minutes) and will be followed by an informal chat with him over a pizza lunch.

**Wednesday, 3/27**

**ANALYSIS SEMINAR
**TITLE: Fair Peano Curves

SPEAKER: Joan Lind, University of Tennessee

TIME: 2:30 PM-3:20 PM

ROOM: Ayres 113

Given a spanning tree of a rectangular grid in some domain, one can create the so-called peano curve that winds around tree. Thus the uniform spanning tree (UST), which is the random family of spanning trees that gives equal weight to each possible spanning tree, gives rise to a random family of peano curves. Lawler, Schramm, and Werner showed that the scaling limit of these curves is SLE(8). We will consider the notion of fair trees, which will lead to a different probability measure on spanning trees, and we will ask about the scaling limit of the corresponding fair peano curves. This is joint work with Nathan Albin and Pietro Poggi-Corradini.

**Thursday, 3/28**

**DOCTORAL DEFENSE
**TITLE: Optimal control strategies in Ecosystem-based Fishery Models

SPEAKER: Mahir Demir, University of Tennessee

TIME: 11:30 AM

ROOM: Claxton 103

His committee consists of Professors: Lenhart (chair), Day, Phan, and Gross (EEB.)

**MATHEMATICAL DATA SCIENCE SEMINAR
**TITLE: Application of Representer theorems from Machine Learning to Optometry and Ophthalmology

SPEAKER: Ram Iyer, Texas Tech University

TIME: 12:30 PM-2:00 PM

ROOM: Ayres 405

Representer theorems have been investigated for the last two decades in machine learning, but their origin is in smoothing data using splines. Kimmeldorf and Wahba (1971) showed that the minimizer for a Tikhonov regularization problem may be represented as a finite linear combination of functions that form the basis for a reproducing kernel Hilbert space (RKHS) generated by the data. We studied the utility of this result for solving a variety of problems in ophthalmology and optometry, where recent advances in imaging technology have made possible the measurement of cross sections of the anterior corneal chamber, and the measurement of higher order aberrations of the human eye. Accuracy and precision in learning the shape of the cornea is extremely important to detect early stages of corneal disease, and in the design of advanced contact lenses to correct higher order aberrations in addition to focus defects and astigmatism. It had long been recognized within optometry that parametric models for corneal shape lead to ill-posed computational problems and high variance in the computed shapes. An application of the Kimmeldorf-Wahba (KW) representer theorem yields the corneal shape as the sum of two functions lying in orthogonal RKHS subspaces of the Sobolev space H^2 (B_? (0)), where B_? (0) is the ball of radius ? centered at the origin. The KW theorem yields a fast global-local learning algorithm for corneal shapes with good statistical properties. In this talk, we will discuss this result and further developments which allowed us to identify objective criteria for the diagnosis ectatic diseases of the cornea, and design of advanced contact lenses for higher order aberration correction.

** JR. COLLOQUIUM
**TITLE: Optimal control techniques applied to management of natural resource models

SPEAKER: Suzanne Lenhart, University of Tennessee and National Institute for Mathematical and Biological Synthesis (NIMBioS)

TIME: 3:40 PM-4:35 PM

ROOM: Ayres 405

Optimal control techniques have been used to investigate management strategies in a variety of models for natural resources. Two applications involving FISH and FIRE will be discussed, incorporating the economic impacts. Harvesting of fishery stock has led to habitat damage. We present a model with spatiotemporal dynamics of a fish stock and its habitat. Techniques of optimal control of PDEs are used to investigate the harvest rates that maximize the discounted value while minimizing the negative effects on the habitat. The number of large-scale, high-severity forest fires occurring is increasing, as is the cost to suppress these fires. We incorporate the stochasticity of the time of a forest fire into our model and explore the trade-offs between prevention management spending and suppression spending.

**Friday, 3/29**

**MATH BIOLOGY SEMINAR**

SPEAKERS: Nathan Pollesch (U.S. Environmental Protection Agency) and Megan Rua (Wright State University)

TIME: 11:15 AM-12:05 PM

ROOM: Ayres 401

In this week's Math Biology seminar, we will reconnect with UTK Math alumnus Dr. Nathan Pollesch and former NIMBioS Postdoctoral Research Fellow Dr. Megan Rua. We will have an informal panel discussion with them via Zoom video conferencing about career trajectories and preparing for what comes after the graduate school/post doc life. If you are interested in being added to the Math Biology Seminar 'BaseCamp' site to receive notices and seminar materials directly, please contact Judy Day at judyday@utk.edu.

**COLLOQUIUM
**TITLE: Lorentzian polynomials

SPEAKER: June Huh, Princeton University

TIME: 3:35 PM-4:35 PM

ROOM: Ayres 405

I will give a gentle overview of my work with Petter Brändén on Lorentzian polynomials (https://arxiv.org/abs/1902.03719), which link continuous convex analysis and discrete convex analysis via tropical geometry. The class contains homogeneous stable polynomials, volume polynomials of convex bodies and projective varieties, as well as some partition functions considered in statistical physics. No specific background will be needed to enjoy the talk.

*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:**

Mar. 18, 2019 (Spring break)

Winter Break