Seminars and Colloquiums
for the week of March 25, 2019
Thomas Weighill, University of Tennessee
David Talmy, University of Tennessee (Microbiology)
Joan Lind, University of Tennessee
Mahir Demir, University of Tennessee
Ram Iyer, Texas Tech University
Suzanne Lenhart, University of Tennessee and National Institute for Mathematical and Biological Synthesis (NIMBioS)
Nathan Pollesch (U.S. Environmental Protection Agency) and Megan Rua (Wright State University)
June Huh, Princeton University
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).
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.
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.
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.
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.
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 firstname.lastname@example.org.
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 email@example.com
Mar. 18, 2019 (Spring break)