### Seminars and Colloquiums for the week of September 24, 2018

SPEAKERS

Monday
Patrick McFaddin, University of South Carolina
Yu-Ting Chen, University of Tennessee
Tuesday
Theodora Bourni, University of Tennessee
Wednesday
Ken Stephenson, University of Tennessee
Thursday
Ibrahim Aslan, University of Tennessee
Julien Paupert, Arizona State University
Friday
David Elzgina, University of Tennessee
Julien Paupert, Arizona State University

TEA TIME
3:00 PM – 3:30 PM
Monday (A408), Tuesday (A406), & Wednesday (A404)
Rooms: Ayres fourth floor
Hosted by: Cara Sulyok and Jack Ryan
Topics: What is the Graduate Student Senate (GSS)?; how to get involved with the GSS; how does the GSS serve graduate students/resources and, as the Mathematics Department, what can the GSS do to better serve you?

Monday, 9/24

#### ALGEBRA SEMINAR

TITLE: Galois descent for exceptional collections on toric varieties
SPEAKER: Patrick McFaddin, University of South Carolina
TIME: 2:30 PM-3:20 PM (note change)
ROOM: Ayres 401 (note change)
Toric varieties (defined over the complex numbers) have proved to be extremely useful test objects for various algebro-geometric questions, as many computations of interest may be phrased entirely in terms of combinatorial data, e.g., fans, cones, polytopes. To study these varieties cohomologically, one considers their associated derived categories, which were described by Kawamata via exceptional collections. Such collections provide an analogue to (semi-)orthonormal bases of an inner-product space. The study of toric varieties defined over arbitrary fields (so-called "arithmetic toric varieties") has been taken up by a number of authors, although much less is known about their derived categories. In this talk, we will discuss an effective Galois descent result for such collections and provide applications to arithmetic toric varieties of low dimension or with a high degree of symmetry. This is joint work with Matthew Ballard and Alexander Duncan.

#### COLLOQUIUM

TITLE: Diffusions in spatial death-birth processes.
SPEAKER: Yu-Ting Chen, University of Tennessee
TIME: 3:35 PM-4:35 PM
ROOM: Ayres 405
In this talk, I will discuss the recent mathematical results for diffusion approximations of a generalized Moran process from the evolutionary game theory. The generalization incorporates arrangement of individuals by graphs and games among individuals. For these additional features, there has been consistent interest in using general spatial structure as a way to explain the ubiquitous game behavior in biological evolutions; the introduction of games leads to technical complications as basic as nonlinearity and asymmetry in the model. The diffusion approximations to be presented in this talk circumvent these complications. A simple diffusion process that holds universally on graphs with mild similarities to random regular graphs is obtained.

Tuesday, 9/25

#### MINIMAL SURFACES SEMINAR

TITLE: Colding-Minicozzi Paper 2-part 3
SPEAKER: Theodora Bourni, University of Tennessee
TIME: 4:00 PM-5:30 PM
ROOM: Ayres 121
We will show that an embedded minimal disk with bounded curvature can be decomposed into a portion with bounded area and a union of disjoint 1/2 stable domains (a notion that will be introduced). Moreover we will show that the total curvature over large balls can be bounded by the area.

Wednesday, 9/26

#### ANALYSIS SEMINAR

TITLE: Parameters for Affine Tori
SPEAKER: Ken Stephenson, University of Tennessee
TIME: 2:30 PM-3:20 PM
ROOM: Ayres 113
As described in my previous talk,

Theorem: Given any triangulation K of a topological torus, there exists a unique modulus w so that a conformal torus T of modulus w supports a circle packing P in the intrinsic (flat) metric and having the combinatorics of K. P is unique up to conformal automorphisms of T.

This is a type of "rigidity" result. Now, however, we may consider affine rather than flat tori. Each is associated with a pair (w,c) of complex numbers, w in the upper half space for the modulus, and complex c for the affine parameter. How much rigidity can we rescue? We have, for a given K, two real input parameters A and B, the scaling of the side-pairing maps, and 4 real output parameters, (w,c). These counts reflect a more general type of rigidity. Among many questions, What w we may obtain?

Thursday, 9/27

#### DIFFERENTIAL EQUATIONS SEMINAR

TITLE: Impulse model of Leptospirosis in Cattle
SPEAKER: Ibrahim Aslan, University of Tennessee
TIME: 2:10 PM-3:10 PM
ROOM: Ayres 113
As one of the most widespread zoonotic disease, Leptospirosis became endemic particularly in tropical and subtropical regions where the environment provides favorable conditions for propagation of the disease. It causes a large economic loss in the livestock industry. In this talk, we introduce an SVIR dynamical system of ordinary differential equations with impulse action of vaccination at certain times in order to investigate whether the disease can be controlled with current vaccine schedules. Some analytical and numerical results will be presented.

#### GEOMETRIC ANALYSIS SEMINAR

TITLE: Presentations for cusped arithmetic hyperbolic lattices
SPEAKER: Julien Paupert, Arizona State University
TIME: 4:00 PM-5:00 PM
ROOM: Ayres 121
We present a general method to compute a presentation for any cusped hyperbolic lattice $\Gamma$, applying a classical result of Macbeath to a suitable $\Gamma$-invariant horoball cover of the corresponding symmetric space. As applications we compute presentations for the Picard modular groups ${\rm PU}(2,1,\mathcal{O}_d)$ for $d=1,3,7$ and the quaternionic lattice ${\rm PU}(2,1,\mathcal{H})$ with entries in the Hurwitz integer ring $\mathcal{H}$. This is joint work with Alice Mark.

Friday, 9/28

#### MATH BIOLOGY SEMINAR

TITLE: Extreme Climate Events and the Ecological Dynamics of Plant-Herbivore Interactions
SPEAKER: David Elzgina, University of Tennessee
TIME: 10:10 AM-11:00 AM
ROOM: Ayres 401

#### COLLOQUIUM

TITLE: Constructing hyperbolic lattices
SPEAKER: Julien Paupert, Arizona State University
TIME: 3:35 PM-4:35 PM
ROOM: Ayres 405
A lattice in a Lie group is a discrete subgroup such that the quotient has finite volume (for example, it may be compact). Classical examples are Z^n in R^n and SL(2,Z) in SL(2,R). The latter is the prototype of a hyperbolic lattice, and has rich geometric and algebraic properties. Starting from this example, we will see how to generalize it two different directions, one more algebraic leading to arithmetic groups and the other more geometric, leading to reflection groups. We will then survey some of the main results and open questions in this area.

#### 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 AT utk DOT edu

Past notices:

Sept. 17, 2018

Sept. 10, 2018

Sept. 3, 2018

Aug. 27, 2018

2017-18

###### last updated: September 2018

Department of Mathematics
College of Arts & Sciences

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Phone: 865-974-2461 Fax: 865-974-6576 Email: math_info@utk.edu

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