### Seminars and Colloquiums for the week of April 2, 2018

SPEAKERS

Monday
Andrew Starnes, University of Tennessee
Jerzy Dydak, University of Tennessee
Angie Cueto, Ohio State University
Tuesday
Kevin Sonnanburg, University of Tennessee
Wednesday
Michael Neilan, University of Pittsburgh
Thursday
Cara Sulyok and Tricia Phillips, University of Tennessee
Noel Walkington, Carnegie Mellon University
Friday
Gustavo Didier, Tulane University

TEA TIME
3:00 PM – 3:30 PM
Monday, Tuesday, & Wednesday
Room: Ayres 401
Hosted by: Cassie Micucci

Monday, April 2

DOCTORAL DEFENSE
Title: Investigating Hulls from the Loewner Equation
Speaker: Andrew Starnes, University of Tennessee
Time: 12:05 PM
Room: Ayres 406
His committee consists of:  Lind (Chair), Maroulas, Stephenson, and Zhou (BAS).

TOPOLOGY/ GEOMETRY SEMINAR
Title: Unifying large scale and small scale II
Speaker: Jerzy Dydak, University of Tennessee
Time: 2:30 PM-3:20 PM
Room: Ayres 112
A topology on a set $X$ is the same as a projection (i.e. an idempotent linear operator) $cl:2^X\to 2^X$ satisfying $A\subset cl(A)$ for all $A\subset X$. That's a good way to summarize Kuratowski's closure operator.

Basic geometry on a set $X$ is a dot product $\cdot:2^X\times 2^X\to 2^Y$. Its equivalent form is an orthogonality relation on subsets of $X$. The optimal case is if the orthogonality relation satisfies a variant of parallel-perpendicular decomposition from linear algebra.

We show that this concept unifies small scale (topology, proximity spaces, uniform spaces) and large scale (coarse spaces, large scale spaces).

In particular, Higson corona, Gromov boundary, \v Cech-Stone compactification, Samuel-Smirnov compactification, and Freudenthal compactification are unified.

ALGEBRA SEMINAR
Title: Anticanonical tropical del Pezzo cubic surfaces contain exactly 27 lines
Speaker: Angie Cueto, Ohio State University
Time: 3:35 PM-4:25 PM
Room: Ayres 112
Since the beginning of tropical geometry, a persistent challenge has been to emulate tropical versions of classical results in algebraic geometry.

The well-known statement "any smooth surface of degree three in P^3 contains exactly 27 lines" is known to be false tropically. Work of Vigeland from 2007 provides examples of cubic surfaces with infinitely many lines and gives a classification of tropical lines on general smooth tropical surfaces in TP^3.

In this talk I will explain how to correct this pathology by viewing the surface as a del Pezzo cubic and considering its embedding iin P^44 via its anticanonical bundle. The combinatorics of the root system of type E_6 and a tropical notion of convexity will play a central role in the construction. This is joint work in progress with Anand Deopurkar.

Tuesday, April 3

STOCHASTICS/PROBABILITY SEMINAR
Title: Extremal theory for long range dependent infinitely divisible processes
Time: 2:10 PM-3:20 PM
Room: Ayres 114
We prove limit theorems of an entirely new type for certain long memory regularly varying stationary infinitly divisible random processes. These theorems involve multiple phase transitions governed by how long the memory is. Apart from one regime, our results exhibit limits that are not among the classical extreme value distributions. Restricted to the one-dimensional case, the distributions we obtain interpolate, in the appropriate parameter range, the alpha-Frechet distribution and the skewed alpha-stable distribution. In general, the limit is a new family of stationary and self-similar random sup-measures with representations based on intersections of independent beta-stable regenerative sets.

DOCTORAL DEFENSE
Title: Blow-ups of Two-Convex, Type-I Mean Curvature Flow
Speaker: Kevin Sonnanburg, University of Tennessee
Time: 3:40 PM
Room: Ayres 404
His committee consists of:  Freire (chair), Denzler, Frazier, and Perfect (EPS).

Wednesday, April 4

COMPUTATIONAL and APPLIED MATHEMATICS (CAM) SEMINAR
Title: Rates of convergence in $W^2_p$-norm for the Monge–Ampère equation
Speaker: Michael Neilan, University of Pittsburgh
Time: 3:35 PM-4:35 PM
Room: Ayres 112
We develop discrete $W^2_p$-norm error estimates for the Oliker-Prussner method applied to the Monge-Amp\`ere equation. This is obtained by extending discrete Alexandroff estimates and showing that  the contact set of a nodal function contains information on its second order differences.  In addition, we show that the size of the complement of the contact set is controlled by the consistency of the method. Combining both observations, we show that the error estimate $\|u - u_h\|_{W^2_{p} \leq C \begin{cases} h^{1/p} \quad &\mbox{if p > d,} \\ h^{1/d} \big(\ln\left(\frac 1 h \right)\big)^{1/d} \quad &\mbox{if p \le d,} \end{cases}$ Numerical examples are given in two space dimensions and confirm that the estimate is sharp in several cases.  This is joint work with Wujun Zhang (Rutgers).

Thursday, April 5

MATH BIOLOGY SEMINAR
TITLE: Optimal management strategies to control local population growth or population spread may not be the same
SPEAKER: Cara Sulyok and Tricia Phillips, University of Tennessee
TIME: 11:10 AM – 12:00 PM
ROOM: Hesler 427

CAM-PDE JOINT SEMINAR
Title: A Tale of Two Fluids
Speaker: Noel Walkington, Carnegie Mellon University
Time: 2:10 PM-3:10 PM
Room: Ayres 114
The Ericksen--Leslie model of nematic liquid crystals and the Oldroyd--B fluid are continuum models of fluids containing elastic molecules. In each instance the momentum equation is coupled to an equation governing the evolution of the elastic components, and numerical schemes to simulate solutions of these equations frequently fail (the high Weissenberg number problem).

The equations for both systems can be derived from Hamiltonian's principle which reveals a subtle balance between inertia, transport, and dissipation. This talk will focus on the structural properties of these equations and the insight this provides into why naive numerical schemes may fail, and the ingredients required to construct stable and convergent numerical schemes.

Friday, April 6

COLLOQUIUM
Title: On multidimensional scaling
Speaker: Gustavo Didier, Tulane University
Time: 3:35 PM-4:35 PM
Room: Ayres 405
Scaling relationships have been found in a wide range of phenomena that includes coastal landscapes, hydrodynamic turbulence, the metabolic rates of animals and Internet traffic. In this talk, we will look into the so-named paradigm of scale invariance, which has been applied in the analysis of systems where no characteristic scale is present. Under scale invariance, a continuum of time scales contributes to the observed dynamics, and the analyst's focus is on identifying mechanisms that relate the scales, often in the form of scaling exponents. We will dedicate special attention to the role played by wavelets in the analysis of self-similar stochastic processes and visit recent contributions to the modeling of multidimensional scaling systems. This is joint work with Patrice Abry (CNRS and ENS-Lyon).

#### 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 colloquium AT math DOT utk DOT edu

Past notices:

3_26_18

3_19_18

3_12_18 (spring break)

3_5_18

2_26_18

2_19_18

2_12_18

2_5_18

1_22_18

1_16_18

12_11_17

12_04_17

11_27_17

11_20_17

11_13_17

11_6_17

10_30_17

10_23_17

10_16_17

10_9_17

10_2_17

9_25_17

9_18_17

9_11_17

9_4_17

8_28_17

###### last updated: May 2018

Department of Mathematics
College of Arts & Sciences

227 Ayres Hall. 1403 Circle Drive. Knoxville TN 37996-1320
Phone: 865-974-2461 Fax: 865-974-6576 Email: math_info@utk.edu