**Seminars and Colloquiums**

for the week of October 28, 2019

for the week of October 28, 2019

*SPEAKERS*

Monday

Louis Gross, UTK

** Tuesday
**Jan Rosinski, UTK

Levi Sledd, Vanderbilt University

**Wednesday**

Tamara Riggs, UTK

**Friday**

Alexandre Freire, UTK

** Tea Time** - cancelled for this week

3:00 pm – 3:30 pm

Monday, Tuesday, & Wednesday

Room: Ayres 401

Hosted by:

Topics:

**Monday, October 28th**

**MATH BIOLOGY SEMINAR
**TITLE: Continuing overview of chaos in dynamical systems

SPEAKER: Louis Gross UTK

TIME: 10:10 AM

ROOM: Claxton 105

**Tuesday, October 29th**

STOCHASTICS/PROBABILITY SEMINAR

TITLE: Stochastic Dini's theorem with applications

SPEAKER: Jan Rosinski, UTK

TIME: 2:10 PM-3:25 PM

ROOM: Ayres 112

Abstract: Abstract: A stochastic version of Dini's theorem was found by Ito and Nisio. It provides a powerful tool to deduce the uniform convergence of stochastic processes from their pointwise convergence. Unfortunately, this tool fails in stronger than uniform modes of convergence, such as Lipschitz or phi-variation convergence, the latter mode being natural for processes processes with jumps. In this work we establish a stochastic version of Dini's theorem in a new framework that covers processes with jumps and strong modes of convergence. We apply these results to Levy driven stochastic differential equations.

**
TOPOLOGY/ GEOMETRY SEMINAR
**TITLE: Assouad-Nagata dimension of C'(1/6) groups

SPEAKER: Levi Sledd, Vanderbilt University

TIME: 11:10-12:25 PM

ROOM: Ayres 114

Abstract: Asymptotic dimension is a quasi-isometry invariant introduced by Gromov in 1993 as a large-scale analogue for Lebesgue covering dimension. A related notion of dimension is Assouad- Nagata asymptotic dimension (or equivalently for discrete spaces, Assouad-Nagata dimension), another quasi-isometry invariant which is bounded below by asymptotic dimension. Since their inception, these two notions of dimension have proven to be useful tools in geometric group the- ory. In 2010, Higes gave examples of countable abelian groups with finite asymptotic dimension and finite but greater Assouad-Nagata dimension. In this talk, we will show how this result can be generalized to finitely generated groups, as follows. We prove that any finitely generated (but not necessarily finitely presented) C(1/6) group has Assouad-Nagata dimension at most 2. Then we use this result to construct, for any n, k in N with n >= 3, a finitely generated group of asymptotic dimension n and Assouad-Nagata dimension n + k.

**Wednesday, October 30th**

**ANALYSIS SEMINAR**

TITLE: An exploration of Fourier eigenvalues and their multiplicities

SPEAKER: Tamara Riggs, UTK

TIME: 2:30 PM

ROOM: Ayres 113

Abstract: The discrete Fourier transform (DFT) of any size is known to have four eigenvalues: 1,-1, i, and -i. A proof of this result will be presented utilizing projection matrices defined in terms of the DFT. We will use these projections to further prove a result concerning the multiplicities of these eigenvalues, a problem that has interesting connections to Gauss sums.

**Friday, November 1st**

**COLLOQUIUM**

TITLE: STATIC STELLAR MODELS WITH COSMOLOGICAL CONSTANT

SPEAKER: Alexandre Freire, UTK

TIME: 3:35 PM

ROOM: Ayres 405

Abstract: I’ll describe the classical general-relativistic model for a star: interior, static solutions to Einstein’s equations with perfect fluid matter, joined to a vacuum solution outside of a compact set. Solutions have surprising (non-Newtonian) properties, such as a universal mass/radius bound. This problem has been studied in the rotationally symmetric case, and it is conjectured that all solutions have this symmetry. In recent work, we extend the classical results to the case of non-zero `cosmological constant’, allowing for non-euclidean (for example, hyperbolic) asymptotics. This is joint work with Ryan Unger.

*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 Dr. Christopher Strickland, cstric12@utk.edu *

**Past notices:**