**Seminars and Colloquiums**

for the week of January 22, 2018

for the week of January 22, 2018

*SPEAKERS*

*Monday*

Logan Higginbotham, University of Tennessee

*Tuesday*

Ryan Unger, University of Tennessee

*Wednesday*

Stefan Richter, University of Tennessee

Mustafa Elmas, University of Tennessee

*Thursday*

Avel GuÈnin-Carlut

Mike Frazier, University of Tennessee

James Murphy, Johns Hopkins University

Lan-Hsuan Huang, University of Connecticut

*Friday*

Lan-Hsuan Huang, University of Connecticut

*TEA TIME -
3:00 pm – 3:30 pm
Monday, Tuesday, & Wednesday: Ayres 401
Hosted by: Hannah Thompson and Jesse Sautel
*

**Monday, January 22nd**

**TOPOLOGY/ GEOMETRY SEMINAR**

TITLE: Asymptotic Filtered Colimits and Coarse Embeddability into Separable Hilbert Spaces

SPEAKER: Logan Higginbotham, University of Tennessee

TIME: 2:30 PM-3:20 PM

ROOM: Ayres 112

We begin the talk with defining the asymptotic filtered colimit of a certain collection of large scale spaces. This construction may be intuitively thought of as a "large scale pasting lemma".† We then investigate some coarse invariants†that are preserved by the construction. In particular, the asymptotic filtered colimit of large scale spaces that coarsely embed into a separable Hilbert space (with additional conditions) coarsely embedds into a separable Hilbert space.

**Tuesday, January 23rd**

**GENERAL RELATIVITY SEMINAR**

TITLE: A positive mass theorem for locally conformally flat Riemannian manifolds

SPEAKER: Ryan Unger, University of Tennessee

TIME: 5:00 PM-6:00 PM

ROOM: Ayres 113

By combining the S^n conformal embedding method of Kuiper and the Cheng-Yau gradient estimate, Schoen and Yau proved in 1988 a type of positive mass theorem for locally conformally flat manifolds in dimensions 7 and higher. (Just enough to solve the Yamabe problem!) Here we discuss the main ideas of the proof, which has a strong potential theoretic flavor.

**Wednesday, January 24th**

**ANALYSIS SEMINAR**

TITLE: Pick kernels and radially weighted Besov spaces, continuation

SPEAKER: Stefan Richter, University of Tennessee

TIME: 2:30 PM-3:20 PM

ROOM: Ayres 113

Let m be a radial measure on the unit ball of C^d, let Rf denote the radial derivative of the analytic function f. For a positive integer N the N-th order weighted Besov space consists of all analytic functions f such that R^N f is square-integrable with respect to m.

We prove a number of results about multipliers and invariant subspaces of such weighted Besov spaces. Some of the results are new even in the case where m is Lebesgue measure.

**COMPUTATIONAL and APPLIED MATHEMATICS (CAM) SEMINAR**

TITLE: A Two Pathways Model for Chemotactic signaling in Azospirillum Brasilense and Tracking and Analysis Software for Free-Swimming Bacteria

SPEAKER: Mustafa Elmas, University of Tennessee

TIME: 3:35 PM-4:35 PM

ROOM: Ayres 113

Chemotaxis is a mechanism by which bacteria efficiently and rapidly respond to changes in the chemical composition of their environment, moving towards chemically favorable environments and away from unfavorable ones. The regulation of chemotaxis in bacteria is achieved by a network of interaction proteins constituting a chemotaxis signal transduction pathway. It has been found recently that most motile bacteria have two or more (Che) systems, whereas the model organism Escherichia coli possesses a single chemotaxis system. We present a novel mathematical model that can be used to understand the properties of biological signaling pathways in Azospirillum Brasilense and derive hypotheses that can be further tested experimentally. This project is joint work with Tanmoy Mukherjee, Dr. Vasilios Alexiades, and Dr. Gladys Alexandre.

We developed tracking software for free-swimming bacteria. The software was implemented in Matlab. The software reconstructs simultaneously the trajectories of all cell bodies by matching its center of mass from frame-to-frame, resulting in individual cell paths. From the cell trajectories, we computed statistic to measure multiple aspects of cell movement such as run average speed, maximum speed, minimum speed, average run time, frequency of reversal, average angle of reversal frequency, and mean square displacement of bacteria. All statistics are computed using custom MATLAB software. This project is joint work with Tanmoy Mukherjee, Lam Vo, Dr. Vasilios Alexiades, Dr. Tian Hong, and Dr. Gladys Alexandre.

**Thursday, January 25th**

**MATH BIOLOGY SEMINAR**

TITLE: Unsupervised learning: why roboticians like it simple

SPEAKER: Avel GuÈnin-Carlut

TIME: 11:10 AM-12:00 PM

ROOM: Hesler 427

**DIFFERENTIAL EQUATIONS SEMINAR**

TITLE: Fractional Laplacian Schrodinger equations

SPEAKER: Mike Frazier, University of Tennessee

TIME: 2:10 PM-3:10 PM

ROOM: Ayres 114

We consider a fractional Laplacian Schrodinger operator L, which is defined like a usual Schrodinger operator except with the fractional Laplacian in place of the standard Laplacian. Our emphasis is on finding the most general conditions on the potential that allow for the existence of solutions. We consider two problems: the inhomogeneous equation Lu = v on the domain, with u=0 on the complement of the domain, and the homogeneous equation Lu=0 on the domain, with u=1 on the complement of the domain. For the second problem u is called the gauge in the probability literature. In the first lecture we consider 2 approaches to the first problem, one via the Lax-Milgram Theorem, and one using Neumann series. We compare the solvability conditions and results arising from each approach.

**MATHEMATICAL DATA SCIENCE SEMINAR**

TITLE: Unsupervised Geometric Learning: Theory and Applications

SPEAKER: James Murphy, Johns Hopkins University

TIME: 3:30 PM-4:30 PM

ROOM: Ayres 405

Machine learning and data science are revolutionizing how humans gain knowledge. Algorithmic tools are making breakthroughs in virtually all scientific areas including computer vision, precision medicine, and geoscience. Despite their empirical successes, machine learning methods are often poorly understood theoretically. We present a mathematical framework for unsupervised learning of data based on geometry. By considering data-dependent metrics on high-dimensional and noisy data, intrinsically low-dimensional structures in the data are revealed. Our algorithms enjoy robust performance guarantees for accuracy and parameter dependence that surpass known results in the case that the intrinsic dimension of the data is small relative to the ambient dimension. In particular, our algorithms are provably robust to large amounts of noise. Our methods of proof combine percolation theory, manifold learning, and spectral graph analysis. Beyond performance guarantees, we present efficient implementations of our algorithms that scale quasilinearly in the number of datapoints, demonstrating the applicability of our methods to the ìbig data" regime. The proposed algorithms are validated on a variety of synthetic and real datasets, and applications to hyperspectral data and other remotely sensed images will be discussed at length. Time permitting, related analysis of ECG signal data for automatic detection of illness will be discussed.

**GEOMETRIC ANALYSIS SEMINAR**

TITLE: Recent progress on the positive mass theorem

SPEAKER: Lan-Hsuan Huang, University of Connecticut

TIME: 5:00 PM-6:00 PM

ROOM: Ayres 113

The positive mass theorem in general relativity asserts that the Arnowitt-Deser-Misner (ADM) mass of an asymptotically flat manifold with the dominant energy condition is nonnegative. Furthermore, if the ADM mass is zero, then the manifold is a slice of Minkowski spacetime. A very important special case, so-called the Riemannian positive mass theorem, was first proved by R. Schoen and S.T. Yau in the 80's. Later, E. Witten gave a different proof of the general case, under a topological condition that the manifold is spin. We will discuss our recent results that hold in greater generality and remove the spin condition.

**Friday, January 26th**

**COLLOQUIUM**

TITLE: The shape of black holes

SPEAKER: Lan-Hsuan Huang, University of Connecticut

TIME: 3:30 PM-4:30 PM

ROOM: Ayres 405

The notion of black holes arise naturally in general relativity to describe a place in space with strong gravitation. We will give a light introduction to differential geometry and discuss the mathematical models for black holes.We will then present the classical Hawking black hole topology theorem, the connection to the positive mass theorem, and some recent progress.

*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:**