Un of Tenn | Math Department

Seminars and Colloquiums
for the week of February 25, 2013

Speakers:

Dr. Luis Finotti, Monday
Dr. Chris Symons, Oak Ridge National Laboratory, Monday
Mr. James Sunkes, Wednesday
Mr. Kyle Austin, Thursday
Prof. Vaughan Jones, Vanderbilt University, Thursday
Prof. Juan Restrepo, University of Arizona, Friday

*** Tea Time this week will be Monday - Wednesday at 3:00 pm.
Hosted this week by Fernando Schwartz. Everyone is welcome! ***

MONDAY, FEBRUARY 25

ALGEBRA SEMINAR
TIME: 3:35 pm
ROOM: Ayres B004
SPEAKER: Dr. Luis Finotti
TITLE: On the ABC Conjecture, part II
ABSTRACT: S. Mochizuki has recently claimed to have prove the ABC Conjecture. This is a very strong conjecture, with numerous consequences in number theory. If correct, it would be the most important result in mathematics since the proof of the Poincaré Conjecture. In this series of talks we will motivate, state, give equivalent statements, prove/discuss consequences and study related problems to the ABC Conjecture. (We will not give Mochizuki's "proof", which is extremely technical and advanced.) At the very least, the first few talks should be accessible to all, including graduate students of other areas.

PROBABILITY SEMINAR
TIME: 3:35 – 4:25
ROOM: Ayres 122
SPEAKER: Dr. Chris Symons, Oak Ridge National Laboratory
TITLE: Large-Scale Graph-Based Learning in Noisy Domains
ABSTRACT: Statistical machine learning has demonstrated the potential to facilitate powerful analyses that that go well beyond human-constructed rule sets and heuristic decision processes. Some of the most promising results utilize newer methods for incorporating more information into the learning process, while maintaining valid assumptions that continue to support theoretical bounds on generalization error. Many of these newer methods are structure-based, in the sense that they use structure found in unlabeled data, alternate problem views, related learning tasks, etc. to uncover a better hypothesis space in which to search for an optimal model. In this talk, I will discuss some of these methods, and modifications thereof, through which we have made demonstrable progress using machine learning to solve real world problems at the Oak Ridge National Laboratory. In particular, I will focus on methods that use the graph Laplacian and how such methods can be scaled effectively and modified for noisy domains.

WEDNESDAY, FEBRUARY 27

ANALYSIS SEMINAR
TIME: 3:35 – 4:25
ROOM: Ayres 114
SPEAKER: Mr. James Sunkes
TITLE: The Fiber Dimension of Analytic Operators
ABSTRACT: In this talk, I will discuss the fiber dimension of an invariant subspace of an analytic operator. The main goal of the seminar is to prove a formula which shows that the fiber dimension is a limit which involves the dimension of the projections onto the orthogonal complements of T^{k}H. The results proven are largely be based on the work on Fang (from 2005). If time permits, we will show a connection between the Fiber Dimension and an algebraic quantity known as the Samuel multiplicity.

THURSDAY, FEBRUARY 28

TOPOLOGY SEMINAR
TIME: 9:40 – 10:30
ROOM: Ayres Hall B004
SPEAKER: Mr. Kyle Austin
TITLE: Svarc Milnor Lemma: A Proof By Definition – 2
ABSTRACT: The purpose of this presentation will be to prove the Svarc-Milnor lemma. I will be following a paper by N. Brodskiy, J. Dydak, and A. Mitra entitled "Svarc-Milnor Lemma: A Proof By Definition". The idea behind the paper is that certain group actions on Metric spaces induce metrics on the groups whose resulting coarse structure can be obtained from the action. Methods of geometric group theory and large scale geometry will be introduced.

DISTINGUISHED LECTURE IN MATHEMATICS
TIME: 3:35
ROOM: Ayres 405
SPEAKER: Prof. Vaughan Jones - Vanderbilt University
TITLE: The classification of low index subfactors
ABSTRACT: I will begin by explaining subfactors and their relations with low dimensional topolgy, physics and analysis. A subfactor N of M is like a subfield of a field in that it has a degree (or index) [M:N] which is in general a real number.

Subfactors of index less than or equal to four are classified by Coxeter-Dynkin diagrams as has been known since the 1980's. A new "exotic" subfactor of index (5+sqrt(13))/2 was discovered by Haagerup in the 1990's and recently a lot of progress has been made and all subfactors of index less than 5 have been classified. The classification is currently being pushed as far as 3+sqrt(5) where new phenomena are expected to occur. Certainly at index 6 the classification becomes infeasible.

The methods of classification are combinatorial in nature and involve some new structures in mathematics. A new construction method inspired by Conway's skein theory has proved useful, especially via a "jellyfish" algorithm which works in the reverse direction of usual skein theory.

Many people have been involved in the classification, notably Morrison, Peters, Snyder, Izumi, Bigelow, Penneys, Tener and the speaker.

Pizza will be served at 3:10 p.m. in Room 401.

FRIDAY, MARCH 1

COLLOQUIUM
TIME: 3:35 - 4:25
ROOM: Ayres 405
SPEAKER: Prof. Juan Restrepo - University of Arizona
TITLE: Mathematical Challenges in Climate Variability
ABSTRACT: A fundamental challenge in climate science is to make
sense of very limited and poorly constrained data. A notable problem in this realm is the question of whether global warming is an industrial era trend or not.

Even though many data gathering campaigns are taking place or are being planned, the very high dimensional state space of the system makes the prospects of climate variability analysis from data alone very tenuous, especially in the near term. The use of models and data, via data assimilation, is one of the strategies pursued to improve climate predictions and retrodictions. I will review some of the challenges with this process, cover some of our group's efforts to meet these.

Problems in which progress can be made by a combination of deterministic and statistical techniques are endemic in climate science and other geosciences. I will also enumerate a prioritized list of problems, which if addressed with careful mathematical treatment, will have a significant impact on climate variability and a variety of other geoscience problems.

Refreshments will be available at 3:15 p.m. in Room 401.

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: