Seminars and Colloquiums
for the week of April 16, 2012
Speaker:
Mr. Vajira Manathunga, Monday
Ms. Beth Lewis, Monday
Mr. Evan Lancaster and Mr. Tyler Massaro, Monday
Dr. Victor Perez-Abreu, Center for Research in Mathematics, CIMAT, Mexico, Monday
Dr. Conrad Plaut, Wednesday
Mr. Zachary Smith, Wednesday
Dr. Dmitry Pelinovsky of McMaster University, Thursday
Dr. Michael Dorff, Brigham Young University, Friday
Undergraduate Conference, Saturday
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. Judy Day.
Monday, April 16
TOPOLOGY SEMINAR
TIME: 2:30 - 3:20 p.m.
ROOM: Ayres Hall G004
SPEAKER: Mr. Vajira Manathunga
TITLE: Upper bounds on the number of linearly independent Vassiliev invariants - 2
ABSTRACT: After briefly introducing the concept of Vassiliev knot invariants, we will outline an argument of Chmutov and Duzhin giving an upper bound on the number of independent invariants in each degree.
ALGEBRA SEMINAR
TIME: 2:30 - 3:20 p.m.
ROOM: Ayres B004
SPEAKER: Ms. Beth Lewis
TITLE: The zero-divisor group of a commutative semigroup - III.
MATH BIOLOGY SEMINAR
TIME: 3:35 – 4:25 p.m.
ROOM: Ayres 113
SPEAKER: Mr. Evan Lancaster and Mr. Tyler Massaro
TITLE: Introduction of Agent-based Models (part 4)
PROBABILITY SEMINAR
TIME: 3:35 - 4:25 p.m.
ROOM: Ayres 122
SPEAKER: Dr. Victor Perez-Abreu, Center for Research in Mathematics, CIMAT, Mexico
TITLE: Free Probability, Random Matrices and Infinite Divisibility. Part II: Random Matrices and Eigenvalues Processes
ABSTRACT: A review of the spectrum of large dimensional matrix processes is presented as well as some applications. We will then consider the Dyson-Brownian process of eigenvalues, presenting law of large numbers and central limit theorems for the traces processes of the matrix-valued Brownian motion.
Wednesday, April 18
TOPOLOGY SEMINAR
TIME: 2:30 - 3:20 p.m.
ROOM: Ayres Hall G004
SPEAKER: Professor Conrad Plaut
TITLE: Discrete Homotopies and the Fundamental Group
ABSTRACT: Discrete homotopies were introduced by Valera Berestovskii and me as a way to define generalized fundamental groups for locally bad spaces. In this talk I will discuss a more geometric application that is joint work with Jay Wilkins: generalizing and strengthening a theorem of Gromov about generators and relators of the fundamental group in a compact Riemannian manifold. I'll give all of the background needed; the theorem is proved in the setting of compact geodesic spaces (no differential geometry needed!), and will be accessible to anyone who knows what metric spaces and the fundamental group are. Background will include the Gromov-Hausdorff metric and Gromov's precompactness theorem, which is a beautiful generalization of the basic fact that a metric space is compact if and only if it is complete and totally bounded. As an application I'll show that in any Gromov-Hausdorff precompact collection of compact metric spaces with a global bound on the number of "short loops", there are at most finitely many possible fundamental groups. This generalizes finiteness theorems of Michael Anderson, Shen-Wei, and Sormani-Wei.
ANALYSIS SEMINAR
TIME: 3;35 - p.m.
ROOM: Ayres Hall 112
SPEAKER: Mr. Zachary Smith
TITLE: A Continuous Version of H^1-BMO duality on the Bidisc
ABSTRACT: The duality of H^1 and BMO is well known in 1 dimension. One might expect that this immediately lifts to 2 dimensions through similar techniques; unfortunately what one expects to be the analogy of BMO does not work. In this talk we will present a paper of Chang and Fefferman which constructs the right space "BMO" on the bidisc and then prove it is the dual to H^1.
Thursday, April 19
COLLOQUIUM
TIME: 2:35 – 3:35 p.m.
ROOM: Ayres Hall 405
SPEAKER: Dr. Dmitry Pelinovsky of McMaster University
TITLE: Bifurcations of asymmetric vortices in symmetric harmonic potentials
ABSTRACT: We show that, under the effect of rotation, symmetric vortices located at the center of a two-dimensional harmonic potential are subject to a pitchfork bifurcation with radial symmetry. This bifurcation leads to the family of asymmetric vortices, which precess constantly along an orbit enclosing the center of symmetry. The radius of the orbit depends monotonically on the difference between the rotation frequency and the eigenfrequency of negative Krein signature associated with the symmetric vortex. We show that both symmetric and asymmetric vortices are spectrally and orbitally stable with respect to small time-dependent perturbations for rotation frequencies exceeding the bifurcation eigenfrequency.
At the same time, the symmetric vortex is a local minimizer of energy for supercritical rotation frequencies, whereas the asymmetric vortex corresponds to a saddle point of energy. For subcritical rotation frequencies, the symmetric vortex is a saddle point of the energy.
This is a joint work with P. Kevrekidis (University of Massachusetts)
Refreshments will be available in Ayres 401 at 3:15 p.m.
Friday, April 20
JR COLLOQUIUM (in conjunction with
Annual Undergraduate Mathematics Conference)
TIME: 3:35 – 4:35 pm
ROOM: Ayres 405
SPEAKER: Dr. Michael Dorff, Brigham Young University
TITLE: "Toy Story 3", the "real" Iron Man Suit, and advising the President of the United States
ABSTRACT: Have you ever been asked "What can you do with a degree in math?" Besides
teaching, many people are clueless on what you can do with strong math skills. For the past three years, I have been hosting a "Careers in Mathematics" seminar and inviting mathematicians to talk about how they use math in their careers from research scientist at Pixar Animation Studios to operations research analyst at the Pentagon in Washington DC. In this talk, we will present some highlights from these mathematicians and their careers.
Dr. Dorff will also be giving a talk at the Undergraduate Math Conference on Saturday, 4/21. This will be in the Shiloh Room of the University Center. See www.math.utk.edu/UGConf/ for more details.
Pizza will be available at 3:15 p.m.
Saturday, April 21
UNDERGRADUATE MATH CONFERENCE
TIME: 9:50 - 10:50 a.m.
ROOM: Shiloh Room, UC
SPEAKER: Dr. Michael Dorff of Brigham Young University
TITLE: Shortest paths, soap films, and mathematics
ABSTRACT: In high school geometry we learn that the shortest path between two points
is a line. In this talk we will explore this idea in several different settings. First, we will apply this idea to finding the shortest path connecting four points. Then we will move this idea up a dimension and
look at a few equivalent ideas in terms of surfaces in 3-dimensional space. Surprisingly, these first two settings are connected through soap films that result when a wire frame is dipped into soap solution. We will use a hands-on approach to look at the geometry of some specific soap films or "minimal surfaces".
This will be in the Shiloh Room of the University Center. See www.math.utk.edu/UGConf/ for more details.
Past notices:
March 19, 2012 - spring break
winter break
Seminars from 2010-2011 academic year
Seminars from 2009-2010 academic year
Seminars from 2008-2009 academic year
Seminars from 2007-2008 academic year
Seminars from 2006-2007 academic year