Definition of homotopy groups, homotopy theory of CW complexes, Huriewich theorem and Whitehead's theorem, Eilenberg-Maclane spaces, fibration and cofibration sequences, Postnikov towers, and obstruction theory. Prerequisite: MATH 7800.

Seminars

Jeffrey Meier (U Texas) - Distinguishing topologically and smoothly doubly slice knots

The purpose of this talk is to show the existence of an infinite family of

smoothly slice knots that are topologically doubly slice, but not smoothly

doubly slice. After outlining what is known about doubly slice knots, I

will present some sufficient conditions for a knot to be topologically

doubly slice, and show how the knots in question satisfy these criteria.

Then, I will outline how the correction terms coming from Heegaard Floer

homology can be used to obstruct these knots from being smoothly doubly

slice. Along the way, we will encounter some very interesting open

questions related to the study of doubly slice knots.

Tea Time

Operator Theory Seminar

Kerchof Hall 326

Speaker: Hannes Thiel, University of Munster

Title: The generator problem for C*-algebras

The generator problem asks to determine for a given C*-algebra the minimal number of generators, i.e., elements that are not contained in a proper C*-subalgebra. It is conjectured that every separable, simple C*-algebra is generated by a single element. The generator problem was originally asked for von Neumann algebras, and Kadison included it as Nr. 14 of his famous list of 20 “Problems on von Neumann algebras”. The general problem is still open, most notably for the free group factors.

With Wilhelm Winter, we proved that every a unital, separable C*-algebra is generated by a single element if it tensorially absorbs the Jiang-Su algebra. This generalized most previous results about the generator problem for C*-algebras.

In a different approach to the generator problem, we define a notion of `generator rank', in analogy to the real rank. Instead of asking if a certain C*-algebra A is generated by k elements, the generator rank records whether the generating k-tuples of A are dense. It turns out that this invariant has good permanence properties, for instance it passes to inductive limits. It follows that every AF-algebra is singly generated, and even more the set of generators is generic (a dense G_delta-set).

Homepage: www.people.virginia.edu/~des5e/sotoa/sotoa.html

Add to Google CalendarMath Physics Seminar

Kerchof Hall 326

Speaker: Rajinder Mavi (UVa)

Title: Dynamics in many body quantum systems (II)

Abstract: See talk (I) in the series. http://pi.math.virginia.edu/mathphys/

Amber Puha (CSU San Marcos) - An Unconventional Functional Central Limit Theorem for the Queue Length Process in a Shortest Remaining Processing Time Queue

http://public.csusm.edu/apuha/

In a shortest remaining processing time (SRPT) queue, the job that requires the least amount of processing time is preemptively served first. One effect of this is that the queue length is small in comparison to the total amount or work in the system (measured in units of processing time). In fact, it is minimized so well that the sequence of queue length processes associated with a sequence of SRPT queues rescaled with standard functional central limit theorem scaling and satisfying standard heavy traffic conditions converges in distribution to the process that is identically equal to zero. This happens despite the fact that under this same regime the rescaled workload processes converge to a non-degenerate reflected Brownian motion. In particular, the queue length process is of smaller order magnitude than the workload process. In the case of processing time distributions that satisfy a rapid variation condition, we implement an alternative, unconventional scaling that leads to a non-trivial limit for the queue length process. This result quantities this order of magnitude difference between queue length and workload processes. We illustrate this result for Weibull processing time distributions.

Add to Google CalendarTBA - TBA

Tea Time

Jonathan Mattingly (Duke) - Stabilization by noise in 2 dimensions

http://fds.duke.edu/db/aas/math/faculty/jonm/

I will consider a large class of two dimensional vector fields with are unstable for some initial conditions. Yet, when noise is added the system becomes uniformly stable and possesses a unique invariant measure. It will be shown that the invariant measure possesses polynomial tails yet attracts all initial data uniformly, exponentially quickly. This is due to a strong equilibrium circulation. I will also show how the systems possesses what might be called "intermittent" behavior despite the noise being uniformly elliptic.

Both heuristic and rigorous arguments will be given. The rigorous arguments will be based on the construction of "sharp" Lyapunov functions adapted to the specific dynamics. This construction will likely be of independent interest.

Both heuristic and rigorous arguments will be given. The rigorous arguments will be based on the construction of "sharp" Lyapunov functions adapted to the specific dynamics. This construction will likely be of independent interest.

" class="addtocalendar" target="_new">Add to Google CalendarGalois Seminar

Clark Hall 102

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MATH 7840

Definition of homotopy groups, homotopy theory of CW complexes, Huriewich theorem and Whitehead's theorem, Eilenberg-Maclane spaces, fibration and cofibration sequences, Postnikov towers, and obstruction theory. Prerequisite: MATH 7800.