Seminars and Colloquia by Series

Skewloops, quadrics, and curvature

Series
Geometry Topology Seminar
Time
Monday, March 14, 2011 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Bruce Solomon – Indiana University –
A smooth loop in 3-space is skew if it has no pair of parallel tangent lines. With M.~Ghomi, we proved some years ago that among surfaces with some positive Gauss curvature (i.e., local convexity) the absence of skewloops characterizes quadrics. The relationship between skewloops and negatively curved surfaces has proven harder to analyze, however. We report some recent progress on that problem, including evidence both for and against the possibility that the absence of skewloops characterizes quadricsamong surfaces with negative curvature.

Lecture series on the disjoint paths algorithm

Series
Graph Theory Seminar
Time
Monday, March 14, 2011 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiiles 168
Speaker
Paul Wollan – School of Mathematics, Georgia Tech and University of Rome
This lecture will conclude the series. In a climactic finish the speaker will prove the Unique Linkage Theorem, thereby completing the proof of correctness of the Disjoint Paths Algorithm.

Inversion of the Born Series in Optical Tomography

Series
Applied and Computational Mathematics Seminar
Time
Monday, March 14, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
John Schotland – University of Michigan, Ann Arbor
The inverse problem of optical tomography consists of recovering thespatially-varying absorption of a highly-scattering medium from boundarymeasurements. In this talk we will discuss direct reconstruction methods forthis problem that are based on inversion of the Born series. In previouswork we have utilized such series expansions as tools to develop fast imagereconstruction algorithms. Here we characterize their convergence, stabilityand approximation error. Analogous results for the Calderon problem ofreconstructing the conductivity in electrical impedance tomography will alsobe presented.

Liquid-crystals are intermediate phases between solid and liquid states

Series
CDSNS Colloquium
Time
Monday, March 14, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Weishi Liu – University of Kansas –
They may flow like fluids but under constraints of mechanical energies from their crystal aspects. As a result, they exhibit very rich phenomena that grant them tremendous applications in modern technology. Based on works of Oseen, Z\"ocher, Frank and others, a continuum theory (not most general but satisfactory to a great extent) for liquid-crystals was formulated by Ericksen and Leslie in 1960s. We will first give a brief introduction to this classical theory and then focus on various important special settings in both static and dynamic cases. These special flows are rather simple for classical fluids but are quite nonlinear for liquid-crystals. We are able to apply abstract theory of nonlinear dynamical systems upon revealing specific structures of the problems at hands.

Contact geometry and Heegaard Floer invariants for noncompact 3-manifolds

Series
Geometry Topology Seminar
Time
Friday, March 11, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Shea Vela-Vick – Columbia University
I plan to discuss a method for defining Heegaard Floer invariants for 3-manifolds. The construction is inspired by contact geometry and has several interesting immediate applications to the study of tight contact structures on noncompact 3-manifolds. In this talk, I'll focus on one basic examples and indicate how one defines a contact invariant which can be used to give an alternate proof of James Tripp's classification of tight, minimally twisting contact structures on the open solid torus. This is joint work with John B. Etnyre and Rumen Zarev.

Lorenz flow and random effect

Series
CDSNS Colloquium
Time
Friday, March 11, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Weiping Li – Oklahoma State University
In this talk, I will explain the correspondence between the Lorenz periodic solution and the topological knot in 3-space.The effect of small random perturbation on the Lorenz flow will lead to a certain nature order developed previously by Chow-Li-Liu-Zhou. This work provides an answer to an puzzle why the Lorenz periodics are only geometrically simple knots.

Coupling at infinity

Series
Stochastics Seminar
Time
Thursday, March 10, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Jonathan Mattingly – Duke University, Mathematics Department
I will discuss how the idea of coupling at time infinity is equivalent to unique ergodicity of a markov process. In general, the coupling will be a kind of "asymptotic Wasserstein" coupling. I will draw examples from SDEs with memory and SPDEs. The fact that both are infinite dimensional markov processes is no coincidence.

Cantor Boundary Behavior of Analytic Functions

Series
Analysis Seminar
Time
Thursday, March 10, 2011 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ka-Sing Lau – Hong Kong Chinese University
There is a large literature to study the behavior of the image curves f(\partial {\mathbb D}) of analytic functions f on the unit disc {\mathbb D}. Our interest is on the class of analytic functions f for which the image curves f(\partial {\mathbb D}) form infinitely many (fractal) loops. We formulated this as the Cantor boundary behavior (CBB). We develop a general theory of this property in connection with the analytic topology, the distribution of the zeros of f'(z) and the mean growth rate of f'(z) near the boundary. Among the many examples, we showed that the lacunary series such as the complex Weierstrass functions have the CBB, also the Cauchy transform F(z) of the canonical Hausdorff measure on the Sierspinski gasket, which is the original motivation of this investigation raised by Strichartz.

First-Fit is Linear on (r+s)-free Posets

Series
Graph Theory Seminar
Time
Thursday, March 10, 2011 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Kevin Milans – University of South Carolina
First-Fit is an online algorithm that partitions the elements of a poset into chains. When presented with a new element x, First-Fit adds x to the first chain whose elements are all comparable to x. In 2004, Pemmaraju, Raman, and Varadarajan introduced the Column Construction Method to prove that when P is an interval order of width w, First-Fit partitions P into at most 10w chains. This bound was subsequently improved to 8w by Brightwell, Kierstead, and Trotter, and independently by Narayanaswamy and Babu. The poset r+s is the disjoint union of a chain of size r and a chain of size s. A poset is an interval order if and only if it does not contain 2+2 as an induced subposet. Bosek, Krawczyk, and Szczypka proved that if P is an (r+r)-free poset of width w, then First-Fit partitions P into at most 3rw^2 chains and asked whether the bound can be improved from O(w^2) to O(w). We answer this question in the affirmative. By generalizing the Column Construction Method, we show that if P is an (r+s)-free poset of width w, then First-Fit partitions P into at most 8(r-1)(s-1)w chains. This is joint work with Gwena\"el Joret.

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