Seminars and Colloquia by Series

It pays to do the right thing: Incentive mechanisms for Societal Networks

Series
ACO Seminar
Time
Tuesday, March 15, 2011 - 16:30 for 1 hour (actually 50 minutes)
Location
Klaus 2443
Speaker
Balaji Prabhakar – Stanford University
Why did kamikaze pilots wear helmets? Why does glue not stick to the inside of the bottle? Why is lemonade made with artificial flavor but dishwashing liquid made with real lemons? How can I avoid traffic jams and be paid for it? While the first three are some of life's enduring questions, the fourth is the subject of a traffic decongestion research project at Stanford University. In this talk, I will briefly describe this project and, more generally, discuss incentive mechanisms for Societal Networks--- networks which are vital for a society's functioning; for example, transportation, energy, healthcare and waste management. I will talk about incentive mechanisms and experiments for reducing road congestion, pollution and energy use, and for improving "wellness" and good driving habits. Some salient themes are: using low-cost sensing technology to make societal networks much more efficient, using price as a signal to co-ordinate individual behavior, and intelligently "throwing money at problems".

Commutator Stories

Series
PDE Seminar
Time
Tuesday, March 15, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Prof. Peter Constantin – Department of Mathematics, University of Chicago –
I'll talk about a couple of commutator estimates and their role in the proofs of existence and uniqueness of solutions of active scalar equations with singular integral constitutive relations like the generalized SQG and Oldroyd B models.

Post-critically finite polynomials

Series
Algebra Seminar
Time
Monday, March 14, 2011 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Patrick Ingram – University of Waterloo
In classical holomorphic dynamics, rational self-maps of the Riemann sphere whose critical points all have finite forward orbit under iteration are known as post-critically finite (PCF) maps. A deep result of Thurston shows that if one excludes examples arising from endomorphisms of elliptic curves, then PCF maps are in some sense sparse, living in a countable union of zero-dimensional subvarieties of the appropriate moduli space (a result offering dubious comfort to number theorists, who tend to work over countable fields). We show that if one restricts attention to polynomials, then the set of PCF points in moduli space is actually a set of algebraic points of bounded height. This allows us to give an elementary proof of the appropriate part of Thurston's result, but it also provides an effective means of listing all PCF polynomials of a given degree, with coefficients of bounded algebraic degree (up to the appropriate sense of equivalence).

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.

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