Seminars and Colloquia Schedule

Modeling synthetic ciliated surfaces

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 11, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Alex Alexeev – Georgia Tech Mechanical Engineering
Biomimetic synthetic cilia can be effectively utilized for regulating microscale transport processes at interfaces. Using computer simulations, we examine how polymeric cilia can be harnessed to control the motion of microscopic particles suspended in a viscous fluid. The cilia are modeled as deformable, elastic filaments and our simulations capture the complex fluid-structure interactions among these filaments, channel walls and surrounding solution. We show that non-motile cilia that are tilted with respect to the surface can hydrodynamically direct solid particles towards channel walls, thereby, inducing their rapid deposition. When synthetic cilia are actuated by a sinusoidal force that is applied at the free ends, the beating cilia can either drive particles downwards toward the substrate or expelled particles into the fluid above the actuated cilial layer. This dynamic behavior can be regulated by changing the driving frequency. The findings uncover new routes for controlling the deposition of microscopic particles in microfluidic devices.

Generalized Kashaev and Turaev-Viro 3-manifold invariants

Series
Geometry Topology Seminar
Time
Monday, April 11, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Nathan Geer – Utah State University
I will consider two constructions which lead to information about the topology of a 3-manifold from one of its triangulation. The first construction is a modification of the Turaev-Viro invariant based on re-normalized 6j-symbols. These re-normalized 6j-symbols satisfy tetrahedral symmetries. The second construction is a generalization of Kashaev's invariant defined in his foundational paper where he first stated the volume conjecture. This generalization is based on symmetrizing 6j-symbols using *charges* developed by W. Neumann, S. Baseilhac, and R. Benedetti. In this talk, I will focus on the example of nilpotent representations of quantized sl(2) at a root of unity. In this example, the two constructions are equal and give rise to a kind of Homotopy Quantum Field Theory. This is joint work with R. Kashaev, B. Patureau and V. Turaev.

Limiting distributions of Betti numbers

Series
Algebra Seminar
Time
Monday, April 11, 2011 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Fernando Rodriguez-Villegas – University of Texas Austin
We will discuss several instances of sequences of complex manifolds X_n whose Betti numbers b_i(X_n) converge, when properly scaled, to a limiting distribution. The varieties considered have Betti numbers which are described in a combinatorial way making their study possible. Interesting examples include varieties X for which b_i(X) is the i-th coefficient of the reliability polynomial of an associated graph.

Towards Optimal Prediction of Chaotic Signals

Series
Math Physics Seminar
Time
Monday, April 11, 2011 - 15:00 for 1 hour (actually 50 minutes)
Location
Howey W505
Speaker
Divarkar Viswanath – Department of Mathematics, University of Michigan

Host: Predrag Cvitanovic, School of Physics

Suppose that x(t) is a signal generated by a chaotic system and that the signal has been recorded in the interval [0,T]. We ask: What is the largest value t_f such that the signal can be predicted in the interval (T,T+t_f] using the history of the signal and nothing more? We show that the answer to this question is contained in a major result of modern information theory proved by Wyner, Ziv, Ornstein, and Weiss. All current algorithms for predicting chaotic series assume that if a pattern of events in some interval in the past is similar to the pattern of events leading up to the present moment, the pattern from the past can be used to predict the chaotic signal. Unfortunately, this intuitively reasonable idea is fundamentally deficient and all current predictors fall well short of the Wyner-Ziv bound. We explain why the current methods are deficient and develop some ideas for deriving an optimal predictor. [This talk is based on joint work with X. Liang and K. Serkh]. To view and/or participate in the webinar from wherever you are, click on:EVO.caltech.edu/evoNext/koala.jnlp?meeting=MvM2Ml2M2tDvDn9n9nDe9v

Robert J. Lang - Origami Informal Folding Session

Series
Other Talks
Time
Monday, April 11, 2011 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 236
Speaker
Robert Lang – Alamo, California
Robert Lang is recognized as one of the foremost origami artists in the world as well as a pioneer in computational origami and the development of formal design algorithms for folding. Join him for an informal folding session before his presentation.

Club Math - From Flapping Birds to Space Telescopes - The Mathematics of Origami

Series
Other Talks
Time
Monday, April 11, 2011 - 17:00 for 1 hour (actually 50 minutes)
Location
Student Success Center, Clary Theater
Speaker
Robert Lang – Alamo, California

Robert J. Lang is recognized as one of the foremost origami artists in the world as well as a pioneer in computational origami and the development of formal design algorithms for folding. With a Ph.D. in Applied Physics from Caltech, he has, during the course of work at NASA/Jet Propulsion Laboratory, Spectra Diode Laboratories, and JDS Uniphase, authored or co-authored over 80 papers and 45 patents in lasers and optoelectronics as well as authoring, co-authoring, or editing 9 books and a CD-ROM on origami. He is a full-time artist and consultant on origami and its applications to engineering problems but moonlights in physics: from 2007-2010 as the Editor-in-Chief of the IEEE Journal of Quantum Electronics.

The last decade of this past century has been witness to a revolution in the development and application of mathematical techniques to origami, the centuries-old Japanese art of paper-folding. The techniques used in mathematical origami design range from the abstruse to the highly approachable. In this talk, I will describe how geometric concepts led to the solution of a broad class of origami folding problems – specifically, the problem of efficiently folding a shape with an arbitrary number and arrangement of flaps, and along the way, enabled origami designs of mind-blowing complexity and realism, some of which you’ll see, too. As often happens in mathematics, theory originally developed for its own sake has led to some surprising practical applications. The algorithms and theorems of origami design have shed light on long-standing mathematical questions and have solved practical engineering problems. I will discuss examples of how origami has enabled safer airbags, Brobdingnagian space telescopes, and more. From 3:30pm-4:30pm, Informal Folding Session will take place in Skiles 236

Navier-Stokes solver using Green's functions

Series
PDE Seminar
Time
Tuesday, April 12, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Prof. Divakar Viswanath – University of Michigan –
The incompressible Navier-Stokes equations provide an adequate physical model of a variety of physical phenomena. However, when the fluid speeds are not too low, the equations possess very complicated solutions making both mathematical theory and numerical work challenging. If time is discretized by treating the inertial term explicitly, each time step of the solver is a linear boundary value problem. We show how to solve this linear boundary value problem using Green's functions, assuming the channel and plane Couette geometries. The advantage of using Green's functions is that numerical derivatives are replaced by numerical integrals. However, the mere use of Green's functions does not result in a good solver. Numerical derivatives can come in through the nonlinear inertial term or the incompressibility constraint, even if the linear boundary value problem is tackled using Green's functions. In addition, the boundary value problem will be singularly perturbed at high Reynolds numbers. We show how to eliminate all numerical derivatives in the wall-normal direction and to cast the integrals into a form that is robust in the singularly perturbed limit. [This talk is based on joint work with Tobasco].

Towards a rigorous upper bound for a scaling problem in thermal convection

Series
Research Horizons Seminar
Time
Wednesday, April 13, 2011 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Maria Westdickenberg – Georgia Tech
Hot fluid expands. Expansion makes a fluid ``parcel'' lighter, causing it to rise. Cold, dense patches of fluid sink. And there we have the thermally induced motion of a fluid sitting on a hot plate... A longstanding open problem in applied analysis is the scaling of the Nusselt number (with respect to the Rayleigh number or, equivalently, system height) in thermal convection. The goal is a fundamental understanding of the effect of buoyancy-induced convection on heat transport in chaotic systems. The commonly held belief that the Nusselt number scales like (Ra)^(1/3) has eluded analytical proof for decades. We will describe the nature of the questions involved, the way that they can be framed (and reframed) mathematically, and the partial successes so far, including a recent preprint by Otto and Seis and a work in progress by the same authors

Weierstrass points on the Drinfeld modular curve X_0(\mathfrak{p})

Series
Algebra Seminar
Time
Wednesday, April 13, 2011 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Christelle Vincent – University of Wisconsin Madison
For q a power of a prime, consider the ring \mathbb{F}_q[T]. Due to the many similarities between \mathbb{F}_q[T] and the ring of integers \mathbb{Z}, we can define for \mathbb{F}_q[T] objects that are analogous to elliptic curves, modular forms, and modular curves. In particular, for \mathfrak{p} a prime ideal in \mathbb{F}_q[T], we can define the Drinfeld modular curve X_0(\mathfrak{p}), and study the reduction modulo \mathfrak{p} of its Weierstrass points, as is done in the classical case by Rohrlich, and Ahlgren and Ono. In this talk we will present some partial results in this direction, defining all necessary objects as we go. The first 20 minutes should be accessible to graduate students interested in number theory.

On the uniqueness sets in the Bergmann-Fock space

Series
Analysis Seminar
Time
Wednesday, April 13, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Mishko Mitkovski – School of Mathematics, Georgia Tech
It is well known that, via the Bargmann transform, the completeness problems for both Gabor systems in signal processing and coherent states in quantum mechanics are equivalent to the uniqueness set problem in the Bargmann-Fock space. We introduce an analog of the Beurling-Malliavin density to try to characterize these uniqueness sets and show that all sets with such density strictly less than one cannot be uniqueness sets. This is joint work with Brett Wick.

Noisy heteroclinic networks and sequential decision making.

Series
Math Physics Seminar
Time
Wednesday, April 13, 2011 - 16:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Yuri Bakhtin – Georgia Tech
I will talk about sequential decision making models based ondiffusion along heteroclinic networks of dynamical systems, i.e.,multiple saddle-type equilibrium points connected by heteroclinicorbits. The goal is to give a precise description of the asymptoticbehavior in the limit of vanishing noise.In particular, I will interpret exit times for stochastic dynamics asdecision making times and give a result on their asymptotic behavior.I will report on extensive data on decision making in no a priori biassetting obtained in a psychology experiment that I ran with JoshuaCorrell (University of Chicago),and compare the data with my theoretical results. I will also showthat the same kind of limiting distribution for exit times appears innonequilibrium models of statistical mechanics.

Sequential Minimum Energy Designs: From Nano Experiments to Global Optimization

Series
School of Mathematics Colloquium
Time
Thursday, April 14, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Jeff Wu – ISyE GATech
Motivated by a problem in the synthesis of nanowires, a sequential space filling design, called Sequential Minimum Energy Design (SMED), is proposed for exploring and searching for the optimal conditions in complex black-box functions. The SMED is a novel approach to generate designs that are model independent, can quickly carve out regions with no observable nanostructure morphology, allow for the exploration of complex response surfaces, and can be used for sequential experimentation. It can be viewed as a sequential design procedure for stochastic functions and a global optimization procedure for deterministic functions. The basic idea has been developed into an implementable algorithm, and guidelines for choosing the parameters of SMED have been proposed. Convergence of the algorithm has been established under certain regularity conditions. Performance of the algorithm has been studied using experimental data on nanowire synthesis as well as standard test functions.(Joint work with V. R. Joseph, Georgia Tech and T. Dasgupta, Harvard U.)

On Steinberg's Conjecture: 3-coloring certain planar graphs

Series
Graph Theory Seminar
Time
Thursday, April 14, 2011 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Peter Whalen – Math, GT
Steinberg's Conjecture states that any planar graph without cycles of length four or five is three colorable. Borodin, Glebov, Montassier, and Raspaud showed that planar graphs without cycles of length four, five, or seven are three colorable and Borodin and Glebov showed that planar graphs without five cycles or triangles at distance at most two apart are three colorable. We prove a statement similar to both of these results: that any planar graph with no cycles of length four through six or cycles of length seven with incident triangles distance exactly two apart are three colorable. Special thanks to Robin Thomas for substantial contributions in the development of the proof.

Rumor Processes on $\bb{N}$

Series
Stochastics Seminar
Time
Thursday, April 14, 2011 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
Fabio Machado – USP san paulo Brazil
We study four discrete time stochastic systems on $\bbN$ modelingprocesses of rumour spreading. The involved individuals can eitherhave an active ora passive role, speaking up or asking for the rumour. The appetite inspreading or hearing the rumour is represented by a set of randomvariables whose distributionsmay depend on the individuals. Our goal is to understand - based on those randomvariables distribution - whether the probability of having an infiniteset of individuals knowing the rumour is positive or not.

FoSoM Panel Discussion

Series
Other Talks
Time
Thursday, April 14, 2011 - 16:00 for 3 hours
Location
Skiles 005
Speaker
Math Alumni – School of Mathematics, Georgia Tech

Refreshments will be served at 3:30.

The Friends of the School of Mathematics present a panel discussion on "Non-Academic Careers: Opportunities and Challenges for Students" A distinguished panel of alumni of the School will present their views on opportunities and challenges for students as they prepare for non-academic careers. The panelists will also answer questions from the audience. Graduate students and undergraduate majors in Mathematics are especially encouraged to attend.

[Special Date] Iterative 3D/4D Cone Beam CT Reconstruction on GPU in Cancer Radiation Therapy

Series
Applied and Computational Mathematics Seminar
Time
Friday, April 15, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Xun Jia – University of California, San Diego, Department of Radiation Oncology
Cone Beam Computer tomography (CBCT) has been broadly applied incancer radiation therapy, mainly for positioning patients to align withtreatment radiation beams. As opposed to tomography reconstruction problemsfor diagnostic purposes, CBCT reconstruction in radiotherapy requires a highcomputational efficiency, since it is performed while patient is lying on acouch, waiting for the treatment. Moreover, the excessive radiation dosefrom frequent scans has become a clinical concern. It is therefore desirableto develop new techniques to reconstruct CBCT images from low dose scans. Inthis talk, I will present our recent work on an iterative low dose CBCTreconstruction technique via total variation regularization and tight frameregularization. It is found that 40~60 x-ray projections are sufficient toreconstruct a volumetric image with satisfactory quality in about 2min. Wehave also studied 4 dimensional CBCT (4DCBCT) reconstruction problem viatemporal non-local means (TNLM) and high quality 4DCBCT images can beobtained. Our algorithms have been fully implemented on a graphicsprocessing unit. Detailed implementation techniques will also be addressed.

Generic rectangulations and pattern-avoiding permutations

Series
Combinatorics Seminar
Time
Friday, April 15, 2011 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Nathan Reading – North Carolina State University
A rectangulation is a tiling of a rectangle by rectangles. The rectangulation is called generic if no four of its rectangles share a corner. We will consider the problem of counting generic rectangulations (with n rectangles) up to combinatorial equivalence. This talk will present and explain an initial step in the enumeration: the fact that generic rectangulations are in bijection with permutations that avoid a certain set of patterns. I'll give background information on rectangulations and pattern avoidance. Then I'll make the connection between generic rectangulations and pattern avoiding permutations, which draws on earlier work with Shirley Law on "diagonal" rectangulations. I'll also comment on two theories that led to this result and its proof: the lattice theory of the weak order on permutations and the theory of combinatorial Hopf algebras.

Atlanta Lecture Series in Combinatorics and Graph Theory III

Series
Other Talks
Time
Saturday, April 16, 2011 - 13:00 for 4 hours (half day)
Location
Klaus 1456
Speaker
Atlanta Lecture Series – School of Mathematics, Georgia Tech
Emory University, the Georgia Institute of Technology and Georgia State University will host a series of 9 mini-conferences from November, 2010 - April 2013. The conferences will stress a variety of areas and feature one prominent researcher giving 2 fifty minute lectures and 4 outstanding southern researchers each giving one fifty minute lecture. There will also be several 30 minute lecturers by young researchers or graduate students. The featured speaker is Maria Chudnovsky, Columbia University. The lectures begin at 1:00 PM Saturday, April 16 and end at noon on Sunday, April 17.