Seminars and Colloquia by Series

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

Please Note: 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

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.

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

Please Note: 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

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.

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.

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.

Southeast Geometry Seminar

Series
Other Talks
Time
Sunday, April 10, 2011 - 09:00 for 8 hours (full day)
Location
Emory University
Speaker
Southeast Geometry Seminar – Emory University
The Southeast Geometry Seminar is a series of semiannual one-day events focusing on geometric analysis. These events are hosted in rotation by the following institutions: The University of Alabama at Birmingham;  The Georgia Institute of Technology;  Emory University;  The University of Tennessee Knoxville.  The following five speakers will give presentations on topics that include geometric analysis, and related fields, such as partial differential equations, general relativity, and geometric topology. Borin Rubin (Louisiana State Univ);  Joseph Fu (Univ of Georgia);  Paul Yang (Princeton U);  Robert Gulliver (Univ of Minnesota);  Ken Stephenson (U of Tennessee).   

Spaces of nonnegatively curved metrics II

Series
Geometry Topology Working Seminar
Time
Friday, April 8, 2011 - 14:05 for 2 hours
Location
Skiles 269
Speaker
Igor Belegradek – Georgia Tech
I will prove contractibility of the space of nonnegatively curved metrics on the 2-sphere via the uniformization, discuss difficulties of extending the result to metrics on the plane, and then discuss similar problems in higher dimensions.

Metropolis Light Transport and Spherical Harmonics in Computer Graphics Rendering

Series
SIAM Student Seminar
Time
Friday, April 8, 2011 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 246
Speaker
Nathan Parrish – School of Electrical and Computer Engineering, Georgia Tech
The discussion will focus on some recent advances in improving performance of rendering 3D scenes. First, a Monte Carlo method based upon the Metropolis algorithm is described. Then a method of using spherical harmonics to generate vectors and matrices which allow efficient high-quality rendering in real time will be described. Finally, a discussion will be made of possible future areas for improving the efficiency of such algorithms.

Research in Mathematics Educational Technology - Current Trends and Future Demands

Series
Other Talks
Time
Friday, April 8, 2011 - 10:30 for 1 hour (actually 50 minutes)
Location
CEISMC, 760 Spring St.
Speaker
Robert Ronau and Christopher Rakes – University of Louisville and Institue for Education Sciences
This systematic review of mathematics educational technology literature identified 1356 manuscripts addressing the integration of educational technology into mathematics instruction. The manuscripts were analyzed using three frameworks (research design, teacher knowledge, and TPACK) and four supplementary lenses (Data sources, outcomes, NCTM Principles, and NCTM Standards) to produce a database to support future research syntheses and meta-analyses. Preliminary analyses of student and teacher outcomes (i.e., knowledge, cognition, affect, and performance) suggest that graphing calculator and dynamic geometry technologies have been abundantly studied, but the strength of the evidence measures (i.e., validity and reliability) may be lacking. More specifically, research on mathematics educational technology appears at first glance to be ubiquitous, the usefulness of this research to practitioners and researchers is limited by lack of attention to research design and validity, reliability, and threats to validity (Rakes et al., 2011). Additionally, much of the research appears to be unorganized, with topics such as graphing calculators studied often, while other topics such as virtual manipulatives understudied (Ronau et al., 2010).

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