Seminars and Colloquia by Series

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).

Geometry of empirical distribution of optimal alignment

Series
Stochastics Seminar
Time
Thursday, April 7, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Heinrich Matzinger – Georgia Tech –
We consider two random sequences of equal length n and the alignments with gaps corresponding to their Longest Common Subsequences. These alignments are called optimal alignments. What are the properties of these alignments? What are the proportion of different aligned letter pairs? Are there concentration of measure properties for these proportions? We will see that the convex geometry of the asymptotic limit set of empirical distributions seen along alignments can determine the answer to the above questions.

Two-term spectral asymptotics for the Dirichlet Laplacian and its fractional powers

Series
Math Physics Seminar
Time
Wednesday, April 6, 2011 - 16:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Leander Geisinger – University of Stuttgart
We study the sum of the negative eigenvalues of the Dirichlet Laplace operatoron a bounded domain in the semiclassical limit. We give a new proof thatyields not only the Weyl term but also the second asymptotic term involvingthe surface area of the boundary of the domain.The proof is valid under weak smoothness assumptions on the boundary and theresult can be extended to non-local, non-smooth operators like fractionalpowers of the Dirichlet Laplacian.(This is joint work with Rupert L. Frank.)

Orthogonal Rational Functions and Rational Gauss-type Quadrature Rules

Series
Analysis Seminar
Time
Wednesday, April 6, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Karl Deckers – Georgia Tech
Consider a positive bounded Borel measure \mu with infinite supporton an interval [a,b], where -oo <= a < b <= +oo, and assume we have m distinctnodes fixed in advance anywhere on [a,b]. We then study the existence andconstruction of n-th rational Gauss-type quadrature formulas (0 <= m <= 2)that approximate int_{[a,b]} f d\mu. These are quadrature formulas with npositive weights and n distinct nodes in [a,b], so that the quadratureformula is exact in a (2n - m)-dimensional space of rational functions witharbitrary complex poles fixed in advance outside [a,b].

Duality in hypergeometric functions and representations of Lie algebras

Series
Research Horizons Seminar
Time
Wednesday, April 6, 2011 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Plamen Iliev – School of Mathematics - Georgia Institute of Technology

Please Note: Hosts: Amey Kaloti and Ricardo Restrepo

By means of examples, I will illustrate the connection between orthogonal hypergeometric polynomials which satisfy interesting spectral and self-dual properties and representations of Lie algebras.

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