Seminars and Colloquia Schedule

A Parallel High-Order Accurate Finite Element Nonlinear Stokes Ice-Sheet Model and Benchmark Experiments

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 4, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Lili Ju – Department of Mathematics, University of South Carolina
In this talk, we present a parallel finite element implementation ontetrahedral  grids of the nonlinear three-dimensional nonlinear Stokes model for thedynamics and evolution of ice-sheets. Discretization is based on a high-orderaccurate  scheme using the Taylor-Hood element pair. Both no-slip and sliding boundary conditions at the ice-bedrock boundary are studied. In addition, effective solvers using preconditioning techniques for the saddle-point system resulting fromthe  discretization are discussed and implemented. We demonstrate throughestablished ice-sheet benchmark experiments that our finite element nonlinear Stokesmodel  performs at least as well as other published and established Stokes modelsin the  field, and the parallel solver is shown to be efficient, robust, and scalable.

The Degree Conjecture for torus knots

Series
Geometry Topology Seminar
Time
Monday, April 4, 2011 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Thao Vuong – Georgia Tech –
I will talk about some progress in proving the Degree Conjecture for torus knots. The conjecture states that the degree of a colored Jones polynomial colored by an irreducible representation of a simple Lie algebra g is locally a quadratic quasi-polynomial. This is joint work with Stavros Garoufalidis.

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

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.

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].

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.)

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.

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).

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.

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.

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).