Seminars and Colloquia Schedule

Numerical methods for highly oscillatory dynamical systems using multiscale structure

Series
Applied and Computational Mathematics Seminar
Time
Monday, September 9, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Seong Jun Kim – GT Math
The main aim of this talk is to design efficient and novel numerical algorithms for highly oscillatory dynamical systems with multiple time scales. Classical numerical methods for such problems need temporal resolution to resolve the finest scale and become very inefficient when the longer time intervals are of interest. In order to accelerate computations and improve the long time accuracy of numerical schemes, we take advantage of various multiscale structures established from a separation of time scales. The framework of the heterogeneous multiscale method (HMM) will be considered as a general strategy both for the design and for the analysis of multiscale methods.(Keywords: Multiscale oscillatory dynamical systems, numerical averaging methods.)

Complete nonnegatively curved planes

Series
Geometry Topology Seminar
Time
Monday, September 9, 2013 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Igor Belegradek – Georgia Tech
It is known that any complete nonnegatively curved metric on the plane is conformally equivalent to the Euclidean metric. In the first half of the talk I shall explain that the conformal factors that show up correspond precisely to smooth subharmonic functions of minimal growth. The proof is function-theoretic. This characterization of conformal factors can be used to study connectedness properties of the space of complete nonnegatively curved metrics on the plane. A typical result is that the space of metrics cannot be separated by a finite dimensional subspace. The proofs use infinite-dimensional topology and dimension theory. This is a joint work with Jing Hu.

Noetherianity for infinite-dimensional toric ideals

Series
Algebra Seminar
Time
Monday, September 9, 2013 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Robert Krone – Georgia Tech –
Given a family of ideals which are symmetric under some group action on the variables, a natural question to ask is whether the generating set stabilizes up to symmetry as the number of variables tends to infinity. We answer this in the affirmative for a broad class of toric ideals, settling several open questions in work by Aschenbrenner-Hillar, Hillar-Sullivant, and Hillar-Martin del Campo. The proof is largely combinatorial, making use of matchings on bipartite graphs, and well-partial orders.

Teaching opportunities at Tech

Series
Professional Development Seminar
Time
Tuesday, September 10, 2013 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Christine Heitsch – Georgia Tech
A panel discussion with Luz Vela-Arevalo, Klara Grodzinsky, Chris Heil, and Dia Sekayi, CETL's Assistant Director for Education.

Towards the directed cycle double cover conjecture

Series
Graph Theory Seminar
Time
Tuesday, September 10, 2013 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Martin Loebl – Charles University
We prove the dcdc conjecture in a class of lean fork graphs, argue that this class is substantial and show a path towards the complete solution. Joint work with Andrea Jimenez.

Potential Theory in the Complex Plane and Polynomials

Series
Research Horizons Seminar
Time
Wednesday, September 11, 2013 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Doron Lubinsky – School of Mathematics
We'll look at some of the basics of potential theory in the complex plane. We'll also discuss how potential theory may be used in studying zeros of polynomials and approximation theory.

Scaling limits for the exit problem for conditioned diffusions via Hamilton-Jacobi equations

Series
Stochastics Seminar
Time
Thursday, September 12, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Yuri Bakhtin – GaTech
The classical Freidlin--Wentzell theory on small random perturbations of dynamical systems operates mainly at the level of large deviation estimates. In many cases it would be interesting and useful to supplement those with central limit theorem type results. We are able to describe a class of situations where a Gaussian scaling limit for the exit point of conditioned diffusions holds. Our main tools are Doob's h-transform and new gradient estimates for Hamilton--Jacobi equations. Joint work with Andrzej Swiech.

Why the brain wiring's might use more than one decay scale

Series
Mathematical Biology Seminar
Time
Thursday, September 12, 2013 - 16:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
R.Stoop – Inst. of Neuroinformatics, ETH, Zurich
We study to what extent cortical columns with their particular wiring, could boost neural computation. Upon a vast survey of columnar networks performing various real-world cognitive tasks, we detect no signs of the expected enhancement. It is on a mesoscopic?intercolumnar?scale that the wiring among the columns, largely irrespective of their inner organization, enhances the speed of information transfer and minimizes the total wiring length required to bind distributed columnar computations towards spatiotemporally coherent results. We suggest that brain efficiency may be related to a doubly fractal connectivity law, resulting in networks with efficiency properties beyond those by scale-free networks and we exhibit corroborating evidence for this suggestion. Despite the current emphasis on simpler, e.g., critical, networks, networks with more than one connectivity decay behavior may be the rule rather than the exception. Ref: Beyond Scale-Free Small-World Networks: Cortical Columns for Quick Brains Ralph Stoop, Victor Saase, Clemens Wagner, Britta Stoop, and Ruedi Stoop, PRL 108105 (2013)

Fourier PCA

Series
ACO Student Seminar
Time
Friday, September 13, 2013 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Ying Xiao – College of Computing, Georgia Tech
Fourier PCA is Principal Component Analysis of the covariance matrix obtained after reweighting a distribution with a random Fourier weighting. It can also be viewed as PCA applied to the Hessian matrix of functions of the characteristic function of the underlying distribution. Extending this technique to higher derivative tensors and developing a general tensor decomposition method, we derive the following results: (1) a polynomial-time algorithm for general independent component analysis (ICA), not requiring the component distributions to be discrete or distinguishable from Gaussian in their fourth moment (unlike in the previous work); (2) the first polynomial-time algorithm for underdetermined ICA, where the number of components can be arbitrarily higher than the dimension; (3) an alternative algorithm for learning mixtures of spherical Gaussians with linearly independent means. These results also hold in the presence of Gaussian noise.

James periodicity and the EHP sequence II

Series
Geometry Topology Working Seminar
Time
Friday, September 13, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Kirsten Wickelgren – Georgia Tech

Note this is a 1 hour seminar (not the usual 2 hours).

Allowing formal desuspensions of maps and objects takes the category of topological spaces to the category of spectra, where cohomology is naturally represented. The EHP spectral sequence encodes how far one can desuspend maps between spheres. It's among the most useful tools for computing homotopy groups of spheres. RP^infty has a cell structure with a cell in each dimension and with attaching maps of degrees ...020202... Note that this sequence is periodic. In fact, it is more than the degrees of these maps which are periodic and a map of Snaith relates this periodicity to the EHP sequence.We will develop the EHP sequence, James periodicity and the relationship between the two.

Affine unfoldings of convex polyhedra

Series
Combinatorics Seminar
Time
Friday, September 13, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Mohammad Ghomi – School of Mathematics, Georgia Tech
A well-known problem in geometry, which may be traced back to the Renaissance artist Albrecht Durer, is concerned with cutting a convex polyhedral surface along some spanning tree of its edges so that it may be isometrically embedded, or developed without overlaps, into the plane. We show that this is always possible after an affine transformation of the surface. In particular, unfoldability of a convex polyhedron does not depend on its combinatorial structure, which settles a problem of Croft, Falconer, and Guy. Among other techniques, the proof employs a topological characterization for embeddings among immersed planar disks.