Seminars and Colloquia by Series

Riemann-Cartan Geometry of Non-linear Dislocation Mechanics

Series
Math Physics Seminar
Time
Monday, April 9, 2012 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Arash Yavari – School of Civil and Environmental Engineering, GT
In this seminar we will show that the nonlinear mechanics of solids with distributed dislocations can be formulated as a nonlinear elasticity problem provided that the material manifold – where the body is stress-free − is chosen appropriately. Choosing a Weitzenböck manifold (a manifold with a flat and metric-compatible affine connection that has torsion) with torsion tensor identified with the given dislocation density tensor the body would be stress-free in the material manifold by construction. For classical nonlinear elastic solids in order to calculate stresses one needs to know the changes of the relative distances, i.e. a metric in the material manifold is needed. For distributed dislocations this metric is the metric compatible with the Weitzenböck connection. We will present exact solutions for the residual stress field of several distributed dislocation problems in incompressible nonlinear elastic solids using Cartan's method of moving frames. We will also discuss zero-stress dislocation distributions in nonlinear dislocation mechanics.

Measures of maximal entropy and integrated density of states for the discrete Schrodinger operator with Fibonacci potential

Series
CDSNS Colloquium
Time
Monday, April 9, 2012 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Dr. Anton Gorodetski – UC Irvine –
The discrete Schrodinger operator with Fibonacci potential is a central model in the study of electronic properties of one-dimensional quasicrystals. Certain renormalization procedure allows to reduce many questions on specral properties of this operator to the questions on dynamical properties of a so called trace map. It turnes out that the trace map is hyperbolic, and its measure of maximal entropy is directly related to the integrated density of states of the Fibonacci Hamiltonian. In particular, this provides the first example of an ergodic family of Schrodinger operators with singular density of states measure for which exact dimensionality can be shown. This is a joint work with D. Damanik.

Discrete Mathematical Biology Working Seminar

Series
Other Talks
Time
Monday, April 9, 2012 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Shel Swenson – Georgia Tech
A discussion of the paper "Understanding the Errors of SHAPE-Directed RNA Structure Modeling" by Kladwang et al (2011).

Plane fields on 3-manifolds II

Series
Geometry Topology Working Seminar
Time
Friday, April 6, 2012 - 14:00 for 2 hours
Location
Skiles 006
Speaker
John Etnyre – Ga Tech

Please Note: Note this is a 2 hour talk.

In this series of talks I will discuss various special plane fields on 3-manifold. Specifically we will consider folaitions and contact structures and the relationship between them. We will begin by sketching a proof of Eliashberg and Thurston's famous theorem from the 1990's that says any sufficiently smooth foliation can be approximated by a contact structure. In the remaining talks I will discuss ongoing research that sharpens our understanding of the relation between foliations and contact structures.

Queues, GUEs and Tubes

Series
ACO Student Seminar
Time
Friday, April 6, 2012 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Christian Houdré – Georgia Tech, School of Mathematics
Consider a series of n single-server queues each with unlimited waiting space and FIFO discipline. At first the system is empty, then m customers are placed in the first queue. The service times of all the customers at all the queues are iid. We are interested in the exit time of the last customer from the last server and that's when queues meet random matrices and GUEs. If the number of customers is a small fractional power of the number of servers, and as such customers stay within a tube, that's when queues encounter Tracy and Widom. This talk will be self contained and accessible to graduate students.

The Shape of Space

Series
Other Talks
Time
Thursday, April 5, 2012 - 16:30 for 1 hour (actually 50 minutes)
Location
Klaus 1443
Speaker
Frank Sottile – Texas A&M University

Please Note: An undergraduate-accessible talk.

In this talk, I will try to give you an idea of how mathematicians manage to say anything meaningful about higher-dimensional spaces, and relate this to the recent proof of the Poincare conjecture that won the Millennium Prize of the Clay Institute. Besides bringing your enquiring minds, at least 50% of the audience needs to bring a belt for those articles will play a key role in our discussion.

Steady water waves in the presence of wind

Series
PDE Seminar
Time
Thursday, April 5, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Samuel Walsh – New York University
In large part, the waves that we observe in the open ocean are created by wind blowing over the water. The precise nature of this process occurs has been intensely studied, but is still not understood very well at a mathematically rigorous level. In this talk, we side-step that issue, somewhat, and consider the steady problem. That is, we prove the existence of small-amplitude traveling waves in a two phase air-water system that can be viewed as the eventual product of wind generation. This is joint work with Oliver Buhler and Jalal Shatah.

Galois groups of Schubert problems

Series
School of Mathematics Colloquium
Time
Thursday, April 5, 2012 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Frank Sottile – Texas A&M
Building on work of Jordan from 1870, in 1979 Harris showed that a geometric monodromy group associated to a problem in enumerative geometry is equal to the Galois group of an associated field extension. Vakil gave a geometric-combinatorial criterion that implies a Galois group contains the alternating group. With Brooks and Martin del Campo, we used Vakil's criterion to show that all Schubert problems involving lines have at least alternating Galois group. My talk will describe this background and sketch a current project to systematically determine Galois groups of all Schubert problems of moderate size on all small classical flag manifolds, investigating at least several million problems. This will use supercomputers employing several overlapping methods, including combinatorial criteria, symbolic computation, and numerical homotopy continuation, and require the development of new algorithms and software.

Two applications of Riemannian geometry: Thermal stresses in solid mechanics and density preserving maps in machine learning.

Series
Research Horizons Seminar
Time
Wednesday, April 4, 2012 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Arkadaş Özakın – Georgia Tech Research Institute
I will present two "real life" applications of Riemannian geometry,one in the field of continuum mechanics, another in the field ofmachine learning (nonlinear dimensionality reduction). I will providequick introductions in order to make the talk accessible to anaudience with no background in either field.

Statistical Multiscale Analysis: From Signal Detection to Nanoscale Photonic Imaging

Series
Stochastics Seminar
Time
Tuesday, April 3, 2012 - 16:05 for 1 hour (actually 50 minutes)
Location
Skyles 006
Speaker
Axel Munk – Institut für Mathematische Stochastik Georg-August-Universität Göttingen
In this talk we will discuss a general concept of statistical multiscale analysis in the context of signal detection and imaging. This provides a large class of fully data driven regularisation methods which can be viewed as a multiscale generalization of the Dantzig selector. We address computational issues as well as the required extreme value theory of the multiscale statistics. Two major example include change point regression and locally adaptive total variation image regularization for deconvolution problems. Our method is applied to problems from ion channel recordings and nanoscale biophotonic cell microscopy.

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