Seminars and Colloquia by Series

Derived functors and Cech cohomology

Series
Other Talks
Time
Wednesday, November 11, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Farbod Shokrieh – Ga Tech
We will show that the construction of derived functors satisfy the required universal property.I will then show that, for any ringed space, the abelian category of all sheaves of Modules has enough injectives. We achieve this by first characterizing injective abelian groups (Baer's theorem).The relation with Cech cohomology will also be studied. In particular, I will show that the first Cech and Grothendieck sheaf cohomology groups are isomorphic for any topological space (without using spectral sequences).

Topological aspects in the theory of aperiodic solids and tiling spaces

Series
Research Horizons Seminar
Time
Wednesday, November 11, 2009 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
Jean Bellissard – School of Mathematics, Georgia Tech –
An assembly of atoms in a solid phase will be described through the notion of Delone sets and related to tilings. The Hull and the tiling space wiill be defined. It will be shown that the tiling space and the Hull can be constructed through an inverse limit of CW-complexes built out of the tiles and of the local patches. From then various cohomologies can be defined and allow to distinguish between these atomic distributions. The question of whether these topological invariant can be seen in experiments will be addressed.

Single neurons with multiple activities

Series
Mathematical Biology Seminar
Time
Wednesday, November 11, 2009 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Gennady Cymbalyuk – Georgia State University, Neuroscience Institute and Dept. of Physics and Astronomy
Bursting, tonic spiking, sub-threshold oscillations and silence are basic robust regimes of activity of a single neuron. The talk will be focused on the co-existence of regimes of activity of neurons. Such multistability enhances potential flexibility to the nervous system and has many implications for motor control and decision making. I will identify different scenarios leading to multistability in the neuronal dynamics and discuss its potential roles in the operation of the central nervous system under normal and pathological conditions.

Classical Solutions of Two Dimensional Inviscid Rotating Shallow Water System

Series
PDE Seminar
Time
Tuesday, November 10, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
Location
Skiles 255
Speaker
Chunjing Xie – University of Michigan, Ann Arbor
In this talk, we will discuss the global existence and asymptotic behavior of classical solutions for two dimensional inviscid Rotating Shallow Water system with small initial data subject to the zero-relative-vorticity constraint. One of the key steps is a reformulation of the problem into a symmetric quasilinear Klein-Gordon system, for which the global existence of classical solutions is then proved with combination of the vector field approach and the normal forms. We also probe the case of general initial data and reveal a lower bound for the lifespan that is almost inversely proportional to the size of the initial relative vorticity. This is joint work with Bin Cheng.

Seip's Interpolation Theorem in Weighted Bergman Spaces

Series
Analysis Working Seminar
Time
Monday, November 9, 2009 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Brett Wick – Georgia Tech
We are going to continue explaining the proof of Seip's Interpolation Theorem for the Bergman Space. We are going to demonstrate the sufficiency of these conditions for a certain example. We then will show how to deduce the full theorem with appropriate modifications of the example.

On the Legendrian and transverse classification of cabled knot types

Series
Geometry Topology Seminar
Time
Monday, November 9, 2009 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Bulent Tosun – Ga Tech
In 3-dimensional contact topology one of the main problem is classifying Legendrian (transverse) knots in certain knot type up to Legendrian ( transverse) isotopy. In particular we want to decide if two (one in case of transverse knots) classical invariants of this knots are complete set of invariants. If it is, then we call this knot type Legendrian (transversely) simple knot type otherwise it is called Legendrian (transversely) non-simple. In this talk, by tracing the techniques developed by Etnyre and Honda, we will present some results concerning the complete Legendrian and transverse classification of certain cabled knots in the standard tight contact 3-sphere. Moreover we will provide an infinite family of Legendrian and transversely non-simple prime knots.

Fast algorithms for the computation of the pseudospectral abscissa and pseudospectral radius.

Series
Applied and Computational Mathematics Seminar
Time
Monday, November 9, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Nicola Guglielmi – Università di L'Aquila –
This is a joint work with Michael Overton (Courant Institute, NYU). The epsilon-pseudospectral abscissa and radius of an n x n matrix are respectively the maximum real part and the maximal modulus of points in its epsilon-pseudospectrum. Existing techniques compute these quantities accurately but the cost is multiple SVDs of order n, which makesthe method suitable to middle size problems. We present a novel approach based on computing only the spectral abscissa or radius or a sequence of matrices, generating a monotonic sequence of lower bounds which, in many but not all cases, converges to the pseudospectral abscissa or radius.

Quasi Non-Integrable Hamiltonian System and its Applications

Series
CDSNS Colloquium
Time
Monday, November 9, 2009 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Dongwei Huang – Tianjin Polytechnic University, China and School of Mathematics, Georgia Tech
Many dynamical systems may be subject to stochastic excitations, so to find an efficient method to analyze the stochastic system is very important. As for the complexity of the stochastic systems, there are not any omnipotent methods. What I would like to present here is a brief introduction to quasi-non-integrable Hamiltonian systems and stochastic averaging method for analyzing certain stochastic dynamical systems. At the end, I will give some examples of the method.

Graph Tiling in Bipartite Graphs

Series
Combinatorics Seminar
Time
Friday, November 6, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
Location
Skiles 255
Speaker
Albert Bush – School of Mathematics, Georgia Tech

Please Note: This is joint work with Dr. Yi Zhao.

Graph tiling problems can be summarized as follows: given a graph H, what conditions do we need to find a spanning subgraph of some larger graph G that consists entirely of disjoint copies of H. The most familiar example of a graph tiling problem is finding a matching in a graph. With the Regularity Lemma and the Blow-up Lemma as our main tools, we prove a degree condition that guarantees an arbitrary bipartite graph G will be tiled by an arbitrary bipartite graph H. We also prove this degree condition is best possible up to a constant. This answers a question of Zhao and proves an asymptotic version of a result of Kuhn and Osthus for bipartite graphs.

Constructing 3-Manifolds Using Dehn Surgery on Handlebodies

Series
Geometry Topology Working Seminar
Time
Friday, November 6, 2009 - 15:00 for 2 hours
Location
Skiles 269
Speaker
Meredith Casey – Georgia Tech
The goal of this talk is to describe simple constructions by which we can construct any compact, orientable 3-manifold. It is well-known that every orientable 3-manifold has a Heegaard splitting. We will first define Heegaard splittings, see some examples, and go through a very geometric proof of this therem. We will then focus on the Dehn-Lickorish Theorem, which states that any orientation-preserving homeomorphism of an oriented 2-manifold without boundary can by presented as the composition of Dehn twists and homeomorphisms isotopic to the identity. We will prove this theorm, and then see some applications and examples. With both of these resutls together, we will have shown that using only handlebodies and Dehn twists one can construct any compact, oriented 3-manifold.

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