Seminars and Colloquia Schedule

Floquet bundles for tridiagonal competitive-cooperative systems

Series
CDSNS Colloquium
Time
Monday, October 8, 2012 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Yi Wang – University of Sciences and Technology of China
For a general time-dependent linear competitive-cooperative tridiagonal system of differential equations, we obtain canonical Floquet invariant bundles which are exponentially separated in the framework of skew-product flows. The obtained Floquet theory is applied to study the dynamics on the hyperbolic omega-limit sets for the nonlinear competitive-cooperative tridiagonal systems in time-recurrent structures including almost periodicity and almost automorphy.

Braess's Paradox in Expanders

Series
Other Talks
Time
Monday, October 8, 2012 - 13:05 for 1 hour (actually 50 minutes)
Location
Klaus 1116W
Speaker
Stephen Young – University of Louisville, Kentucky –
Expander graphs are known to facilitate effective routing and most real-world networks have expansion properties. At the other extreme, it has been shown that in some special graphs, removing certain edges can lead to more efficient routing. This phenomenon is known as Braess¹s paradox and is usually regarded as a rare event. In contrast to what one might expect, we show that Braess¹s paradox is ubiquitous in expander graphs. Specifically, we prove that Braess¹s paradox occurs in a large class of expander graphs with continuous convex latency functions. Our results extend previous work which held only when the graph was both denser and random and for random linear latency functions. We identify deterministic sufficient conditions for a graph with as few as a linear number of edges, such that Braess¹s Paradox almost always occurs, with respect to a general family of random latency functions. Joint work with Fan Chung and Wenbo Zhao. (* Note that this is an ARC/Theory Seminar and is in Klaus 1116W *)

Numerical Methods for Fully Nonlinear Second Order Partial Differential Equations

Series
Applied and Computational Mathematics Seminar
Time
Monday, October 8, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
005
Speaker
Xiaobing Feng – University of Tennessee
In this talk I shall present some latest advances on developing numerical methods (such as finite difference methods, Galerkin methods, discontinuous Galerkin methods) for fully nonlinear second order PDEs including Monge-Ampere type equations and Hamilton-Jacobi-Bellman equations. The focus of this talk is to present a new framework for constructing finite difference methods which can reliably approximate viscosity solutions of these fully nonlinear PDEs. The connection between this new framework with the well-known finite difference theory for first order fully nonlinear Hamilton-Jacobi equations will be explained. Extensions of these finite difference techniques to discontinuous Galerkin settings will also be discussed.

Classification of minimal surfaces in $S^5$ with constant contact angle

Series
Geometry Topology Seminar
Time
Monday, October 8, 2012 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Rodrigo Montes – Univerity of Curitiba, Brazil –
In this talk we introduce the notions of the contact angle and of the holomorphic angle for immersed surfaces in $S^{2n+1}$. We deduce formulas for the Laplacian and for the Gaussian curvature, and we will classify minimal surfaces in $S^5$ with the two angles constant. This classification gives a 2-parameter family of minimal flat tori of $S^5$. Also, we will give an alternative proof of the classification of minimal Legendrian surfaces in $S^5$ with constant Gaussian curvature. Finally, we will show some remarks and generalizations of this classification.

Linear series on metrized complexes of algebraic curves

Series
Algebra Seminar
Time
Monday, October 8, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Matthew Baker – Georgia Tech
A metrized complex of algebraic curves over a field K is, roughly speaking, a finite edge-weighted graph G together with a collection of marked complete nonsingular algebraic curves C_v over K, one for each vertex; the marked points on C_v correspond to edges of G incident to v. We will present a Riemann-Roch theorem for metrized complexes of curves which generalizes both the classical and tropical Riemann-Roch theorems, together with a semicontinuity theorem for the behavior of the rank function under specialization of divisors from smooth curves to metrized complexes. The statement and proof of the latter result make use of Berkovich's theory of non-archimedean analytic spaces. As an application of the above considerations, we formulate a partial generalization of the Eisenbud-Harris theory of limit linear series to semistable curves which are not necessarily of compact type. This is joint work with Omid Amini.

Positive Equilibrium Solutions in Structured Population Dynamics

Series
PDE Seminar
Time
Monday, October 8, 2012 - 16:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Christoph Walker – University of Hannover, Germany
The talk focuses on positive equilibrium (i.e. time-independent)solutionsto mathematical models for the dynamics of populations structured by ageand spatial position. This leads to the study of quasilinear parabolicequations with nonlocal and possibly nonlinear initial conditions. Weshallsee in an abstract functional analytic framework how bifurcationtechniquesmay be combined with optimal parabolic regularity theory to establishtheexistence of positive solutions. As an application of these results wegivea description of the geometry of coexistence states in a two-parameterpredator-prey model.

Discrete Mathematical Biology Working Seminar

Series
Other Talks
Time
Tuesday, October 9, 2012 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
David Murrugarra – Georgia Tech
A discussion of the paper "External Control in Markovian Genetic Regulatory Networks" by Datta et al (2003).

Nonlinear Mechanics, Morphology and Instability of Thin Structures

Series
Other Talks
Time
Tuesday, October 9, 2012 - 13:00 for 1 hour (actually 50 minutes)
Location
MRDC Building, Room 4211
Speaker
Zi Chen – Washington University in St. Louis

<a href="http://www2.me.gatech.edu/www/calendar/view_seminar.asp?speaker=Zi%20Che... target="_blank">Speaker's Bio</a>. <br />
Host: David Hu, School of Mechanical Engineering

Mechanical forces play a key role in the shaping of versatile morphologies of thin structures in natural and synthetic systems. The morphology and deformation of thin ribbons, plates and rods and their instabilities are systematically investigated, through both theoretical modeling and table-top experiments. An elasticity theory combining differential geometry and stationarity principles is developed for the spontaneous bending and twisting of ribbons with tunable geometries in presence of mechanical anisotropy. Closed-form predictions are obtained from this theory with no adjustable parameters, and validated with simple, table-top experiments that are in excellent agreement with the theoretical predictions. For large deformation of ribbons and plates, a more general theory is developed to account for mechanical instability (slap-bracelet type) induced by geometric nonlinearity, due to the competition between inhomogeneous bending and mid-plane stretching energy. This comprehensive, reduced parameter model leads to unique predictions about multistability that are validated with a series of table-top experiments. Furthermore, this study has been extended to interpret a different type of snap-through instability that the Venus flytrap has been actively employing to capture insects for millions of years, and the learnt principle is used to guide the design of bio-mimetic flytrap robot.

Selectable Reduced Rank Regression and Principle Component Analysis

Series
Stochastics Seminar
Time
Tuesday, October 9, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skyles 005
Speaker
Yiyuan She – Florida State University
Rank reduction as an effective technique for dimension reduction is widely used in statistical modeling and machine learning. Modern statistical applications entail high dimensional data analysis where there may exist a large number of nuisance variables. But the plain rank reduction cannot discern relevant or important variables. The talk discusses joint variable and rank selection for predictive learning. We propose to apply sparsity and reduced rank techniques to attain simultaneous feature selection and feature extraction in a vector regression setup. A class of estimators is introduced based on novel penalties that impose both row and rank restrictions on the coefficient matrix. Selectable principle component analysis is proposed and studied from a self-regression standpoint which gives an extension to the sparse principle component analysis. We show that these estimators adapt to the unknown matrix sparsity and have fast rates of convergence in comparison with LASSO and reduced rank regression. Efficient computational algorithms are developed and applied to real world applications.

Energetics of the Euler equation and a self-similar blow-up

Series
PDE Seminar
Time
Tuesday, October 9, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Roman Shvydkoy – University of Illinois at Chicago
The existence of self-similar blow-up for the viscous incompressible fluids was a classical question settled in the seminal of works of Necas, et al and Tsai in the 90'. The corresponding scenario for the inviscid Euler equations has not received as much attention, yet it appears in many numerical simulations, for example those based on vortex filament models of Kida's high symmetry flows. The case of a homogeneous self-similar profile is especially interesting due to its relevance to other theoretical questions such the Onsager conjecture or existence of Landau type solutions. In this talk we give an account of recent studies demonstrating that a self-similar blow-up is unsustainable the Euler system under various weak decay assumptions on the profile. We will also talk about general energetics of the Euler system that, in part, is responsible for such exclusion results.

Towards the proof of diffusion in the Jupiter-Sun restricted three body problem (second, final part)

Series
Dynamical Systems Working Seminar
Time
Tuesday, October 9, 2012 - 16:30 for 1.5 hours (actually 80 minutes)
Location
Skiles 06
Speaker
Maciej Capinski – Georgia Tech
In the talk we will present a mechanism of diffusion in the Planar Circular Restricted Three Body Problem. The mechanism is similar to the one that appeared in the celebrated work of V. I. Arnold [Dokl. Akad. Nauk SSSR 156 (1964), 9–12]. Arnold conjectured that this phenomenon, usually called Arnold diffusion, appears in the three body problem. The presented method is a step towards a proof of the conjecture. In this second, and final part of the talk, we discuss how to prove transversal intersections of invariant manifolds in the circular problem and how these lead to diffusion in the elliptic problem.

Solvable Schroedinger equations with trigonometric potentials: From quantum $A_N$ (Sutherland to $E_8$ trigonometric models

Series
Analysis Seminar
Time
Wednesday, October 10, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Alexander Turbiner – Nuclear Science Institute, UNAM, Mexico
A brief overview of some integrable and exactly-solvable Schroedinger equations with trigonometric potentials of Calogero-Moser-Sutherland type is given.All of them are characterized bya discrete symmetry of the Hamiltonian given by the affine Weyl group,a number of polynomial eigenfunctions and eigenvalues which are usually quadratic in the quantum number, each eigenfunction is an element of finite-dimensionallinear space of polynomials characterized by the highest root vector, anda factorization property for eigenfunctions. They admitan algebraic form in the invariants of a discrete symmetry group(in space of orbits) as 2nd order differential operator with polynomial coefficients anda hidden algebraic structure. The hidden algebraic structure for $A-B-C-D$-series is related to the universal enveloping algebra $U_{gl_n}$. For the exceptional $G-F-E$-seriesnew infinite-dimensional finitely-generated algebras of differential operatorswith generalized Gauss decomposition property occur.

Divisors on graphs, connected flags, and syzygies

Series
Combinatorics Seminar
Time
Friday, October 12, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Farbod Shokrieh – Georgia Tech
Associated to every finite graph G there is a canonical ideal which encodes the linear equivalences of divisors on G. We study this ideal and its associated initial ideal. We give an explicit description of their syzygy modules and the Betti numbers in terms of the "connected flags" of G. This resolves open questions posed by Postnikov-Shapiro, Perkinson-Perlmen-Wilmes, and Manjunath-Sturmfels. No prior knowledge in advanced commutative algebra will be assumed. This is a joint work with Fatemeh Mohammadi.