Seminars and Colloquia by Series

Autonomous and Intelligent Systems at United Technologies Research Center

Series
Other Talks
Time
Tuesday, April 7, 2015 - 09:00 for 1 hour (actually 50 minutes)
Location
TSRB Auditorium
Speaker
Andrzej Banaszuk United Technologies Research Center
We will present a broad overview of UTRC’s research initiative in Autonomous and Intelligent Systems (AIS) that was created to conceive, develop and mature a broad range of intelligent mobile robotic systems and capabilities to enhance and support the diverse array of businesses that comprise the United Technologies Corporation. While initial efforts have been focused on Sikorsky Aircraft unmanned rotorcraft, the initiative is now expanding to include other aerospace and commercial applications, as well. The research, conducted by a diverse team of researchers in robotics, dynamical systems, control, applied mathematics, computer vision, and computer science (in partnership with several leading universities including CMU, MIT, UPenn, and UCB) includes: • Real-time algorithms for dynamic collision avoidance in an obstacle-rich environment using probabilistic roadmaps. • Navigation with imperfect and intermittent sensors in GPS degraded environments. • Multi-vehicle missions including efficient robotic search algorithms based on ergodic theory methods. • Collaborative motion planning for multiple aerial and ground robots in large, cluttered environments, trading off mission objectives while satisfying logical/spatial/temporal constraints. • Intelligent system design methodology including architectures for autonomy, human-machine systems, and formal verification. We will conclude with research problems of interest to UTRC and discuss existing and future career and internship opportunities in the broad area of autonomy and robotics.

Control of Oscillators, Temporal Homogenization, and Energy Harvest by Super-Parametric Resonance

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 6, 2015 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Prof. Molei TaoGeorgia Tech School of Math.
We show how to control an oscillator by periodically perturbing its stiffness, such that its amplitude follows an arbitrary positive smooth function. This also motivates the design of circuits that harvest energies contained in infinitesimal oscillations of ambient electromagnetic fields. To overcome a key obstacle, which is to compensate the dissipative effects due to finite resistances, we propose a theory that quantifies how small/fast periodic perturbations affect multidimensional systems. This results in the discovery of a mechanism that reduces the resistance threshold needed for energy extraction, based on coupling a large number of RLC circuits.

Tightness of positive rational surgeries

Series
Geometry Topology Seminar
Time
Monday, April 6, 2015 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Bulent TosunUniversity of Virginia
Existence of a tight contact structure on a closed oriented three manifold is still widely open problem. In this talk we will present some work in progress to answer this problem for manifolds that are obtained by Dehn surgery on a knot in three sphere. Our method involves on one side generalizing certain geometric methods due to Baldwin, on the other unfolds certain homological algebra methods due to Ozsvath and Szabo.

Computer assisted proofs in KAM theory

Series
CDSNS Colloquium
Time
Monday, April 6, 2015 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Alex HaroUniv. of Barcelona
We present a methodology to rigorously validate a given approximation of a quasi-periodic Lagrangian torus of a symplectic map. The approach consists in verifying the hypotheses of a-posteriori KAM theory based of the parameterization method (following Rafael de la Llave and collaborators). A crucial point of our imprementation is an analytic Lemma that allows us to control the norm of periodic functions using their discrete Fourier transform. An outstanding consequence of this approach it that the computational cost of the validation is assymptotically equivalent of the cost of the numerical computation of invariant tori using the parametererization method. We pretend to describe some technical aspects of our implementation. This is a work in progress joint with Jordi-Lluis Figueras and Alejandro Luque.

Cellular Binomial Ideals

Series
Algebra Seminar
Time
Friday, April 3, 2015 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Laura Felicia MatusevichTexas A&M
Primary decomposition is a fundamental operation in commutative algebra. Although there are several algorithms to perform it, this remains a very difficult undertaking in general. In cases with additional combinatorial structure, it may be possible to do primary decomposition "by hand". The goal of this talk is to explain in detail one such example. This is joint work with Zekiye Eser; no prerequisites are assumed beyond knowing the definitions of "polynomial ring" and "ideal".

Limit theorems for composition of functions

Series
Stochastics Seminar
Time
Thursday, April 2, 2015 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Michael AnshelevichTexas A&M
I will discuss the limit theorems for composition of analytic functions on the upper-half-plane, and the analogies and differences with the limit theorems for sums of independent random variables. The analogies are enhanced by recalling that the probabilistic limit theorems are really results about convolution of probability measures, and by introducing a new binary operation on probability measures, the monotone convolution.This is joint work with John D. Williams.

The Filippov moments solution on the intersection of two and three manifolds

Series
Dissertation Defense
Time
Thursday, April 2, 2015 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Fabio DifonzoSchool of Mathematics, Georgia Tech
We consider several possibilities on how to select a Filippov sliding vector field on a co-dimension 2 singularity manifold, intersection of two co-dimension 1 manifolds, under the assumption of general attractivity. Of specific interest is the selection of a smoothly varying Filippov sliding vector field. As a result of our analysis and experiments, the best candidates of the many possibilities explored are based on so-called barycentric coordinates: in particular, we choose what we call the moments solution. We then examine the behavior of the moments vector field at the first order exit points, and show that it aligns smoothly with the exit vector field. Numerical experiments illustrate our results and contrast the present method with other choices of Filippov sliding vector field. We further generalize this construction to co-dimension 3 and higher.

Two Lax systems for the Painleve II equation

Series
Analysis Seminar
Time
Thursday, April 2, 2015 - 11:05 for 1 hour (actually 50 minutes)
Location
rm 005
Speaker
Karl LiechtyDePaul University

Please Note: Karl Liechty is the winner of the 2015 Szego prize in orthogonal polynomials and special functions.

I will discuss two different Lax systems for the Painleve II equation. One is of size 2\times 2 and was first studied by Flaschka and Newell in 1980. The other is of size 4\times 4, and was introduced by Delvaux, Kuijlaars, and Zhang in 2010. Both of these objects appear in problems in random matrix theory and closely related fields. I will describe how they are related, and discuss the applications of this relation to random matrix theory.

Concrete Chern classes, the cyclic quantum dilogarithm and the Bloch group

Series
Algebra Seminar
Time
Wednesday, April 1, 2015 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Stavros GaroufalidisGatech
The talk involves an explicit formula for the Chern class on K_3(F), F=number field, givenin terms of the cyclic quantum dilogarithm on the Bloch group of F. Such a formula constructsexcplicitly units in number fields, given a complete hyperbolic 3-manifold, and a complex root ofunity, and those units fit in the asymptotic expansion of quantum knot invariants. The existence ofsuch a formula was conjectured 4 years ago by Zagier (and abstractly follows from Voevodsky's work),and the final solution to the problem was given in recent joint work of the speaker with FrankCalegari and Don Zagier. The key ingredient to the concrete formula is a special function, thecyclic quantum dilogarithm, from a physics 1993 paper of Kashaev and others. The connection of thisformula with physics, and with the Quantum Modular Form Conjecture of Zagier continues with jointwork with Tudor Dimofte. But this is the topic of another talk.

Representability of Cohomology

Series
Geometry Topology Student Seminar
Time
Wednesday, April 1, 2015 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Benjamin IdeGeorgia Tech
In this talk, I prove that there is a bijection between [X, K(\pi, n)] and H^n(X; \pi). The proof is a good introduction to obstruction theory.

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