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Series: Analysis Seminar

Abstract: Shift-invariant (SI) spaces play a prominent role in the study
of wavelets, Gabor systems, and other group frames. Working in the
setting of LCA groups, we use a variant of the Zak transform to classify
SI spaces, and to simultaneously
describe families of vectors whose shifts form frames for the SI spaces
they generate.

Series: Geometry Topology Seminar

The mapping class group of the plane minus a Cantor set naturally appears in many dynamical contexts, including group actions on surfaces, the study of groups of homeomorphisms on a Cantor set, and complex dynamics. In this talk, I will present the 'ray graph', which is a Gromov-hyperbolic graph on which this big mapping class group acts by isometries (it is an equivalent of the curve graph for this surface of infinite topological type). If time allows, I will give a description of the Gromov-boundary of the ray graph in terms of long rays in the plane minus a Cantor set. This involves joint work with Alden Walker.

Series: GT-MAP Seminars

The workshop will launch the thematic semesters on Dynamics (Fall 2017) and Control (Spring 2018) for GT-MAP activities.
This is a two-day workshop, the first day focusing on the theme of
Dynamics, and the second day focusing on the theme of Control. There
will be light refreshments throughout the event.
The workshop will be held in the Klaus building Room 2447. More information at http://gtmap.gatech.edu/events/gt-map-workshop-dynamics-and-control

Series: Geometry Topology Seminar

We will give different topological very simple statements that seem not to have been noticed, although they are of the level
of Brouwer’s fixed point theorem. The main result is: Let F be a compact subset of the manifold M. Assume g:F->M is a continuous map which is the identity on the boundary (or frontier) of F, then the image g(F) contains either F or M\F.

Series: GT-MAP Seminars

GT MAP sponsored "Workshop on Dynamical Systems" to mark the retirement of Prof. Shui Nee Chow. Full day August 10- 11.
After nearly 30 years at Georgia Tech, Prof. Shui Nee Chow
has officially retired. This workshop will see several of his former
students, post-docs, and friends, coming together to thank Shui Nee for
his vision, service, and research, that so greatly impacted the School
of Mathematics at Georgia Tech.
The workshop will be held in the Klaus building Room 1447. More information at http://gtmap.gatech.edu/events/workshop-dynamical-system

Series: Geometry Topology Seminar

Not yet

Series: Other Talks

Georgia Tech is the site of the 2017 SIAM Conference on Applied
Algebraic Geometry (July 31 to August 4). This biennial meeting is an activity of the
Activity Group in Applied Geometry of SIAM, the Society for Industrial and Applied Mathematics. The SIAM Activity Group in Algebraic Geometry aims to bring together researchers who use algebraic geometry in industrial and applied mathematics.
"Algebraic geometry" is interpreted broadly to include at
least algebraic geometry, commutative algebra, noncommutative algebra,
symbolic and numeric computation, algebraic and geometric combinatorics,
representation theory, and algebraic topology.
These methods have already seen applications in biology, coding
theory, cryptography, combustion, computational geometry, computer
graphics, quantum computing, control theory, geometric design,
complexity theory, machine learning, nonlinear partial differential
equations, optimization, robotics, and statistics.
School of Mathematics professors Greg Blekherman, Anton Leykin, and Josephine Yu lead the local organizing committee.

Series: Other Talks

Dates: July 27-29 (Thu-Sat). Schedule will appear here.
These tutorials are intended to appeal to participants with any level of prior M2 experience. The topics will range from the basic functionality of M2 to modeling problems in the M2 language to more specialized tutorials on algebraic statistics and numerical algebraic geometry. We will also reserve ample time for practice and Q&A sessions.
Registration is free, but please fill the form here.

Series: CDSNS Colloquium

When perturbed with a small periodic forcing, two (or more) coupledconservative oscillators can exhibit instabilities: trajectories thatbecome unstable while accumulating ``unbounded'' energy from thesource. This is known as Arnold diffusion, and has been traditionallyapplied to celestial mechanics, for example to study the stability ofthe solar system or to explain the Kirkwood gaps in the asteroid belt.However, such phenomenon could be extremely useful in energyharvesting systems as well, whose aim is precisely to capture as muchenergy as possible from a source.In this talk we will show a first step towards the application ofArnold diffusion theory in energy harvesting systems. We will consideran energy harvesting system based on two piezoelectric oscillators.When forced to oscillate, for instance when driven by a small periodicvibration, such oscillators create an electrical current which chargesan accumulator (a capacitor or a battery). Unfortunately, suchoscillators are not conservative, as they are not perfectly elastic(they exhibit damping).We will discuss the persistence of normally hyperbolic invariantmanifolds, which play a crucial role in the diffusing mechanisms. Bymeans of the parameterization method, we will compute such manifoldsand their associated stable and unstable manifolds. We will alsodiscuss the Melnikov method to obtain sufficient conditions for theexistence of homoclinic intersections.

Series: Geometry Topology Seminar