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Series: Other Talks

NOTE: This is the first in a forthcoming series of colloquia in quantum mathematical physics that will take place this semester. The series is a spin-off of last year's QMath conference, and is intended to be of broad interest to people wanting to know the state of the art of current topics in mathematical physics.

We shall make an overview of the interplay between the geometry of tubular neighbourhoods of Riemannian manifold and the spectrum of the associated Dirichlet Laplacian. An emphasis will be put on the existence of curvature-induced eigenvalues in bent tubes and Hardy-type inequalities in twisted tubes of non-circular cross-section. Consequences of the results for physical systems modelled by the Schroedinger or heat equations will be discussed.

Series: Other Talks

Introduction of the new Faculty, Postdocs, Academic Professionals and Staff.

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: Other Talks

First, we present a necessary and sufficient
conditions for accessibility of bilinear systems evolving on semisimple
(matrix) Lie groups. From this, we derive a controllability criterion
for parallel connections of bilinear systems which gets a if-and-only-if
condition in the case of compact Lie groups. Finally, we present a key
application from quantum control.

Series: Other Talks

The TraX project
is an inter-university effort, involving researchers from 8
universities, aimed at elucidating the geometric structures in phase
space which determine the speed and nature of chemical reactions and how
they are affected by external influences such as light pulses or noise.
The effort is highly interdisciplinary and it involves Mathematics
(Dynamical Systems), Numerical Computations, Physics, and Chemistry all
working together to understand experimental phenomena and make
predictions.
The project has been funded by the European Research Council,
Mathematics Division for 4 years and it will sponsor visits of European
scientists to GT and provide opportunities for graduate students to
collaborate in this area. http://traxkickoff.gatech.edu/

Series: Other Talks

Rhythm is a great thing. It therefore follows that several rhythms at
once is even greater. Learn 2:3, 3:4, and 4:5, and a little bit about fractions.
Polyrhythms when sped up, lead to harmony and scales. Slower polyrhythms
happen in celestial mechanics. A little bit of music, a little bit of
mathematics.

Series: Other Talks

Mozghan Entekhabi (Wichita State University)
Radial Limits of Bounded Nonparametric Prescribed Mean Curvature Surfaces ;
Miyuki Koiso (Kyushu University)
Stability and bifurcation for surfaces with constant mean curvature ;
Vladimir Oliker (Emory University)
Freeform lenses, Jacobian equations, and supporting quadric method(SQM) ;
Sungho Park (Hankuk University of Foreign Studies)
Circle-foliated minimal and CMC surfaces in S^3 ;
Yuanzhen Shao (Purdue University)
Degenerate and singular elliptic operators on manifolds with singularities ;
Ray Treinen (Texas State University)
Surprising non-uniqueness for the 2D floating ball ;
See http://www.math.uab.edu/sgs/ for abstracts and further details.

Series: Other Talks

New and proposed interplanetary missions increasingly require the
design of trajectories within challenging multi-body environments that
stress or exceed the capabilities of the two-body design methodologies
typically used over the last several decades. These current methods
encounter difficulties because they often require appreciable user
interaction, result in trajectories that require significant amounts of
propellant, or miss potential mission-enabling options. The use of
dynamical systems methods applied to three-body and multi-body models
provides a pathway to obtain a fuller theoretical understanding of the
problem that can then result in significant improvements to trajectory
design in each of these areas. In particular, the computation of
periodic Lagrange point and resonant orbits along with their associated
invariant manifolds and heteroclinic connections are crucial to finding
the dynamical channels that provide new or more optimal solutions. These
methods are particularly effective for mission types that include
multi-body tours, Earth-Moon transfers, approaches to moons, and
trajectories to asteroids. The inclusion of multi-body effects early in
the analysis for these applications is key to providing a more complete
set of solutions that includes improved trajectories that may otherwise
be missed when using two-body methods.
This seminar will focus on two representative trajectory design
applications that are especially challenging. The first is the design of
tours using flybys of planets or moons with a particular emphasis on
the Galilean moons and Europa. In this case, the exploration of the
design space using the invariant manifolds of resonant and Lyapunov
orbits provides information such as the resonance transitions that are
required as part of the tour. The second application includes endgame
scenarios, which typically involve an approach to a moon with an
objective of either capturing into orbit around the moon or landing on
the surface. Often, the invariant manifolds of particular orbits may be
used in this case to provide a wide set of approach options for both
capture and landing analyses. New methods will also be discussed that
provide a foundation for rigorously analyzing the transit of
trajectories through the libration point regions that is necessary for
the approach and capture phase for bodies such as Europa and the Moon.
These methods provide a fundamentally new method to search for the
invariant manifolds of orbits and hyperbolic invariant sets associated
with libration points while giving additional insight into the dynamics
of the flow in these regions.

Series: Other Talks

This is a 3-day conference celebrating the 25th anniversary of the ACO Program. For more details about the conference please visit http://aco25.gatech.edu/