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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/

Series: Other Talks

Tentative schedule: 9-12: mini-presentations, informal discussion, Q&A, led by Jose Rodriguez (numerical decomposition), Elizabeth Gross (reaction networks), Dan Bates (numerical AG for sciences and engineering); 12-1: lunch; 1pm+: catch flights, continue talking in groups.

This is an informal get-together of the Joint Meetings participants and locals interested in various aspects of Numerical Algebraic Geometry. This area combines numerical analysis and nonlinear algebra in algorithms that found various applications in other parts of mathematics and outside.
(If interested in joining, email leykin@math.gatech.edu)

Series: Other Talks

1. One day before the election, the statistics site 538 predicted a 70% chance of a Clinton victory. How do we judge the quality of probabilistic prediction models? Ultimately every quant finance model has a probabilistic prediction model at its core, for instance the geometric Brownian Motion is the core of Black-Scholes. I will explain the Basel Traffic Ligths Framework and then I'll ask the audience to think how the framework can be extended. 2. Multi-factor local volatility. I will explain Dupire's local volatility model and ask how this model can be extended to a multi-factor framework. 3. Model overfitting. There are objective criteria for statistical model overfitting, such as AIC. Such criteria don't exist for risk-neutral derivatives pricing models.

Series: Other Talks

Series: Other Talks

THis is an international meeting that will take place 8-11 October. See http://qmath13.gatech.edu/ for more details.

Series: Other Talks

Series: Other Talks

We will describe an etale version of Bloch groups and regulators which for the case of number fields that take values in quotients of units of their rings of integers. Joint work with Frank Calegari and Stavros Garoufalidis

Series: Other Talks

The goal of this group is to read carefully the book "Introduction to Chaos in non-equilibrium stat. Mechanics". There will be several speakers. AThe first lecture will be a quick introduction to thermodynamics and statistical mechanics for mathematicians. We hope to explain the physical basis of the problems to mathematicians who have no background in physics and also cover some of the mathematical subtleties that are often overlooked in physiscs courses.

Series: Other Talks

All School of Mathematics faculty, staff and postdocs are invited to attend this welcome event which will open with a short presentation and introducing new members to the School. Lunch will be provided.