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Series: Other Talks

In school, we learned that fluid flow becomes simple in two
limits. Over long lengthscales and at high speeds, inertia dominates and the
motion can approach that of a perfect fluid with zero viscosity. On short
lengthscales and at slow speeds, viscous dissipation is important. Fluid
flows that correspond to the formation of a finite-time singularity in the
continuum description involve both a vanishing characteristic lengthscale
and a diverging velocity scale. These flows can therefore evolve into final
limits that defy expectations derived from properties of their initial
states. This talk focuses on 3 familiar processes that belong in this
category: the formation of a splash after a liquid drop collides with a dry
solid surface, the emergence of a highly-collimated sheet from the impact of
a jet of densely-packed, dry grains, and the pinch-off of an underwater
bubble. In all three cases, the motion is dominated by inertia but a small
amount of dissipation is also present. Our works show that dissipation is
important for the onset of splash, plays a minor role in the ejecta sheet
formation after jet impact, but becomes irrelevant in the break-up of an
underwater bubble. An important consequence of this evolution towards
perfect-fluid flow is that deviations from cylindrical symmetry in the
initial stages of pinch-off are not erased by the dynamics. Theory,
simulation and experiment show detailed memories of initial imperfections
remain encoded, eventually controlling the mode of break-up. In short, the
final outcome is not controlled by a single universal singularity but
instead displays an infinite variety.

Series: Other Talks

Dynamical systems with multiple time scales have invariant
geometric objects that organize the dynamics in phase space. The slow-fast
structure of the dynamical system leads to phenomena such as canards,
mixed-mode oscillations, and bifurcation delay. We'll discuss two projects
involving chemical oscillators. The first is the analysis of a simple
chemical model that exhibits complex oscillations. Its bifurcations are
studied using a geometric reduction of the system to a one-dimensional
induced map. The second investigates the slow-fast mechanisms generating
mixed-mode oscillations in a model of the Belousov-Zhabotinsky (BZ)
reaction. A mechanism called dynamic Hopf bifurcation is responsible for
shaping the dynamics of the system.
This webminar will be broadcast on evo.caltech.edu (register, start EVO,
webminar link is evo.caltech.edu/evoNext/koala.jnlp?meeting=MMMeMn2e2sDDDD9v9nD29M )

Series: Other Talks

In a wide range of applications, we deal with long sequences of slowly changing matrices or large collections of related matrices and corresponding linear algebra problems. Such applications range from the optimal design of structures to acoustics and other parameterized systems, to inverse and parameter estimation problems in tomography and systems biology, to parameterization problems in computer graphics, and to the electronic structure of condensed matter. In many cases, we can reduce the total runtime significantly by taking into account how the problem changes and recycling judiciously selected results from previous computations. In this presentation, I will focus on solving linear systems, which is often the basis of other algorithms. I will introduce the basics of linear solvers and discuss relevant theory for the fast solution of sequences or collections of linear systems. I will demonstrate the results on several applications and discuss future research directions.

Series: Other Talks

This talk will be the oral examination for Meredith Casey.

I will first discuss the motivation and background information necessary to
study the subjects of branched covers and of contact geometry. In
particular we will give some examples and constructions of topological
branched covers as well as present the fundamental theorems in this area.
But little is understood about the general constructions, and even less
about how branched covers behave in the setting of contact geometry, which
is the focus of my research. The remainder of the talk will focus on the
results I have thus far and current projects.

Series: Other Talks

Martin Gardner (1914-2010) "brought more mathematics to more millions than anyone else," according to Elwyn R. Berlekamp, John H. Conway & Richard K. Guy. Who was this man, how was he so influential, and will his legacy matter in the 22nd century? We'll try to answer these questions.This event is part of a one-day global celebration of the life of Martin Gardner. See www.g4g-com.org for information on Atlanta's Celebration of Mind party.

Series: Other Talks

Hosted by Renato DC Monteiro, ISyE.

Intersection cuts are generated from a polyhedral cone and a convex set S
whose interior contains no feasible integer point. We generalize these cuts
by replacing the cone with a more general polyhedron C. The resulting
generalized intersection cuts dominate the original ones. This leads to a
new cutting plane paradigm under which one generates and stores the
intersection points of the extreme rays of C with the boundary of S rather
than the cuts themselves. These intersection points can then be used to
generate deeper cuts in a non-recursive fashion.
(This talk is based on joint work with Francois Margot.)

Series: Other Talks

Series: Other Talks

In this presentation, we show a significant role that symmetry, a fundamental concept in convex geometry, plays in determining the power of robust and finitely adaptable solutions in multi-stage stochastic and adaptive optimization problems. We consider a fairly general class of multi-stage mixed integer stochastic and adaptive optimization problems and propose a good approximate solution policy with performance guarantees that depend on the geometric properties such as symmetry of the uncertainty sets. In particular, we show that a class of finitely adaptable solutions is a good approximation for both the multi-stage stochastic as well as the adaptive optimization problem. A finitely adaptable solution specifies a small set of solutions for each stage and the solution policy implements the best solution from the given set depending on the realization of the uncertain parameters in the past stages. To the best of our knowledge, these are the first approximation results for the multi-stage problem in such generality. (Joint work with Vineet Goyal, Columbia University and Andy Sun, MIT.)

Series: Other Talks

The why and how of applying to graduate school, with examples of different opportunities drawn from the past 10 years of undergraduate mathematics majors that have gone on to programs in EE, Physics, Applied Math, Statistics, Math, and even Public Policy. Useful for all undergraduate math majors. This is part of the regular Club Math meetings.

Series: Other Talks

This talk should be non-technical except the last few slides. The talk is

based on a work done in collaboration with Denis Charles, Max Chickering,

Nikhil Devanur, and Manan Sanghi, all from Microsoft.

Lopsided bipartite graphs naturally appear in advertising setting. One side
is all the eyeballs and the other side is all the advertisers. An edge is
when an advertiser wants to reach an eyeball, aka, ad targeting. Such a
bipartite graph is lopsided because there are only a small number of
advertisers but a large number of eyeballs. We give algorithms which have
running time proportional to the size of the smaller side, i.e., the number
of advertisers. One of the main ideas behind our algorithm and as well as
the analysis is a property, which we call, monotonic quality bounds. Our
algorithm is flexible as it could easily be adapted for different kinds of
objective functions.
Towards the end of the talk we will describe a new matching polytope. We
show that our matching polytope is not only a new linear program describing
the classical matching polytope, but is a new polytope together with a new
linear program. This part of the talk is still theoretical as we only know
how to solve the new linear program via an ellipsoid algorithm. One feature
of the polytope, besides being intriguing, is that it has some notion of
fairness built in. This is important for advertising since if an advertiser
wants to reach 10 million users of type A or type B, advertiser won't
necessarily be happy if we show the ad to 10 million users of type A only
(though it fulfills the advertising contract in a technical sense).