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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).

Series: Other Talks

This mini-conference will feature about six speakers on various topics in additive combinatorics.

Series: Other Talks

Anton Leykin is an invited speaker presenting "Certified numerical solving of systems of polynomial equations"

East Coast Computer Algebra Day (ECCAD) is an informal one-day meeting for those active or interested in computer algebra. It provides opportunities to learn and to share new results and work in progress. The schedule includes invited speakers, a panel discussion, and contributed posters and software demonstrations. Importantly, plenty of time is allowed for unstructured interaction among the participants. Researchers, teachers, students, and users of computer algebra are all welcome! Visit ECCAD for more details.