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Series: Research Horizons Seminar

Hyperbolic 3-manifolds is a great class of 3-dimensional geometric objects with interesting topology, a rich source of examples (practially one for every knot that you can draw), with arithmetically interesting volumes expressed in terms of dialogarithms of algebraic numbers, and with computer software that allows to manipulate them. Tired of abstract existential mathematics? Interested in concrete 3-dimensional topology and geometry? Or maybe Quantum Topology? Come and listen!

Series: Research Horizons Seminar

In dynamical systems, the long term behavior is organized by invariant manifolds that serve as landmarks that organize the traffic. There are two main theorems (established around 40-60 years ago) that tell you that these manifolds persist under small perturbations: KAM theorem and the theory of normally hyperbolic manifolds. In recent times there have been constructive proofs of these results which also lead to effective algorithms which allow to explore what happens in the border of the applicability of the theorems. We plan to review the basic concepts and present the experimental results.

Series: Research Horizons Seminar

Abstract: Four dimensions is unique in many ways. For example, n-dimensional Euclidean space has a unique smooth structure if and only if n is not equal to four. In other words, there is only one way to understand smooth functions on R^n if and only if n is not 4. There are many other ways that smooth structures on 4-dimensional manifolds behave in surprising ways. In this talk I will discuss this and I will sketch the beautiful interplay of ideas (you got algebra, analysis and topology, a little something for everyone!) that go into proving R^4 has more that one smooth structure (actually it has uncountably many different smooth structures but that that would take longer to explain).

Series: Research Horizons Seminar

I will discuss the variational approach to determining the stability of pendant liquid drops. The outline will include some theoretical aspects and questions which currently can only be answered numerically.

Series: Research Horizons Seminar

This is a will be a panel made of two senior grad students, a post doc and a faculty member. The panelists will answer questions and give advice to younger graduate students on a range of topics including how to be a good citizen of the department and choosing an advisor.
The panelists are Dr. Kang, Dr. Kelly Bickel, Albert Bush, and Chris Pryby.

Series: Research Horizons Seminar

The standard map is a widely studied area-preserving system with application to many natural phenomena. When unperturbed, every orbit of this map lies on an invariant circle. In this talk we will explore what happens to these circles when the system is perturbed, employing both analytical and numerical tools. I will conclude by discussing some active areas of current research.

Series: Research Horizons Seminar

We'll look at some of the basics of potential theory in the complex plane. We'll also discuss how potential theory may be used in studying zeros of polynomials and approximation theory.

Series: Research Horizons Seminar

Have you heard the urban legend that an experienced college
recruiter can make an initial decision on whether or not to read your
resume in less than six seconds? Would you like to see if your current resume can survive the six-second glance?Would you like to improve your chances of surviving the initial cut? Do you know what happens to your resume once you hand it to the recruiter? How do you craft a resume that competes with 100,000 other resumes? Dr. Matthew Clark has supported college recruiting efforts for a
variety of large corporations and is a master at sorting resumes in six
seconds or under. Join us August 28th, 2013 in Skiles 005 at noon for a discussion of how most industry companies handle resumes,
what types of follow up activities are worth-while, and, how to improve
your chances of having your resume pass the "six second glance".

Series: Research Horizons Seminar

I will give an overview of how lattices in R^n are providing a powerful new mathematical foundation for cryptography. Lattices yield simple, fast, and highly parallel schemes that, unlike many of today's popular cryptosystems (like RSA and elliptic curves), even appear to remain secure against quantum computers. What's more, lattices were recently used to solve a cryptographic "holy grail" problem known as fully homomorphic encryption.
No background in lattices, cryptography, or quantum computers will be necessary for this talk -- but you will need to know how to add and multiply matrices.

Series: Research Horizons Seminar

A 1986 article with this title, written by M. Zuker and published by the AMS, outlined several major challenges in the area. Stating the folding problem is simple; given an RNA sequence, predict the set of (canonical, nested) base pairs found in the native structure. Yet, despite significant advances over the past 25 years, it remains largely unsolved. A fundamental problem identified by Zuker was, and still is, the "ill-conditioning" of discrete optimization solution approaches. We revisit some of the questions this raises, and present recent advances in considering multiple (sub)optimal structures, in incorporating auxiliary experimental data into the optimization, and in understanding alternative models of RNA folding.