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Series: Research Horizons Seminar

Many physical models without dissipation can be written in a Hamiltonian
form. For example, nonlinear Schrodinger equation for superfluids and
Bose-Einstein condensate, water waves and their model equations (KDV,
BBM, KP, Boussinesq systems...), Euler equations for inviscid fluids,
ideal MHD for plasmas in fusion devices, Vlasov models for collisionless
plasmas and galaxies, Yang-Mills equation in gauge field theory etc.
There exist coherent structures (solitons, steady states, traveling
waves, standing waves etc) which play an important role on the long time
dynamics of these models. First, I will describe a general framework to
study linear stability (instability) when the energy functional is
bounded from below. For the models with indefinite energy functional
(such as full water waves), approaches to find instability criteria will
be mentioned. The implication of linear instability (stability) for
nonlinear dynamics will be also briefly discussed.

Series: Research Horizons Seminar

Please note the delayed start for this week only.

The main focus of this talk is a class of asymptotic methods called
averaging. These methods approximate complicated differential equations
that contain multiple scales by much simpler equations. Such
approximations oftentimes facilitate both analysis and computation. The
discussion will be motivated by simple examples such as bridge and
swing, and it will remain intuitive rather than fully rigorous. If time
permits, I will also mention some related projects of mine, possibly
including circuits, molecules, and planets.

Series: Research Horizons Seminar

In this talk, we will discuss what entails being a front-office
quant at JP Morgan in the Emerging Markets group. We discuss
why Emerging Markets is viewed as its own asset class and what there is to
model. We also give practical examples of things we look at on a daily
basis. This talk aims to be informal and to appeal to a wide audience.

Series: Research Horizons Seminar

We will discuss methods for solving polynomial equations with integer solutions using the loops on the space of all complex
solutions to the same equations. We will then state generalizations of this method due to A. Grothendieck.

Series: Research Horizons Seminar

There is a beautiful idea that one can study spaces by
studying associated geometric objects. More specifically one can
associate to a manifold (that is some space) a symplectic or contact
manifold (that is the geometric object). The question is how useful is
this idea. We will discuss this idea and related questions for subspaces
(that is immersions and embeddings) with a focus on curves in the plane
and knots in three space. If time permits we will discuss powerful new
tools from contact geometry that allow one use this idea to construct
invariants of knots and more generally embeddings and immersions in any
space.

Series: Research Horizons Seminar

This talk is intended to be a cocktail of many things. I will start
with standard random matrices (called GUE in the slang) and formal
computations which leads one to the main problem of counting planar
diagrams. This was done by physicists, though the main computation of
generating functions for such planar diagrams go through an analytic
tools. Here I will change the topic to analysis, and get through with
the help of Chebyshev polynomials and how these can be used to solve a
minimization problem and then from there to compute several generating
functions of planar diagrams. Then I will talk about
tridiagonalization which is a main tool in matrix analysis and point out
an interesting potential view on this subject.

Series: Research Horizons Seminar

There is a long standing asymptotic relationship in several areas of
analysis, between polynomials and entire functions of exponential type.
Many extremal problems for polynomials of degree n turn into analogous
extremal problems for entire functions of exponential type, as the
degree n approaches infinity. We discuss some of the old such as
Bernstein's constant on approximation of |x|, and recent work on
Plancherel-Polya and Nikolskii inequalities.

Series: Research Horizons Seminar

Here is a classical theorem. Consider a bijection (just a set map!)
from the Euclidean plane to itself that takes 0 to 0 and takes the
points on an arbitrary line to the points on a (possibly different
line). The theorem is that such a bijection always comes from a linear
map. I'll discuss various generalizations of this theorem in geometry,
topology, and algebra, ending with a discussion of some recent, related
research on the topology of surfaces.

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? Should you have different resumes for online submission and handing to decision makers? How many different resumes should you prepare before you go to the career fair? Does it really take 30 revisions of your resume before it is ready to be submitted? 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 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

Note: This is a special time for Research Horizons.

Special seminar title: The idea of studying the geometry and topology of
finite metric spaces has arisen due to the fact that almost all kinds of
data sets arising in science or the commercial world are equipped with a
metric. This has led to the development of cohomology theories applicable
to finite metric spaces, which allow one to construct "measurements" of the
shape of the data sets. We will define these theories and discuss their
properties. We will also describe their applications, and suggest
directions of future research on them.