We will have three panelists who have recently found jobs: Aaron Wong, Assistant Professor, tenure track at Nevada State College, Henderson, Nevada, Mark Colarusso, Visiting Assistant Professor, University of Notre Dame, Indiana, and Dan Rogalski, Assistant Professor, UCSD. They will describe their experiences applying for an academic job. Some of the questions they will answer are: How many applications should I send out? How do I prepare for an interview? What should I write in my cover letter and resume? What are important qualifications for a teaching job, postdoc job, tenure track research job?
The discussion will be followed by a question and answer period.

For two graphs $S$ and $T$, the constrained Ramsey number $f(S, T)$ is the minimum $n$ such that every edge coloring of the complete graph on
$n$ vertices (with any number of colors) has a monochromatic subgraph isomorphic to $S$ or a rainbow subgraph isomorphic to $T$. Here, a
subgraph is said to be rainbow if all of its edges have different
colors. It is an immediate consequence of the Erd\H{o}s-Rado
Canonical Ramsey Theorem that $f(S, T)$ exists if and only if $S$ is a
star or $T$ is acyclic. Much work has been done to determine the rate
of growth of $f(S, T)$ for various types of parameters. When $S$ and
$T$ are both trees having $s$ and $t$ edges respectively, Jamison,
Jiang, and Ling showed that $f(S, T) \leq O(st^2)$ and conjectured
that it is always at most $O(st)$. They also mentioned that one of
the most interesting open special cases is when $T$ is a path. We
study this case and show that $f(S, P_t) = O(st\log t)$, which differs
only by a logarithmic factor from the conjecture. This substantially
improves the previous bounds for most values of $s$ and $t$.

Highway traffic flows are generally modeled by partial differential equations
(PDEs). These models are used by traffic engineers for
road design, planning or management. However, they
often fail to capture important features of
empirical traffic flow studies, particularly at small
scales. In this talk, I will propose a fairly simple stochastic model for
highway traffic flows in the form of a nonlinear stochastic partial differential
equation (SPDE) with random
coefficients driven by a Poisson random measure. I will discuss the
well posedness of the proposed equation as well as the
corresponding inverse problem that I will illustrate by its
calibration to high resolution traffic data from highway
101 in Los Angeles. I will also present a more sophisticated spde
in the form of a system of coupled hyperbolic-parabolic equations.

Varieties were originally studied by comparing them with
the hypersurfaces that are their generic projections--curves
in the plane and surfaces in three-space, for example. In
low dimensions, the fibers of these generic projections are
pretty well understood, but there are serious obstructions
to extending this understanding to all dimensions.
I'll survey what's known, explain some examples, and present
a new conjecture about these fibers. A connection with the
regularity of powers of an ideal (asymptotic regularity)
plays an interesting role.

The computational approximation of solutions of complex systems such as the Navier-Stokes equations is often a formidable task. For example, in feedback control settings where one often needs solutions of the complex systems in real time, it would be impossible to use large-scale finite element or finite-volume or spectral codes. For this reason, there has been much interest in the development of low- dimensional models that can accurately be used to simulate and control complex systems. We review some of the existing reduced-order modeling approaches, including reduced-basis methods and especially methods based on proper orthogonal decompositions techniques. We also discuss a new approach based on centroidal Voronoi tessellations. We discuss the relative merits and deficiencies of the different approaches and also the inherent limitations of reduced-order modeling in general.