In this talk we utilize a support vector machine feature selection
procedure via concave minimization to solve the well-known Disputed
Federalist Papers classification problem. First we find a separating
plane that classifies correctly all the training set consisting of
papers of known authorship, based on the relative frequencies of three
words only. Then, using this three-dimensional separating plane, all
of the 12 disputed papers ended up on one side of the separating
plane. Our result coincides with previous statistical and
combinatorial method results.

Cells are highly sophisticated information processing devices, sensing diverse inputs Abstract:to make complex decisions. Yet despite increasingly elegant ways to measure pathway outputs, we largely lack control over the inputs delivered to the cell in space and time. I will describe how optogenetic techniques can overcome this challenge to control the exact combinations, dynamics, and spatial locations of pathway activity in live cells. Applied to mammalian growth factor signaling, they revealed the Ras/Erk module accurately transmits a huge range of steady-state and dynamic signals to downstream response programs. A light-based screen uncovered many of these dynamics-sensitive responses, including a cell-cell communication circuit acting through IL-6 family cytokines.

Invariant theory is a beautiful field. The area dates back
over 100 years to the work of Hilbert, Klein, Gauss, and many others.
It is a very active area of research today, particularly from the
viewpoint of algebraic geometry and combinatorics. It also has far
reaching applications in representation theory, coding theory,
mathematical modeling, and even air target recognition. (I just
happened to run across this last application on google and it will
*not* be explained.)

In this talk, I aim to illustrate the beauty of Noncommutative
Invariant Theory. All basic notions will defined. Namely, I will
explain the noncommutative analogues of each of the following terms:
"groups", "acting on", "polynomial rings". I will also provide an
overview of recentwork pertaining to quantum group actions on
(noncommutative) regular algebras. The results discussed here are
from joint works with Kenneth Chan, Pavel Etingof, Ellen Kirkman,
Yanhua Wang, and James Zhang: see arXiv:math/1210.6432, 1211.6513,
1301.4161, 1303.7203.

We study Hodge theory for symplectic Laplacians on compact
symplectic manifolds with boundary. These Laplacians are novel as they
can be associated with symplectic cohomologies and be of fourth-order.
We prove various Hodge decompositions and use them to obtain the
isomorphisms between the cohomologies and the spaces of harmonic fields
with certain prescribed boundary conditions. In order to establish
Hodge theory in the non-vanishing boundary case, we are required to
introduce new concepts such as the J!Dirichlet boundary condition and
the J!Neumann boundary condition. When the boundary is of contact
type, these conditions are closely related to the Reeb vector field.
Another application of our results is to solve boundary value problems
of differential forms.

An isogeny graph is a graph whose vertices are principally polarized
abelian varieties and whose edges are isogenies between these varieties. In
his thesis, Kohel described the structure of isogeny graphs for elliptic
curves and showed that one may compute the endomorphism ring of an elliptic
curve defined over a finite field by using a depth first search algorithm
in the graph. In dimension 2, the structure of isogeny graphs is less understood and existing algorithms for computing endomorphism rings are very expensive.
We fully describe the isogeny graphs between genus 2 jacobians with complex multiplication,
with the assumptions that the real multiplication subring is maximal and
has class number one. We derive a depth first search algorithm for computing endomorphism rings locally at prime numbers,
if the real multiplication is maximal. To the best of our knowledge, this is the first DFS-based algorithm in genus 2. (Joint work with Emmanuel Thomé).

In biomolecular and colloidal systems, the dielectric environment often depends on the local ionic concentrations. Recent experiments and molecular dynamics simulations have revealed quantitatively such dependence, and indicated that the electrostatic interaction in a system with such a dependence can be significantly different from that predicted by theories assuming a uniform dielectric constant. In this work, we develop a mean-field model for the electrostatic interactions with ionic concentration-dependent dielectrics. We minimize the electrostatic free energy of ionic concentrations using Poisson's equation with a concentration-dependent dielectric coefficient to determine the electrostatic potential. Our analysis leads to the the corresponding generalized Boltzmann distributions of the equilibrium ionic concentrations that is quite different from the usual ones with a uniform dielectric constant We show by constructing an example that the free-energy functional is in fact nonconvex. This implies the existence of multiple local minimizers, a property that can be of physical significance. By numerical computations using our continuum model, we find many interesting phenomena such as the non-monotone ionic concentration profile near a charged surface, and the unusual shift of concentration peak due to the increase of surface charge density. It is clear that the effect of local dielectrics has a significant impact on the system and our models and results have potential applications to large biological systems. This is joint work with Bo Li and Shenggao Zhou.

I'll present an assortment of quantum phenomena that are actually quite easy to understand mathematically. I will provide the necessary background.

We prove asymptotic stability of shear flows close to the planar, periodic Couette flow in the 2D incompressible Euler equations. That is, given an initial perturbation of the Couette flow small in a suitable regularity class, specifically Gevrey space of class smaller than 2, the velocity converges strongly in L2 to a shear flow which is also close to the Couette flow. The vorticity is asymptotically mixed to small scales by an almost linear evolution and in general enstrophy is lost in the weak limit. Joint work with Nader Masmoudi. The strong convergence of the velocity field is sometimes referred to as inviscid damping, due to the relationship with Landau damping in the Vlasov equations. Recent work with Nader Masmoudi and Clement Mouhot on Landau damping may also be discussed.