Synthetic aperture radar (SAR) uses relative motion to produce fine resolution images from microwave frequencies and is a useful tool for regular monitoring and mapping applications. Unfortunately, if target distance is estimated poorly, then phase errors are incurred in the data, producing a blurry reconstruction of the image. In this talk, we introduce a multistatic methodology for determining these phase errors from interferometry-inspired combinations of signals. To motivate this, we first consider a more general problem called phase retrieval, in which a signal is reconstructed from linear measurements whose phases are either unreliable or unavailable. We apply certain ideas from phase retrieval to resolve phase errors in SAR; specifically, we use bistatic techniques to measure relative phases and then apply a graph-theoretic phase retrieval algorithm to recover the phase errors. We conclude by devising an image reconstruction procedure based on this algorithm, and we provide simulations that demonstrate stability to noise.

In the classification of (commutative) projective surfaces, one first classifies minimal models for a given birational class, and then shows that any surface can be blown down at a finite number of curves to obtain a minimal model.

Artin has proposed a similar programme for noncommutative surfaces (that is, domains of $GK$-dimension 3). In the generic ``rational'' case of rings birational to a Sklyanin algebra, the likely candidates for minimal models are the Sklyanin algebra itself and Van den Bergh's quadric surfaces. We show, using our previously developed noncommutative version of blowing down, that these algebras are minimal in a very strong sense: given a Sklyanin algebra or quadric $R$, if $S$ is a connected graded, noetherian overring of $R$ with the same graded ring of fractions, then $S=R$.

This is a joint work with Rogalski and Stafford.

2015 was the Centinnial year of Einstein's General Theory of Relativity, and fittingly concluded with the discovery of gravitational waves, which he had predicted. Despite knowing the key physical principles, Einstein was only able to formulate his theory after learning differential geometry from mathematician Marcel Grossmann in 1912. In a sense, General Relativity simply $is$ applied differential geometry. This talk will sketch the key ideas of differential geometry and how they apply to Einstein's theory of gravity. The presentation will emphasize ideas and pictures, rather than equations.

In this talk we will try to discuss the
following questions:

1. What is the space of distributions? What are its key
properties? Why do we need it? How do we use it?

2. What is a function space? What are the nice properties that
we would like our function spaces to possess?

3. Why is the Gagliardo seminorm defined the way it is?

4. How do interpolation theory and Littlewood-Paley theory come
into play in the study of Slobodeckij spaces?

5. For what values of $s$ and $p$, $\partial^\alpha: W^{s,p}(\Omega)\rightarrow
W^{s-|\alpha|,p}(\Omega)$ is a well defined bounded linear
operator for all $\alpha\in \mathbb{N}_0^n$? Why do we care about
this question?

The asymmetric simple exclusion process (ASEP) is a model from statistical physics that describes the dynamics of particles hopping right and left on a finite 1-dimensional lattice. Particles can enter and exit at the left and right boundaries, and at most one particle can occupy each site. The ASEP plays an important role in the study of non-equilibrium statistical mechanics and has appeared in many contexts, for instance as a model for 1-dimensional transport processes such as protein synthesis, molecular and cellular transport, and traffic flow. Moreover, it displays rich combinatorial structure: one can compute the stationary probabilities for the ASEP using fillings of certain tableaux. In this talk, we will discuss some of the combinatorial results from the past decade as well as recent developments, including combinatorial formulae for a two-species generalization of the ASEP and a remarkable connection to orthogonal polynomials. This talk is based on joint works with X. Viennot and separately with S. Corteel and L. Williams.