Extracting knowledge and providing insights into the complex
mechanisms underlying noisy high-dimensional data sets is of utmost
importance in many scientific domains. Networks are an example of
simple, yet powerful tools for capturing relationships among entities
over time. For example, in social media, networks represent
connections between different individuals and the type of interaction
that two individuals have. In systems biology, networks can represent
the complex regulatory circuitry that controls cell behavior.
Unfortunately the relationships between entities are not always
observable and need to be inferred from nodal measurements.

I will present a line of work that deals with the estimation of
high-dimensional dynamic networks from limited amounts of data. The
framework of probabilistic graphical models is used to develop
semiparametric models that are flexible enough to capture the dynamics
of network changes while, at the same time, are as interpretable as
parametric models. In this framework, estimating the structure of the
graphical model results in a deep understanding of the underlying
network as it evolves over time. I will present a few computationally
efficient estimation procedures tailored to different situations and
provide statistical guarantees about the procedures. Finally, I will
demonstrate how dynamic networks can be used to explore real world
systems.

An infinite dimensional Lie algebra is locally finite if every
finitely generated subalgebra is finite dimensional. On one extreme are the
simple, locally finite Lie algebras. We provide structure theorems which
describe such algebras over fields of positive characteristic. On the other
extreme are the maximal, locally solvable Lie algebras, which are Borel
subalgebras. We provide a theorem which shows that such Lie algebras are
stabilizers of maximal, generalized flags, which is a generalization of
Lie's theorem. We will finish by describing some new directions in the
study of these Lie algebras.

How does one measure area? As an example, how can one determine the area of a region on a map for the purpose of real estate appraisal? Wouldn't it be great if there were an instrument that would measure the area of a region by simply tracing its boundary? It turns out that there is such an instrument: it is called a planimeter. In this talk we will discuss a particular type of planimeter called the compensating polar planimeter. There will be a little bit of history and some analysis involving line integrals and Green's theorem. Finally, there will be a chance to see and touch actual examples of these fascinating instruments from the speaker's collection.

We consider a random model for directed graphs whereby an arc is placed from one vertex to another with a prescribed probability
$p_{ij}$ which may vary from arc to arc. Using perturbation bounds as well as Chernoff inequalities, we show that the stationary
distribution of a Markov process on a random graph is concentratednear that of the “expected” process under mild conditions. These
conditions involve the ratio between the minimum and maximum in- and out-degrees, the ratio of the minimum and maximum entry in the
stationary distribution, and the smallest singular value of the transition matrix. Lastly, we give examples of applications of our
results to known models of directed graphs.

I will talk about work in progress joint with Yuguang Zhang,
trying to relate Boucksom et al's solution to the non-archimedean Monge-Ampere
equation on K3 surfaces to the real Monge-Ampere equation on the skeleton.

In this talk, we will first introduce some basic fact on the Maximal
slice and its brief history. we will also try to review some existence
and non-existence result in Minkowski space. Then, we will show that
the Bernstein Theorem in ADS space fails.

The integers do not admit any nontrivial derivations. We will explain
how the operation $x \to$ ${x-x^p \over p}$ can be thought of as a replacement for
the derivative operator on the integers. After the introduction we hope
to explain some recent work on the meaning of "linearity" in this theory.

I will begin with an introduction to the subfactor
classification program, which has two main focuses: restricting the
list of possible principal graphs, and constructing examples when the
graphs survive known obstructions. I will discuss recent joint work
with Liu and Morrison which classifies 1-supertransitive subfactors
without intermediates with index in $(3+\sqrt{5},6.2)$. We show there
are exactly 3 examples corresponding to a BMW algebra and two
"twisted" variations.

I give a bad math talk. Over the past several years, I have kept a list of all of the bad things speakers have done during their talks, and I will incorporate them into a single horrible talk and discuss each of the bad aspects afterwards. In the end, it will be entertaining and informative; and hence, not such a bad math talk after all.

Fano varieties are in some sense the simplest type of
algebraic varieties. They are the algebraic analogue of manifolds
with positive curvature, such as spheres. In low dimensions one can
classify Fano varieties (where for an algebraic geometer low means up
to dimension three) and as the dimension increases, they form bounded
families, so that one can in principle classify Fano varieties in all
dimensions.

In this talk we explain some of the known and conjectured results,
both for an explicit classification, and for some of the boundedness
results.