Author: Alex Robinson

Title: From Congruent Numbers to Modular Forms

Abstract: A positive integer is called a congruent number if it is the area of a
right triangle with rational sides. The problem of giving a criterion for
deciding if a number is congruent has been open for hundreds of years. The
best answer known was given by Tunnell in 1983, using many deep results
from modern Number Theory. His work will give a completely satisfactory
answer, once the Birch and Swinnerton-Dyer conjecture gets proved.

In this talk we will introduce, in a way as friendly as possible, the main
ingredients needed to understand Tunnell’s result: elliptic curves,
modular forms, and some deep theorems concerning them.

Title: Piecewise Deterministic Markov Processes and Metal Grain Coarsening

Abstract: In material science, individual metal grains obey surprisingly simple rules.  However, geometric considerations can create difficulties when attempting to analyze the bulk properties of metals.  In this talk, we’ll describe a mean field model using piecewise deterministic Markov processes which converts the geometric problem of grain evolution to one of analysis and stochastic processes.  In particular, we’ll show that densities of grains approach a law of large numbers described by a partial differential equation.

Title: How Analytics Professionals Make the World Go Round

Abstract:

It’s hard to open a business magazine, walk through an airport or even participate in an executive meeting and NOT see or hear reference to analytics. Recognized as the currency of business, mathematics or analytics are empowering decision-making at new levels. A trend that started with CIOs is spreading throughout the C-Suite – Everyone wants ANALYTICS!

What exactly are these analytics professionals doing? What types of real-world problems are they solving? Are they actually applying the math, statistics and operations research tools they learned in their courses? What other skills or certifications do they have?  What opportunities are there for graduate studies in analytics?
Hear from Anne Robinson and John Williamson of Verizon Wireless.  Anne Robinson holds a Ph.D. in Industrial Engineering from Stanford University and served as President of INFORMS, the largest professional organization for both practitioners and academics in the field of Analytics/Operations Research.  John Williamson holds a M.B.A. in Supply Chain Management from Penn State University.  There will be an opportunity to speak with the presenters following the talk.

Title: Hierarchical Social Network Models with Applications in the Social Sciences

Abstract: The term “social network analysis” includes most quantitative methods for analyzing relational data and these methods are both exploratory and inferential. For inference, there are a variety of social network statistical models to represent the stochastic nature of network relationships.  In this talk, I will present social network models that are written as Hierarchical Bayes models and describe how these generative models can be used in the social sciences which often involve multiple partially exchangeable networks.

Title: Lattice paths between two boundaries

Abstract: Dyck paths are lattice paths with steps N=(0,1) and E=(0,1) starting
at (0,0), ending at (n,n), and never going below the diagonal y=x.
Among the many interesting facts known about Dyck paths, one is that
the parameters ‘number of E steps at the end’ and ‘number of returns
to the diagonal’ have a symmetric joint distribution, meaning that to
each Dyck path we can bijectively associate another one where these
parameters are interchanged.

I will show that this symmetry property applies not only to Dyck
paths, but more generally to lattice paths with N and E steps that lie
between any two fixed boundaries. Finally, I will discuss how these
lattice paths are related to other objects in combinatorics, such as
matroids, semistandard Young tableaux and k-triangulations.

This is joint work with Martin Rubey.

Title: Learning from systematic descriptions of mathematics professional development

Abstract:  In this talk I present emerging results from a systematic
review of publications on mathematics professional development. The
research team reviewed over 170 papers published between 1992 and 2010
to address the following research questions: What do we know about the
design and conduct of mathematics PD being studied by researchers and
how are these PD characterized in research reports? The conceptual
framework included six elements: theory, context, goals, content,
format, and activities.

Title: Random Groups at Density 1/2

Abstract: Random groups in the density model (with density 0<d<1) have
presentations with a random set of (2m-1)^{dk} relators of length k on
m generators. The classic theorem in the density model states that for
d>1/2, random groups are asymptotically almost surely trivial or
isomorphic to Z/2Z, while for d<1/2, random groups are asymptotically
almost surely infinite hyperbolic. This summer our research group
studied random groups at d=1/2 and found both infinite hyperbolic
groups and trivial groups are generic, depending on how we tuned
certain parameters.