Category: Events

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.

Title: The World’s Greatest Game

Abstract: Analogy pervades all our thinking, our everyday speech and our trivial conclusions as well as artistic ways of expression and the highest scientific achievements.” This quote, from George Pòlya, is from his book, “How to Solve It”. If you have a problem that you want to solve, this is the book and, possibly, the talk for you. We’ll follow Pòlya’s four-step method as we discuss questions from different areas: probability, geometry and life and, as a plus, we’ll learn to visualize something people often think is imaginary.

Bio: Pamela Gorkin is a Professor in the Mathematics Department here at Bucknell.

Title: Twitter’s Influence on TV Ratings, And Other TV Mathematics

Abstract: Nielsen’s TV Ratings are used as the currency with which key business decisions are made across the media industry. What TV programs remain on the air, which advertisements you see during commercial breaks, and when you are able to watch your favorite shows on Hulu are all questions answered by analyzing ratings and other Nielsen data. Recent technology has rapidly changed how and when people watch TV, thus quickly increasing the demand for enhanced data to give TV Networks and Advertisers a thorough understanding of the current TV landscape. Using various forms of TV Mathematics, exciting new conclusions, like whether Twitter influences TV Ratings, can be made.

Bio: Allison Gibson, an Associate Media Analytic Consultant at Nielsen, graduated from Bucknell in May 2013 with a double major in Mathematics and Italian Studies and a minor in Film Studies. While at Bucknell, she was a Tour Guide and Tour Guide Student Coordinator, Co-Founder and Musical Director of The Offbeats A Cappella group, and Vice President of Food (Public Relations) for the Mathematical Association of America. Allison has been working at Nielsen, a Fortune 500 Company known for the Nielsen TV Ratings system, since graduating about a year and a half ago. She started her career as a Research Analyst providing a wide variety of media-related data to many of Nielsen’s TV, Advertiser, and Agency clients. As of August of this year, she is an Associate Media Analytic Consultant working primarily with clients like FOX Networks, AMC Networks, Tech companies (i.e. Amazon, EBay) and the Telecom sector (i.e. Verizon, AT&T).