Speaker: Gideon Zamba (U. Iowa)

Title: Recurrence of Subsequent Malignancies following Diagnosis of and Treatment for Hodgkin Lymphoma Diagnosis

Abstract: Hodgkin’s Lymphoma (HL) is a type of cancer that affects the lymphatic system and compromises the body’s ability to fight infection. HL typically starts in white blood cells. HL occurs when a specific type of cell, the Reed-Stenberg cell, is present in the host’s system, causing the body’s infection fighting cells to develop a mutation in their DNA. Each year, there are several thousand people in the United States and worldwide who develop HL. Although there are many prognostic factors for HL and post treatment malignancies, it has also been hypothesized that initial treatment after diagnosis may be associated with subsequent new malignancies or death. We explored the association between prognostic factors and subsequent malignancies using the Oncology Registry at the University of Iowa Hospitals and Clinics. In this exploration we account for subject random effect through a gamma frailty model for recurrent events, which acts multiplicatively and jointly on both the hazard of new malignancies and the hazard of death. The parameters of the model were iteratively estimated using a penalized marginal likelihood approach. The findings suggest a significant within subject correlation, and a significant treatment effect on both the hazard of recurrence and the hazard of death.

Speaker: Elizabeth Gross (San Jose State U.)

Title: Goodness of fit of statistical network models

Abstract: Exponential random graph models (ERGMs) are families of distributions defined by a set of network statistics and, thus, give rise to interesting graph theoretic questions. Indeed, goodness-of-fit testing for these models can be achieved if we know how to sample uniformly from the space of all graphs with the same network statistics as the observed network. Examples of commonly used network statistics include edge count, degree sequences, k-star counts, and triangle counts. In this talk, we will introduce exponential random graph models, discuss the geometry of these models, and show the role toric ideals play in determining the quality of model fit.

Speaker:

Leslie Hogben

Iowa State University and American Institute of Mathematics

Title:

Power domination and zero forcing: Using graphs to model real-world problems

Abstract:

A graph $G = (V, E)$ is a set of vertices $V = {1, dots , n}$ and set of edges $E$ of

two element sets of vertices. A graph can be used to model connections between

vertices, such as airline routes between cities, internet connections, a quantum

system, or an electric power network.

Power domination and zero forcing are related coloring processes on graphs.

We start with a set of vertices colored blue and the rest colored white. We apply

a color change rule to color the white vertices blue. A set of blue vertices that

can color all vertices blue by using the power domination color change rule (or

zero forcing color change rule) is called a power dominating set (or a zero forcing

set). Finding a such set allows us to solve various problems, and a minimum

such set can provide an optimal solution.

In an electric power network, a power dominating set (blue vertices) gives

a set of locations from which monitoring units can observe the entire network.

In a quantum system, a zero forcing set (blue vertices) gives a set of locations

from which the entire system can be controlled.

This talk will describe power domination and zero forcing processes on

graphs and some of their applications.

A Talk Story in Number Theory.

There is a childish misconception that the occupation of a professional mathematicians

is to operate with very big numbers. That is presumably primarily applicable to those who

do Number Theory. In this talk, I will show that this sometimes may be not too far from truth.

The talk is supposed to be entertaining and is directed to grad students willing to get a rough idea

about what it takes (and what it may give) to choose Number Theory as a research speciality.

Speaker: Claus Sorensen (UCSD)

Title: Local Langlands in rigid families

Abstract: The local Langlands correspondence attaches a representation of GL(n,F) to an n-dimensional representation of the Galois group of F (a local field). In the talk I will report on joint work with Johansson and Newton, in which we interpolate the correspondence in a family across eigenvarieties for definite unitary groups U(n). The latter are certain rigid analytic varieties parametrizing Hecke eigensystems appearing in spaces of p-adic modular forms. These varieties carry a natural coherent sheaf and we show that its dual fibers are built from the local Langlands correspondence by taking successive extensions; even at the non-classical points. Our proof employs certain elements of the Bernstein center which occur in Scholze’s trace identity. The first half of the talk is intended for a general audience with a limited background in number theory.

Speaker: Rohit Nagpal

Title: Stability in the high dimensional cohomology of certain arithmetic groups

Abstract: Borel-Serre duality relates high dimensional cohomology of arithmetic groups to the low dimensional homology of these groups with coefficients in the Steinberg representation. We recall Bykovskii’s presentation for the Steinberg representation and explain its connection to modular symbols. Next, we describe the Steinberg representation as an object in a symmetric monoidal category, and use its presentation to describe an action of the free skew commutative algebra. Finally, we perform a Gröbner-theoretic analysis of this action to obtain new information on the homology of certain arithmetic groups with coefficients in the Steinberg representation. For example, we show that the sequence of homology groups H_1(Gamma_n(3), St_n) exhibit representation stability. This is an ongoing project with Jeremy Miller and Peter Patzt.