Analysis Seminar : Alexander Volberg (Michigan State) @ Keller 402
Nov 21 @ 3:30 pm – 4:30 pm

Title : Poincaré type inequalities on Hamming cube via martingale inequalities.

Abstract : Harmonic analysis is intimately related with martingale estimates.
But there is another type of discrete analysis, namely, harmonic analysis on Hamming cube (the math. foundation of Big Data science) that seemed to be disjoint from this relationship. We show how many classical (and some new) estimates on Hamming cube follow from martingale estimates. We also show why this is related to solving certain non-linear PDE of Monge–Ampère type and with classical inequalities in Gaussian spaces.

Talk Story with Heiner Dovermann
Dec 1 @ 3:30 pm – 4:30 pm
Lei Liu’s Master presentation @ Keller Hall 401
Dec 8 @ 1:30 pm – Dec 8 @ 2:15 pm
Colloquium Paul Terwilliger (U. Wisconsin) @ Keller 401
Jan 12 @ 3:30 pm – 4:30 pm
Undergraduate Seminar: Gideon Zamba (U. Iowa) @ Keller 402
Jan 18 @ 3:00 pm – 4:00 pm

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.

Colloquium: Elizabeth Gross (San Jose State U.) @ Post 127
Jan 19 @ 3:30 pm – 4:30 pm

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.

Colloquium: Leslie Hogben (Iowa State U.) @ Post 127
Feb 1 @ 3:00 pm – 4:00 pm

Leslie Hogben
Iowa State University and American Institute of Mathematics

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

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.

Talk Story with Pavel Guerzhoy
Feb 9 @ 3:30 pm – 4:30 pm

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.