Geneseo Mathematics Colloquium Schedule
Monday, September 22, 3:00-3:50pm
Tanzy Love, University of Rochester Medical Center
Department of Biostatistics and Computational Biology
Combining Repeated Measurements on Distinct Scales with Censoring
We analyze data collected in a somatic embryogenesis experiment carried out on Zea mays (corn) at Iowa State University. The main objective of the study was to identify the set of genes in maize that actively participate in embryo development and to do so, embryo tissue was sampled and analyzed at various time periods and under different mediums and light conditions. As is the case in many microarray experiments, the operator scanned each slide multiple times in order to find the slide-specific ‘optimal’ laser and sensor settings. The multiple readings of each slide are repeated measurements on different scales with differing censoring; they cannot be considered to be replicate measurements in the traditional sense. Yet it has been shown that the choice of reading can have an impact on genetic inference. We propose a hierarchical modeling approach to estimating gene expression that combines all available readings on each spot and accounts for censoring in the observed values. We assess the statistical properties of the proposed expression estimates using a simulation experiment. As expected, combining all available scans using an approach with good statistical properties results in expression estimates with noticeably lower bias and root mean squared error relative to other approaches that have been proposed in the literature. Inferences drawn from the somatic embryogenesis experiment which motivated this work changed drastically when data were analyzed using the standard approaches or using the methodology we propose.
Friday, October 17, 4:00-5:00pm
Farbod Shokrieh, Cornell University
Chip-firing games and Riemann-Roch theory for graphs
A "divisor" on a graph is simply a configuration of dollars (integer numbers) on its vertices. In each step of a "chip-firing game" you are allowed to select a vertex and then lend one dollar to each of its neighbors, or borrow one dollar from each of its neighbors. The mathematical structure arising from this process is very rich and beautiful. For example, this process produces a canonical abelian group whose size is the number of spanning trees of the graph. Moreover, in this setting, there is an analogue of the classical "Riemann-Roch theorem". This talk is mostly expository, so it will be self-contained and aimed at a general mathematical audience.
Thursday, October 30, 2:30-3:30pm
Paul Wenger, Rochester Institute of Technology
Unique Saturation and Eigenvalue Methods for Graphs
There is a long history of using tools from linear algebra for problems in graph theory. In this talk, we present various results that are proved by analyzing the eigenvalues of the adjacency matrix of a graph. Two classic results in this area are the Friendship Theorem of Erdős, Rényi, and Sós, and the Hoffman-Singleton characterization of Moore graphs of diameter 2. We will use uniquely saturated graphs to explore eigenvalue techniques and demonstrate a surprising connection between Moore graphs and friendship graphs.
Wednesday, November 5, 2:30-3:30pm
Tony Macula, SUNY Geneso
An Example of Using Maple in Abstract Algebra
This is a mathematical software talk that addresses topics accessible to students who have successfully completed a course in Linear Algebra. I will discuss how the Maple mathematical software package can be used to exhibit finite fields and perform matrix computations over those fields.
Wednesday, November 19, 2:30-3:45pm
Gary Towsley and Jeff Johannes, SUNY Geneso
A Concise History of Calculus
A lively overview of over two thousand years of calculus history. Not only who-did-what along the way, but the cultural and sociological causes and effects of the calculus. Strongly recommended for anyone who has taken or is taking calculus.
Friday, November 21, 2:30-3:30pm
Elizabeth Cherry, Rochester Institute of Technology
Mathematical Modeling of Cardiac Arrhythmias
Under normal conditions, electrical waves propagate through the heart in a coordinated manner to initiate an efficient mechanical contraction that pumps blood throughout the body. In pathologic states, the coordinated propagation of these electrical waves can break down and degenerate into localized, ineffectual contractions associated with dangerous cardiac arrhythmias. Studying the mechanisms responsible for disruption of cardiac wave propagation experimentally is difficult for many reasons, including limited access to quantities of interest and biological variability. Mathematical modeling of cardiac electrical wave propagation can overcome these obstacles but presents a new set of challenges. In this talk, I will discuss the basics of cardiac arrhythmias as well as experimental techniques to study them. I will show how mathematical models based on differential equations can be used to describe the propagation of electrical waves in cardiac tissue as well as how these models can be solved computationally, along with limitations to this type of approach. Finally, I will give examples of how mathematical modeling can help to elucidate the dynamics of cardiac arrhythmias.
Wednesday, December 3, 2:45-3:45pm
Olympia Nicodemi, SUNY Geneso
Learning with Leibniz
As a follow-up to our annual survey of the History of Calculus, I will take a closer look at how Leibniz thought about his new invention. The goal of the talk is to see the Fundamental Theorem of Calculus play out in his terms. Similar to how we think about it? Different from how we think about it? YES!