## Fall 2018 – Summer 2019 – Abstracts

Wednesday, October 31, 2018.  Mathematics Colloquium.

Prof. Tyrone Crisp, Department of Mathematics and Statistics, University of Maine.
“Representations of finite groups: from $S_n$ to $GL_n$ and into the wilderness”
3:30 – 4:20 pm, Hill Auditorium, Barrows (ESRB). Snacks at 3:15pm.

Abstract: In representation theory one studies the ways in which an abstract group can be represented by linear transformations of a vector space. The case where the group is a symmetric group $S_n$ and the vector space is finite-dimensional over the complex numbers has been intensively studied since the beginnings of the subject. In this talk I shall explain how the well-understood theory for $S_n$ can be used to organize the representation theory of other families of groups, such as hyperoctohedral groups and finite general linear groups. I shall also present some work in progress which aims to apply similar techniques to families of groups whose representations we cannot reasonably expect to classify.

This talk will be aimed at a general mathematical audience.

Wednesday, November 6, 2017. Teaching workshop.

Prof. Natasha Speer and Jen Tyne, Department of Mathematics and Statistics, University of Maine.
“i-Clickers”
3:30 – 4:20 pm, Hill Auditorium, Barrows (ESRB). Snacks at 3:15pm.

Some faculty are using clickers for the first time, and others are considering using clickers in future semesters. This workshop will be focused on math classes, including how to manage clicker questions, what makes an effective math/stats clicker question, and more. Even if you have never thought about using clickers in your classroom, we welcome you to join us!

Wednesday, January 30, 2019. Mathematics Colloquium.

Prof. Robert Franzosa, Department of Mathematics and Statistics, University of Maine.
“Two Talks in One”
3:30 – 4:20 pm, Hill Auditorium, Barrows (ESRB). Snacks at 3:15pm.

Abstracts:
True/False Cards: A Hands-on Deductive Reasoning Calculator
The True/False deck of cards can be used for a hands-on approach to basic deductive reasoning topics typically seen in an introductory abstract mathematics course. I will show how the deck can be used to compare propositions for equivalence, identify tautologies, identify contradictions, construct truth tables, construct valid arguments, and solve logic puzzles.

What is a Walk a Game Worth?
The Baseball Simulator is a baseball simulation program that replays Major League Baseball games and seasons using team statistics. I will introduce the program and show how it can be used as a baseball analytics tool to answer questions like: How many more wins would a team have if they drew one more walk per game during the season

Wednesday, February 4, 2019. Mathematics Colloquium.

Dr. Joan Ferrini-Mundy, President, University of Maine and the University of Maine at Machias.
“Integrating Research, Policy, and Practice in Mathematics Education: What Does It Mean to “Make a Difference”? “
3:00 – 4:00 pm, Hill Auditorium, Barrows (ESRB). Refreshments will be served.

Abstract: What does it mean for educational research to “make a difference?” Using examples from mathematics education, I will explore relationships among basic, foundational, applied, and use-inspired research. Research on student learning, teaching, and instructional materials has impacted and informed federal and state policy, reform and transformation efforts, and educational practice both by design and by serendipity. We will discuss key grand challenges in education today, both in Maine and beyond, and the potential for research to have a role in their solution.

This colloquium is co-sponsored with the Maine Center for Research in STEM Education (RiSE Center)

Wednesday, March 6, 2019. Mathematics Colloquium.

Prof. Julian Rosen, Department of Mathematics and Statistics, University of Maine.
“How to take a picture of something very far away”
3:30 – 4:20 pm, Hill Auditorium, Barrows (ESRB). Refreshments will be served at 3:15pm.

Abstract: Very long baseline interferometry (VLBI) is a technique for imaging distant celestial objects. VLBI involves combining simultaneous observations from an array of telescopes spread across the globe, allowing much greater resolution than a single telescope could provide. However, recovering an image from VLBI data is mathematically difficult because the data is almost always sparse and noisy. In this talk, I will describe some of the mathematics of VLBI.

Wednesday, April 3, 2019. Mathematics Colloquium.

Prof. Timothy Boester, Department of Mathematics and Statistics, University of Maine.
“Scaffolding student thinking: two examples of describing changing quantities”
3:30 – 4:20 pm, Hill Auditorium, Barrows (ESRB). Refreshments will be served at 3:15pm.

Abstract: What types of questions or classroom experiences can help students learn how to describe changing quantities? This talk will connect two different projects focused on the research of student thinking of covariation, the “reasoning about values of two or more quantities varying simultaneously” (Thompson & Carlson, 2017).

First we’ll examine how a sixth grade classroom developed meta-representational competence of the slope of linear functions. Then we’ll turn our attention to how the Pathways Pre-Calculus curriculum, currently used in MAT 122, develops the concept of exponential growth.

Wednesday, April 17, 2019. Mathematics Colloquium.

Dr. Frank Thorne, University of South Carolina.
“An Analytic Perspective on Arithmetic Statistics”
3:30 – 4:20 pm, Hill Auditorium, Barrows (ESRB). Refreshments will be served at 3:15pm.

Abstract: Arithmetic statistics is the science of counting arithmetic objects –number fields, class groups, and so on. Often, problems can be separated into two parts: first, prove a “parametrization theorem”, connecting these objects to lattice point counting problems; second, carry out the lattice point counting problem. In this talk, I will give an overview of this subject area with a focus on the second part — how can we count lattice points efficiently, and what kinds of theorems can one expect to obtain as a result?

Friday, April 19, 2019. Graduate Seminar.

Jaeho Choi, MA Mathematics Candidate, University of Maine.
“Generalized Derivatives for Nonsmooth Problems”
3:00 – 4:00 pm, Room 421, Neville Hall.

Abstract: Derivative information is useful for many problems found in science and engineering that require equation solving or optimization. Driven by its utility and mathematical curiosity, researchers over the years have developed a variety of generalized derivatives. In this talk, we will focus our attention on Clarke’s generalized derivative for Lipschitzian functions, which roughly is the smallest convex set containing all nearby derivatives of a domain point of interest. Clarke’s generalized derivative possesses a strong theoretical and numerical toolkit analogous to that of the classical derivative. This includes, for example, nonsmooth equation-solving and optimization methods, as well as nonsmooth versions of the MVT and the implicit function theorem. However, it is generally difficult to calculate Clarke’s generalized derivative. We will discuss pros and cons of Clarke’s generalized derivative in the finite dimensional setting and recent tools developed to calculate Clarke’s generalized derivative in a straightforward way. We will end the talk by stating the goal of our work, which is to extend Clarke’s theory and their recent tools to Banach spaces so that they can be used to tackle problems that are naturally set in infinite dimensions.

Tuesday, April 23, 2019. Graduate Seminar.

Puspanjali Subudhi, MA Mathematics Candidate, University of Maine.
“The Conway-Maxwell-Poisson Distribution and its Application”
10:00 – 11:00 am, Room 421, Neville Hall.

Abstract: The Poisson distribution is generally employed to analyze discrete data. However it’s reliance on a single parameter limits its flexibility in many applications. In this talk we will present a data set where the Poisson distribution does not fit . To analyze such a data we will present more flexible model with more than one parameter. The structural properties of the proposed model will be presented and a data set using the new model will be analyzed.

Thursday, April 25, 2019. Mathematics Colloquium.

Kevin Roberge, Department of Mathematics and Statistics, University of Maine.
“A Story About Small and Large Things”
3:30 – 4:20 pm, Hill Auditorium, Barrows (ESRB). Refreshments will be served at 3:15pm.

Abstract: Are you at your limit with limits? Does your life need more infinitely large and infinitesimal numbers? Do you enjoy complicated semantic conversations in and around the foundations of mathematics? If you said yes to those questions, you might enjoy learning more about Internal Set Theory, created by Edward Nelson in the seventies as an attempt to recreate Abraham Robinson’s Nonstandard analysis starting from set theory. Nonstandard Analysis is a rigorous treatment of infinitesimal and infinitely large real numbers. Internal Set Theory pulls back the curtain and supposes that these nonstandard elements were there all along, not only within the real numbers but within any infinite set. We’ll begin and end with the Dirac delta function taking a circuitous tour of the amazing and the odd within Internal Set Theory.

Tuesday, May 7, 2019. Graduate Seminar.

Puspanjali Subudhi, MA Mathematics Candidate, University of Maine.
“Analysis of Survival Data by Weibull Conway-Maxwell Poisson”
10:00 – 11:00 am, Room 421, Neville Hall.

Abstract: In life testing and survival analysis, sometimes the components are arranged in series and parallel system and the number of components are unknown. This unknown number of components considered to be random , following an appropriate probability mass function. More specifically , this problem arises in cancer clinical trials where the number of metastasis cells (Clonogens), denoted by N , is unknown and the event occurs as soon as one of the clonogens metastasized. In the damage models, the number of cracks unknown and the event occurs as soon as the first failure occurs.
In this presentation we will present the survival data with baseline distribution, as Weibull and the distribution of N as Conway-Maxwell-Poisson distribution. This gives rise to four parameter in the model and increasing, decreasing , bathtub and upside bathtub failure rate.

Tuesday, May 7, 2019. Graduate Seminar.

Ariel Farber, MA Mathematics Candidate, University of Maine.
“Poisson Processes: Background and Beginning to Build Models”
12:30 am – 1:30 pm, Room 421, Neville Hall.

Abstract: Real-world events are often modeled using known probability distributions that behave similarly to the events themselves in nature. However, many distributions prove difficult to work with when developing such models. For this reason, Poisson processes are often utilized to model discrete events in continuous time. Characteristics of Poisson processes lend themselves to both simulating the behavior of events and deriving differential equations that describe the system. These characteristics will be presented and used to begin derivation of an epidemiological model.