Geneseo Mathematics Colloquium Schedule
Thursday, February 3, 4:00 - 4:50pm
Olympia Nicodemi, SUNY Geneseo
How many real numbers are there?
In this talk we will find out if infinity comes in sizes and we will find out how many really real numbers there are. We hope that it will be accessible and interesting to all students, majors or not.
Wednesday, February 16, 2:30 - 3:20pm
Douglas Haessig, University of Rochester
An introduction to number theory, from a p-adic point-of-view
Many number theorists are interested in the solution sets of multivariable polynomial equations. For example, Fermat's last theorem asks about integer solutions of the polynomial equation xn + yn = zn. In this talk, we will see how the solution set of a conic (quadratic equation) depends on the domain of the variables. This will lead us into defining "p-adic numbers." After discussing a few theorems to see how p-adic analysis works, and how p-adic geometry looks, we will employ the p-adics to count the number of (finite field) solutions to a famous cubic equation using differential equations.
Wednesday, March 2, 2:30 - 3:20pm
Jane Cushman, Buffalo State University
Which cup material holds hot water the hottest, the longest?
Using a temperature probe, TI-84, boiling water and various cup material (Styrofoam, paper and ceramic), data will be collected. The data will be shared with the participants and everyone will analyze the data to determine which cup material held the hot water the hottest and longest. Which do you think will?
This talk is aimed at pre-service teachers and mathematics majors; there are no pre-requisites.
Thursday, March 24, 4:00 - 4:50pm
Jonathan Hoyle, Eastman Kodak
A Mathematician in the Real World
"How much Mathematics is really used out there in the real world?" The answer to that question of course varies, depending on your definition of "real world". Obviously, a different level of Mathematics would be used by a statistician than would be by the owner of a pizza parlor. My "real world" is one as a software developer, and I will talk about some of the Mathematics with which I have been involved. These include work at DuPont, Kodak, and writing forensic DNA software used to identify victims of the World Trade Center attacks on 9/11.
Thursday, April 7, 4:00 - 4:50pm
Ryan Gantner, St. John Fisher College
It’s time to play Hackenbush!
Let’s play a game. The only things we’ll need are several red and blue sticks. Oh, and some interesting mathematical theories. The game is called “Hackenbush”, and it is fairly simple to play. In this presentation, we’ll develop some theory of partisan combinatorial games to help us better understand what is the best way to play the game. It turns out that the game positions can be given number values in a meaningful way. Then, we can ask what happens when randomness is added to the game, which is an ongoing area of research.
Level: No fancy mathematical concepts are used, though we will encounter the idea of a probability distribution on a set of numbers.
Thursday, April 21, 4:00 - 4:50pm
Bonnie Jacob, Rochester Institute of Technology
A discrete challenge based on optical imaging
Diffuse optical imaging is a method of imaging that consists of reconstructing the optical parameters inside a medium using data gathered at the boundary. Optical imaging has wide appeal in medical applications in particular because the light that is used does not harm the patient. Despite the appeal of optical imaging, however, difficulty in obtaining high quality images has prevented it from being widely used in clinics. One way to get a better reconstruction is to choose the source cleverly.
Motivated by this problem, we consider a discrete version of the typical optical tomography model: a network in which each node is designated as either "scattering" or "absorbing." We consider how the structure of the network, the location of the different classes of nodes in the network, and the initial location of the signal --- the "source"--- all influence our ability to recover each node's classification.
Helpful co-requisites: This talk will relate well to topics from an elementary linear algebra course.