Fall 2010 Colloquium
Talks (unless otherwise indicated) are in Olin 1 from 4–5 PM on Mondays. Refreshments begin at 3:30. If you would like to talk, please email Fernando Gouvêa or Jim Scott. We are just beginning to line up speakers for Spring 2011.
| Schedule | |
| Sept. 20 |
Fernando Q. Gouvêa Colby College Why 1+2+3+4+… = –1/12 More |
| Sept. 27 |
Stephen D. Sears Maine CDC Unlocking Public Health Surveillance in Maine More |
| Oct. 4 | No colloquium talk. |
| Oct. 18 |
David Mumford Brown University Newton and Leibniz Scooped: What Happened in the Spice-Laden Hills of Kerala in 1400? More |
| Oct. 25 |
Aba Mbirika Bowdoin College From Lewis Carroll to an Interesting Conjecture — the Rabbit Hole Exposed!? More |
| Nov. 1 |
Robert Franzosa University of Maine Orono The Games of Fencepost and Hex and How They Help Prove the Brouwer Fixed Point Theorem More |
| Nov. 8 |
Katherine Socha Director of Education Policy, Math for America Sea Battles, Benjamin Franklin's Oil Lamp, and Jellybellies More |
| Nov. 15 |
Peter Wong Bates College Japanese Temple Geometry — the tradition of sangaku in Edo Japan More |
Nov. 22 |
| Nov. 29 | |
| Dec. 6 | |
Abstracts
September 20
Why 1+2+3+4+…=–1/12
Fernando Q. Gouvêa, Colby College
Both Euler and Ramanujan agreed that this is correct. Come find out why, and why it might actually matter.
September 27
Unlocking Public Health Surveillance in Maine
Stephen D. Sears, Maine CDC
Have you ever wondered about public health surveillance in Maine?
How do we follow disease trends?
How do we gather information on Influenza or Lyme Disease or see if
heat illnesses increase in the summer?
This presentation will describe the Maine CDC data surveillance program, review collected public health information, describe a clinical case of possible public health importance and discuss the structure and authority of public health surveillance in Maine. Examples will include Influenza, Brucella, heat illness and Lyme Disease. All will describe the routine and emergency response to infections and environmental disease in Maine.
October 18
Newton and Leibniz Scooped: What Happened in the
Spice-Laden Hills of Kerala in 1400?
David Mumford, Brown University
It is universally accepted wisdom that Newton and Leibniz "invented" calculus. Only recently has an amazing book been translated from Malayalam which shows that a small group of Brahmins in a cluster of villages on the Nila river dug deeply into both mathematics and astronomy, integrating, differentiating and expanding trigonometric functions as well as anticipating much of Copernicus' work. I will survey some aspects of the two millenia long tradition of Indian math and describe this, its crowning achievement.
October 25
From Lewis Carroll to an Interesting Conjecture
— The Rabbit Hole Exposed!?
Aba Mbirika, Bowdoin College
In 1866, Reverend Charles Lutwidge Dodgson (better known as Lewis Carroll) devised a way to compute determinants of an n×n matrix using only determinants of 2×2 minors. His algorithm became known as “condensation of determinants.” Much rich history surrounded the time before and after Carroll's contribution.
In the early 1980s, Robbins, Rumsey and Mills looked down the rabbit hole and discovered a peculiar but rather fascinating object there in Wonderland, namely, alternating sign matrices. These objects are natural generalizations of permutation matrices, which we know much about. However, simply counting the number of n×n alternating sign matrices proved to be a formidable task. It soon became apparent that some proposed conjectures absolutely had to be true, but the proofs eluded all until very recently. The proof (in 1995) brought together aspects of invariant theory, partitions and plane partitions, symmetric functions, hypergeometric series, and statistical mechanics.
Knowing how to compute a 2-by-2 determinant (or being willing to learn) is the only prerequisite for the talk. This talk will be about the road to this proof and the beauty and simplicity of the conjectures. Robbins wrote, “These conjectures are of such compelling simplicity that it is hard to understand how any mathematician can bear the pain of living without understanding why they are true.” Want to go down the rabbit hole? Let's take a look!
November 1
The Games of Fencepost and Hex and How They Help Prove
the Brouwer Fixed Point Theorem
Robert Franzosa, University of Maine Orono
We will explore a couple of games (Fencepost and Hex) and the Brouwer Fixed Point Theorem, and we will see how properties of the games can be used to prove the theorem.
November 8
Sea Battles, Benjamin Franklin's Oil Lamp, and
Jellybellies
Katherine Socha, Director of Education Policy, Math for America
"During our passage to Madeira, the weather being warm, and the cabbin windows constantly open for the benefit of the air, the candles at night flared and run very much, which was an inconvenience. At Madeira we got oil to burn, and with a common glass tumbler or beaker, slung in wire, and suspended to the cieling of the cabbin, and a little wire hoop for the wick, furnish'd with corks to float on the oil, I made an Italian lamp, that gave us very good light...." (Benjamin Franklin, December 1, 1762, letter to John Pringle)
Observations of real phenomena have led to mathematical modeling of surface water waves, interfacial waves, and Lagrangian coherent structures, among other examples. This expository talk will provide a quick tour of the (mostly advanced undergraduate level) mathematics needed to describe idealized versions of the rings formed by striking a surface of water with a large object (like a bomb), the oil-water waves observed by Founding Father Benjamin Franklin on his voyage to Madeira, and the motion of nutrient-laden water being swept into the underbelly of swimming jellyfish.
November 15
Japanese Temple Geometry — the tradition of sangaku in
Edo Japan
Peter Wong, Bates College
The Japanese people have a custom of dedicating painted votive plaques to shrines or temples, expressing their thanks and offering their prayers. During the Edo period (1603–1867), when Japan was almost completely isolated from the western world, mathematicians, professional and amateur alike, dedicated votive tablets (sangaku) on which mathematical problems were written and solved. Most sangaku problems were geometric, usually with beautifully drawn colored figures. The practice of hanging sangaku tablets, an early form of publication, helped popularize wasan (traditional Japanese mathematics) in Edo Japan. In this lecture, I will give a brief introduction to sangaku and its history.