Lectures on Elections and Fair Division
Steven Brams, Professor of Politics at New York University, will give twp public lectures
at Hobart and William Smith Colleges, on October 2 and 3. The lectures will deal with the mathematics of election and of fair division.
The first lecture is titled, "Is There a Better Way to Elect a President?"
and will be presented at 7:00 PM on Tuesday, October 7, in the Geneva Room.
This talk is based on Professor Brams' recent article of the same name in which he describes the properties of approval voting, where voters can approve as many candidates as they like in a multicandidate election. This system has been adopted by the Mathematical Association of America (MAA), the American Mathematic Society (AMS) and several other professional societies. Brams argues that this system is a much simpler and more practical option than the plurality U.S. voting system. In addition, he will discuss other systems such as ranking systems and grading systems which have been widely discussed in mathematical fields.
The second lecture is titled, "The Win-Win Solution:
Guaranteeing Fair Shares to Everybody" and will be presented in Room Napier 201
at 4:00 PM on Wednesday, October 3. Professor Brams describes this talk as follows: Cutting up a cake, dividing up the property in an estate, determining the border in an international dispute--such problems of fair division are ubiquitous. Beginning with "I cut, you choose," I will illustrate how rigorous methods can be applied to the analysis of a variety of procedures for allocating goods (or "bads" like chores), or for deciding who wins on what issues in a dispute. In particular, I will focus on procedures which provide "envy-free" allocations, in which everybody thinks he or she received the largest portion and hence does not envy anybody else.
Posted 26 September 2012
Movie Night: The Proof
For over 350 years, some of the greatest minds of science struggled to prove what was known as Fermat's Last Theorem -- the idea that a certain simple equation had no solutions. Now hear from the man who spent seven years of his life cracking the problem, read the intriguing story of an 18th century woman mathematician who hid her identity in order to work on Fermat's Last Theorem, and demonstrate that a related equation, the Pythagorean Theorem, is true.
Andrew Wiles devoted much of his career to proving Fermat's Last Theorem, a challenge that perplexed the best minds in mathematics for 300 years. In 1993, he made front-page headlines when he announced a proof of the problem, but this was not the end of the story; an error in his calculation jeopardized his life's work. In this interview, Wiles recounts how he came to terms with the mistake, and eventually went on to achieve his life's ambition.
The department will show the movie on Thursday, December 1st at 7:30pm in Albright Auditorium. Refreshments will be provided. Bring your friends!
Posted 23 November 2011
If Copernicus and Kepler Had Computers: An Introduction to Model-Building and Computational Science
On Thursday, November 17th at 5:00pm, Dr. Charles Van Loan, a SIAM Visiting Lecturer, will give a talk in Napier 201 that connects mathematics and computer science. If you watch Mars against the backdrop of the fixed stars, then night after night you'll see rather steady progress across the zodiac. But every so often, the planet appears to "back-up" before continuing on its forward trek. This periodic, retrograde motion wreaks havoc with a model of the solar system that places each planet on a steadily rotating circle with Earth at the center. Ptolemy did a pretty good job patching up the model by placing each planet on a small rotating circle whose center is on the rim of a larger rotating circle. The path traced out is called an epicycle and it offers some explanation for Mars' orbital wanderings. The epicycle model lasted for centuries until Copernicus set the record straight by suggesting that the Earth revolved around the sun along with the other planets. But would he have been so bold a scientist if he had access to 2011 computers? Or would he have just mouse-clicked his way into fame, developing a simulation package that supported further tinkering with the Ptolemaic model? (Refreshments will be served.)
Posted 11 November 2011
A Mathematical Model of T Cell Exhaustion Caused by HBV/HDV
On Wednesday, November 9th at 4:30pm, Hobart Mathematics Major Yaoxin Liu '12 will discuss his summer research project in Napier 201. In patients with chronic hepatitis B infection, the immune system becomes exhausted, losing its effectiveness over time. Co-infection with another virus, Hepatitis Delta, reduces the amount of HBV in the blood, and so may relieve the exhaustion. During the Summer Research Program last summer, Yixiao Sha, Yaoxin Liu and Prof. Jonathan Forde developed an ordinary differential equation model of the interactions of these two viruses and the immune system to study the effect of a second infection on immune exhaustion. Sha, Liu and Forde started by studying the four dimensional model with only HBV infection, and then added the second virus, HDV. They also analyzed various steady states and their stability for both systems. All the stability conditions are found for the four dimensional system with only HBV infection. For the five dimensional system with HDV, numerical simulations show the existence of positive steady states representing chronic coinfection. The model suggests that co-infection does not reduce the exhaustion level, but increases damage due to general inflammation. (Refreshments will be served beforehand.)
Posted 4 November 2011
Mathematical Models of Bone Biochemistry with Applications to the Treatment of Osteoporosis
On Wednesday, October 26th at 4:30pm in Napier 201 the Department of Mathematics and Computer Science will host Dr. David Ross of Rochester Institute of Technology. Dr. Ross is a SIAM Visiting Lecturer and will be giving a talk entitled: "Mathematical Models of Bone Biochemistry with Applications to the Treatment of Osteoporosis".
In humans and other mammals the skeleton is continuously remodeled, that is, dissolved and rebuilt; human bone has an annual turnover rate of about 10 percent. Understanding the biochemical processes of bone remodeling is important to the development of treatments for the disease osteoporosis, which is characterized by low bone mass, and which puts those who have it at risk of bone fractures. Osteoporosis results from an imbalance in the biochemical remodeling process, when resorption-the chemical breakdown of old bone-outstrips the formation of new bone. The most common cause of osteoporosis is age-related hormone change, the reduction of estrogen in women after menopause, and the reduction of testosterone in older men. Roughly 20 percent of women over the age of 50 have osteoporosis.
In this talk Professor Ross will discuss dynamical system models of bone remodeling that are used to simulate bone remodeling and to study the effects of various treatments for the condition. He will focus on the ways in which the dynamical systems capture the important biochemical features of the remodeling process, and he will discuss modeling methodology and the ways in which models are used. (Refreshments will be served beforehand.)
Posted 20 October 2011
Two-faced: The Cantor set and notions of size
The department will host the first colloquium of the semester with Dr. Emilie Wiesner of Ithaca College speaking about the Cantor set. The Cantor set is a specially constructed infinite set; it has earned its name from an appearance in an 1883 paper of the mathematician Georg Cantor. The Cantor set has many remarkable properties, and Dr. Wiesner will be talking about a few of them. In particular, she'll discuss how two ways of defining size ("measure" and "cardinality") lead to two very different ideas of how big this set really is! The talk will take place on Thursday, September 29th at 4:45pm in Napier 201. Refreshments will be served beforehand.
Posted 23 September 2011
Save the Date!
Math/CS faculty, majors, and minors: The Mathematics and Computer Science Department's Annual Dinner will be held on Thursday, April 21st in the Barn. Mark your calendars! Come to celebrate another great year of mathematics and computer science and congratulate this year's prize winners! Hope to see you there!
Posted 12 March 2011
Colloquium: VIREOS: An Integrated, Bottom-Up, Educational Operating Systems Project with FPGA Support
On Thursday, March 3rd at 4:45pm in Napier 201, Prof. Marc Corliss will share results from his recent work. This talk will present the VIREOS project, a new operating system designed specifically for the classroom. VIREOS is a simple, Unix-like, operating system, which runs on the Larc educational architecture. A VIREOS/Larc system can either be simulated or run on a pre-configured FPGA. The VIREOS project is
well integrated with an introductory computer architecture course (using Larc) and the assignments are structured in a similar fashion: using a bottom-up approach. The project includes several resources available on the Web, which help reduce the overhead of adopting VIREOS. Finally, VIREOS has been used in one operating systems course already, and, overall, it was well received by students. (Refreshments will be served beforehand.)
Posted 1 March 2011
Colloquium: Discovering the missing piece: 4-connected, 4-regular, claw-free graphs of odd order
On Tuesday, February 22 at 4:45 in Napier 201, mathematics majors Trevor Gionet '12 and Yixiao Sha '12 will speak about their summer research experience last summer. In 1995, Plummer published a paper in which he gave a characterization of the 4-regular, 4-connected, claw-free graphs. Based on that work, he and Hartnell published a paper on 4-connected, claw-free, well-covered graphs a year later. However, in his 1995 paper, Plummer inadvertently omitted some of the graphs
with odd order. Last summer Trevor and Yixiao were working on a related question under the direction of Prof. Erika King when they discovered this omission. Together they completed Plummer's characterization of all 4-connected, 4-regular, claw-free graphs, and then showed the implications this has on the well-covered graphs he and Hartnell determined. In addition, they characterized the 4-connected, 4-regular, claw-free, well-dominated graphs. The talk will be exploring the route they took to these findings. In addition, Yixiao will share her experiences presenting their work at the Nebraska Conference for Undergraduate Women in Mathematics in January. (Refreshments will be served beforehand.)
Posted 1 March 2011
Colloquium: The Wide World of Mathematical Biology
The first departmental colloquium of the Spring 2011 semester will be Prof. Jonathan Forde speaking about his research. He will present a talk on Wednesday, February 9 at 4:00pm in Gulick 206A. After a brief introduction to what mathematical biology is and why it is a growing area of active research, Forde will present preliminary results from some of his current research projects: immune therapy for HIV, treatment of hepatitis delta virus and the ecology of plant-herbivore-carnivore systems. He will also give a preview of the upcoming summer research program on modeling infectious disease. (Refreshments will be served beforehand.)
Posted 1 March 2011