## Why Did Lagrange Prove the Parallel Postulate?

09/19/2007 - 4:00pm
09/19/2007 - 6:00pm
Category:
Colloquium
Speaker:
Dr. Judith Grabiner (Pitzer College)
Abstract:

In 1806, Joseph-Louis Lagrange (1736-1813) read a memoir proving Euclid's parallel postulate to the Institut de France in Paris, but stopped, as the story goes, saying "I have to think about this some more." We'll look at Lagrange's still unpublished Paris manuscript on this subject, and place this activity in the context of his mathematical career. We will look also at how the ideas in this manuscript are related to Lagrange's philosophy of mathematics, Newton's physics, and Leibniz's Principle of Sufficient Reason. Finally, we will reflect on what this episode tells us about eighteenth-century attitudes toward geometry, space, and the universe.

Where:
Seaver North Auditorium 645 N. College Avenue, Pomona College
Misc. Information:

Coffee & cookies at 4:00 p.m.
Wine and cheese after the talk, Harry Mullikin Room, Millikan 209

The dinner will be hosted by Jim Hoste. If interested in attending, call Ext. 73258

## Optimization of a delay-differential model of the immune response to cancer vaccines

09/26/2007 - 4:00pm
09/26/2007 - 7:00pm
Category:
Colloquium
Speaker:
Dr. Ami Radunskaya ( Pomona College )
Abstract:

Can mathematical models be truly helpful in medical applications? In this talk I will present a new mathematical model developed with immunologist Sarah Hook that uses delay-differential equations to model the immune kinetics in response to tumor antigen. Differential equations with delays occur in many applications, and, mathematically,

they pose considerable challenges in their analysis. In particular, the introduction of delays makes it difficult to analytically apply control techniques to this problem.

The aim of this work is to model the T cell immune response to a vaccine with the goal that the model can be used to aid in the optimisation of vaccine-induced cellular immune responses. Since these responses are much more difficult to measure than antibody levels, often the only option available for researchers and clinicians is the "Goldilocks'' approach to cancer vaccination: give not too much of the vaccine, or too little and give it not too often or too few times.

In this talk I will discuss some of the mathematical difficulties presented by delay-differential models, and will describe several mathematical methods that can be used to suggest immunization protocols that would optimize the immune response.

No previous knowledge of immunology or control theory will be assumed.

Where:
The Founder's Room* in Honnold Library *Directions: Enter the library under the bridge. Just inside the door there is a Welcome Desk. Tell the staff member that you're there for the Math Colloquium, and he/she will direct you.
Misc. Information:

Coffee & cookies at 4:00 p.m.

Wine and cheese after the talk.

Due to Prof. Radunskaya's schedule, there will be no dinner after the talk.

## Critical points and solvability of boundary value problems

09/12/2007 - 4:00pm
09/12/2007 - 7:00pm
Category:
Colloquium
Speaker:
Dr. Alfonso Castro (Chair, Harvey Mudd College Math Department)
Abstract:

Principles for the existences of critical points will be discussed and applied to the solvability of boundary value problems. Terms such as deformation lemma, mountain pass lemma, Palais-Smale condition, and saddle point principle will be explained.

Where:
Millikan 134, Pomona College
Misc. Information:

Coffee 4:00 - Pomona College, Millikan 209
Talk 4:15 - Pomona College, Millikan 134
Wine and Cheese 5:15 - Pomona College Millikan 209

Dinner hosted by Prof. Ellis Cumberbatch (Claremont Graduate University)

## Recent Insights into A^{\infty} and the Jones Factorization Theorem

10/17/2007 - 4:00pm
10/17/2007 - 7:00pm
Category:
Colloquium
Speaker:
Dr. Winston Ou (Scripps College)
Abstract:

The theory of the structure of weights, which reached a peak in the 1980 with the eponymous "factorization theorem'' of Peter Jones, is by now no longer young. Yet despite its middle age, it is still capable of some aesthetically satisfying surprises. We will present a brief introduction to the theory and describe how some recent insights have simplified our understanding of the later refinement (Cruz-Uribe-Neugebauer, 1995) of Jones's result to simultaneously incorporate "reverse Hölder'' class information.

Where:
Millikan 134, Pomona College
Misc. Information:

Coffee & cookies at 4:00 p.m. @ Harry Mullikin Room, Millikan 209
**************************
The dinner will be hosted by Prof. Erica Flapan right after the talk.
If interested in attending, call Ext. 18711.

## The Impact of Ballistics on Mathematics

10/03/2007 - 4:00pm
10/03/2007 - 7:00pm
Category:
Colloquium
Speaker:
Dr. Shawn McMurran (California State University, San Bernardino)
Abstract:

What is the trajectory of a projectile launched into the air? Archimedes, Tartaglia, Galileo, Torricelli, Descartes, Newton and Bernoulli are just a few among the many mathematicians who had investigated this question by the time it caught the attention of Leonhard Euler. Not to mention that his boss at the time was more than a little interested in specific applications of the solution, such as determining the horizontal range of a musket ball with 3/4 inch diameter and an initial velocity of 1700 feet per second when fired at an angle of 45 degrees.

The 18^th century saw significant advances in the analysis of the trajectory of a projectile in air. In the first half of this century, Benjamin Robins, a British mathematician and military engineer, published New Principles of Gunnery, the first book to deal extensively with external ballistics. Robins' work motivated a deeper mathematical analysis of projectile motion and invited commentary'' from Euler. In this talk we consider the influence of Robins' work and look at how Euler used it to attack the problem of projectile motion.

Where:
The Founder's Room in Honnold Library *Directions: Enter the library under the bridge. Just inside the door there is a Welcome Desk. Tell the staff member that you're there for the Math Colloquium, and he/she will direct you.
Misc. Information:

Coffee & cookies at 4:00 p.m. Wine and cheese after the talk.
The dinner will be hosted by Mario Martelli. If interested in attending, call Ext. 78979

## How mathematics departments can improve prospective teachers' mathematical content knowledge for teaching

10/10/2007 - 4:00pm
10/10/2007 - 7:00pm
Category:
Colloquium
Speaker:
Dr. Stacy Brown (Pitzer and Claremont McKenna Colleges)
Abstract:

“Now is a time of great interest in K-12 mathematics education. Student performance, curriculum, and teacher education are the subjects of much scrutiny and debate. Studies of the mathematical knowledge of prospective and practicing U.S. teachers suggest ways to improve their mathematical educations” (Conference Board of the Mathematical Sciences, 2001)

Elementary school teachers are the public face of mathematics. (Phillip Wagreich, Mathematician)

In this talk, I will share findings from studies indicating that we should be concerned about U.S. teachers’, including prospective teachers’, mathematical content knowledge for teaching. Using recent research findings and vignettes from classroom lessons, I will elaborate on the notion of mathematical content knowledge for teaching and illustrate how teaching mathematics, even to young children, may entail more mathematical thinking on the teacher’s behalf than one might expect. I will then consider recent recommendations for the mathematical preparation of teachers and how mathematics departments have enacted these recommendations. In so doing, I hope to convey to the audience the distinct and important contribution that mathematicians are uniquely qualified to make toward the improvement of the mathematics education of teachers and consequently, school age children.

Where:
Millikan 134, Pomona College
Misc. Information:

Coffee at 4:00 p.m. Wine and cheese after the talk.

Harry Mullikin Room, Millikan 209

The dinner will be hosted by Prof. Judith Grabiner

## Scary boundaries and harmonic measures

10/31/2007 - 4:00pm
10/31/2007 - 7:00pm
Category:
Colloquium
Speaker:
Dr. Michael O'Neill (Claremont McKenna College)
Abstract:

The theory of harmonic measure describes the way in which a random particle in a domain first hits the boundary. It also, and equivalently, gives a description of the boundary behavior of solutions to Laplace's equation in a given, perhaps very complicated, domain.

A brief survey of harmonic measures in the plane and in space will be followed by a discussion of some analogs of classical theorems about exit behavior of Brownian motion in simply connected planar domains to the case of multiply connected planar domains and to some classes of "nice'' domains in three dimensions. There are many interesting open questions in the area and we will try to talk about a few of them. The talk will be accessible to undergraduates.

Where:
<a href="http://www.pomona.edu/tours/campusmap/home.shtml">Millikan 134</a> (Pomona College)
Misc. Information:

Coffee & cookies at 4:00 p.m.

Wine & Cheese after the talk.

Harry Mullikin Room, Millikan 209

**************************

The dinner will be hosted by Prof. Harish Bhat.

If interested in attending, call Ext. 77261.