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Mathematics

Previous Events

Tuesday, October 5, at 4:15 p.m.
Searles Science Building, Room 217.
The Math Department Seminar Talk will be presented by Professor Bob Devaney

"The Fractal Geometry of the Mandelbrot Set".

Abstract: In this lecture we describe several folk theorems concerning the Mandelbrot set. While this set is extremely complicated from a geometric point of view, we will show that, as long as you know how to add and how to count, you can understand this geometry completely. We will encounter many famous mathematical objects in the Mandelbrot set, like the Farey tree and the Fibonacci sequence. And we will find many soon-to-be-famous objects as well, like the “Devaney” sequence.
A reception will be held at 4:00 in Searles 214.

Tuesday, March 2, 2010   
Tracy McKay '06, Iowa State University
12:10-12:40, Hutchinson Room, Thorne Dining Hall

Tuesday, March 30, 2010   
Li-Mei Lim, Brown University
12:10-12:40, Hutchinson Room, Thorne Dining Hall

Tuesday, April 6, 2010   
Professor Margaret Robinson '79, Mt. Holyoke College
7:00-8:00pm, Searles 217
Holmes Lecture Series
Robinson, a professor of mathematics at Mount Holyoke College, will give a talk titled "Two Ways to Count the Solutions to Polynomial Equations" The lecture is open to the public and admission is free.

Robinson's talk will introduce the general idea of a generating function that is, to quote mathematician Herbert Wilf, "a clothesline on which we hang up a sequence of numbers for display." It will look at examples of generating functions for different polynomials and discuss what is known about them. Her talk will conclude with the "tantalizing, sometimes frustrating," questions about what is not known and about how these generating functions relate to the Igusa local zeta function.

Professor Margaret Robinson '79, Mt. Holyoke CollegeMargaret Robinson, a member of the Bowdoin class of 1979, went on to earn her Ph.D. at Johns Hopkins University. A number theorist whose work combines analysis, algebra, and topology to understand number theoretic objects such as zeta functions, her work has been funded by numerous grants from the National Science Foundation, the National Security Agency, and the Mathematics Association of America. She has also directed several Research Experience for Undergraduates summer institutes at Mount Holyoke, and this year received the Mount Holyoke College Faculty Award for Teaching.

The Cecil T. and Marion C. Holmes Mathematics Lecture was established in 1977 by friends, colleagues, and former students to honor Cecil T. Holmes, a member of the faculty for 39 years and Wing Professor of Mathematics.

Tuesday, April 13, 2010   
Professor Emily Dryden '99, Bucknell University
12:10-12:40, Hutchinson Room, Thorne Dining Hall

Bowdoin Math Lectures 2010Monday, May 3, 2010   
Professor Glenn Stevens, Boston University
7:30-8:30pm, TBA
Christie Lecture Series

Tuesday, May 4, 2010  
Professor Glenn Stevens, Boston University
4:00-5:00pm, TBA
Christie Lecture Series

Department Seminar

Tuesday, September. 22
Kelvin Mischo

Tuesday, October 27, 2009
Prof. Noah Keiserman, Bowdoin College

Tuesday, November 10, 2009
Scott Taylor
Reception in Searles 214 at 4:15 PM
Lectures in Searles 217 at 4:15 PM

Tuesday, November 17, 2009
Prof. Carrie Diaz Eaton, University of Tennessee
A Mathematical Model of Mutualism and Co-evolution
Mutualists are individuals, populations or species that benefit each other.   One example of a well studied mutualism is that of the figs and fig-wasps, a system which boasts an estimated 750 fig tree species and 1300 fig wasp species.  How does the interaction between mutualists affect their co-evolution?  I introduce a difference equation model describing the change in allege frequencies at three diallelic loci in plant and pollinator and study it using both analytical and numerical results.  I then generalize the model to account for asynchronous flowering populations as seen in figs, and discuss the evolutionary implications of the results.  In particular, I focus on how one might re-interpret expected associations between the phylogenetic trees  of mutualists.
Reception in Searles 214 at 4:15 PM
Lectures in Searles 217 at 4:15 PM

Student Seminar Series

Tuesday, Sept. 22, 12:10-12:40pm
Prof. Michael King, Bowdoin College
"Patterns in Primes"

Tuesday, Oct. 6, 12:10-12:40pm
Prof. Adam Levy, Bowdoin College
"Optimization for Dummies"

Monday, Oct. 19, 7:30-8:30pm
Searles 315
Dr. Lawren Smithline, Institute for Defense Analyses
"A Cryptic Letter to Thomas Jefferson"

On Christmas Day, 1801, Thomas Jefferson received a letter from University of  Pennsylvania professor Robert Patterson. The last page of the letter was written using a cipher Patterson was proposing for all future confidential presidential communications.   Patterson withheld the key to its decryption, writing,

"I may safely defy the united ingenuity
 of the whole human race to decypher [such writing]
 to the end of time."

It remained unsolved until last year.  Using methods from mathematical biology, computer science, statistics, and mathematics, Lawren Smithline, a researcher at the Institute for Defense Analyses in Princeton, New Jersey, broke the code. The lecture is sponsored in part by the Computer Science, Government, and Mathematics Departments, as well as the Lecture and Concerts Committee.

If you would like to try and crack the code yourself, the cipher manuscript is  available from the Library of Congress at:

http://memory.loc.gov/master/mss/mtj/mtj1/025/0300/0304.jpg

Dr. Smithline's work is described in a recent Wall Street Journal article: Two  Centuries On, a Cryptologist Cracks a Presidential Code.  But beware, the article contains spoilers! Two Centuries On, a Cryptologist Cracks a Presidential Code

Annual Math Pumpkin Carving Party

Annual Math Pumpkin Carving PartyEach year students and faculty in the mathematics department celebrate Halloween by carving pumpkins. The "Math-o-Lanterns" carved are later displayed in various locations around Searles Science Building.

Speaker: BurilloTuesday January 29, 2008
Mathematics Department Seminar
Speaker: José Burillo
Universitat Politècnica de Catalunya
4:15 in Searles 217.
Reception at 4:00.
Title: Amenable groups and the Banach-Tarski Paradox

Abstract:
The Banach-Tarski paradox states that one can split a ball of radius 1 in a finite number of sets which, rearranged by isometries of R3, would combine to give a ball of radius 2, or, in another version, two balls of radius 1. The paradox is related to non-measurable sets and the Axiom of Choice. But a fact not widely known is that the paradox is closely related to the intrinsic structure of the group of isometries of the space R3. In this talk we will explore this relationship between the paradox and groups, introducing the key concept of amenability, and finally showing that since the group of isometries of R2 is amenable, the paradox is not possible in R2.

 The Banach-Tarski paradox

Friday, February 1
David Vogan, Massachusetts Institute of Technology, speaking at Bowdoin College
CBB Algebra-Topology Colloquium Series

Speaker: Fisher Tuesday, February 19
Searles 217 4:15pm
Reception at 4:00 in Searles 214
David Fisher, Indiana University-Bloomington, speaking at Bowdoin College
COARSE DIFFERENTIATION OF QUASI-ISOMETRIES AND RIGIDITY FOR SOLVABLE GROUPS

Abstract: In the early 80’s Gromov initiated a program to study finitely generated groups up to quasi-isometry. This program was motivated by rigidity properties of lattices in Lie groups. A lattice Г in a group G is a discrete subgroup where the quotient G/Г has finite volume. Gromov’s own major theorem in this direction is a rigidity result for lattices in nilpotent Lie groups.

In the 1990’s, a series of dramatic results led to the completion of the Gromov program for lattices in semisimple Lie groups. The next natural class of examples to consider are lattices in solvable Lie groups, and even results for the simplest examples were elusive for a considerable time. I will discuss joint work with Eskin and Whyte in which we prove the first results on quasi-isometry classification of lattices in solvable Lie groups. The results are proven by a method of coarse differentiation, which I will outline.

I will also describe some interesting results concerning groups quasi-isometric to homogeneous graphs that follow from the same methods.

CBB Algebra-Topology Colloquium Series

Speaker: Parshall Monday, February 25, 2008
7:30-8:30pm Searles 315
Cecil T. & Marion C. Holmes Lecture
Professor Karen Parshall, History and Mathematics University of Virginia
The Internationalization of Mathematics in a World of Nations

Abstract: Mathematics has a history both grounded in time and place and, to some extent, transcendent of time and place.  As an area of inquiry—but more fundamentally as a language through which to interpret nature—it has the ability to transcend time and place, even though for given time periods it may make sense to speak at least loosely of Mesopotamian or Greek or medieval Islamic or Chinese or European … mathematics.  Over the course of the nineteenth and through the twentieth century, mathematics became not only a language but also an endeavor shared and developed internationally.  How did this transformation occur?  This talk will attempt to shed light on the answer to that question.

Tuesday, February 26
Searles 217 4:15pm
Reception at 3:45 in Searles 214
Karen Parshall, Professor of History and Mathematics University of Virginia
Algebra: Creating New Mathematical Entities in Victorian Britain
Mathematics Department Seminar

Abstract:  Analytic geometry and mathematical physics may have interested a majority of mathematicians in Victorian Britain, but algebra also served to focus their mathematical attention.  In the century's first half, algebraic work centered on the development of the so-called "symbolical algebra" and the creation of new algebras, while in its second, the theory of invariants dominated and the abstract theory of groups witnessed key developments.  Underlying much of this research was the philosophical question of how free mathematicians were to create new mathematical entities.  The Victorian British response was, ultimately, "quite."/p>

Tuesday, March 4
Helen Wong
Quantum Invariants for Three-Dimensional Manifolds
Mathematics Department Seminar

Friday, March 7
Ross Geoghegan, Binghamton University, speaking at Bates College
CBB Algebra-Topology Colloquium Series

Tuesday, March 18
Joseph Silverman, Brown University, speaking at Bates College
CBB Algebra-Topology Colloquium Series

March 25
Tom Mac Gregor
The Bloch Constant for Conformal Mappings
Mathematics Department Seminar

April 1
Steve Fisk
TBA
Mathematics Department Seminar

Monday, April 21
Kiran Kedlaya, Massachusetts Institute of Technology, speaking at Bowdoin College
CBB Algebra-Topology Colloquium Series

Student Seminar Series

Tuesday, September 23, 2008
Revenge of the Irrationals
Prof. Jennifer Taback, Bowdoin College
12:00-12:40pm, Hutchinson Room, Thorne Dining Hall

Tuesday, October 7, 2008
Tuning with Triangles
Prof. Leon Harkleroad, Bowdoin College
12:00-12:40pm, Hutchinson Room, Thorne Dining Hall

Sangaku - a mathematical tradition in Edo JapanThursday, October 23, 2008
Sangaku - a mathematical tradition in Edo Japan
Prof. Peter Wong, Bates College
7:00-8:00pm, Searles 217

Wed. November 5, 2008
Dr. Michael Kleber, Google
7-8pm

Tuesday, December 2, 2008
TBA
Prof. Mary Lou Zeeman, Bowdoin College

12:00-12:40pm, Hutchinson Room, Thorne Dining Hall

Wednesday, Nov 28, 2007
7:30pm in the Lancaster Lounge in Moulton Union, Bowdoin College
Mary Lou Zeeman, R. Wells Johnson Professor of Mathematics, Bowdoin College
R. Wells Johnson Inaugural Lecture & CBB Mathematical Biology Seminar

Title: Mathematical Modeling in Biology: What is it? And How is it Useful?

Abstract: We will describe some of the ways that math can be harnessed to dive into biological mysteries. For example: What happens when three species compete for the same resources? Why do diseases come in cycles? And how is ovulation triggered?

*The Lunchtime Mathematics Seminar is a series of short talks throughout the semester covering fun and unusual mathematical topics  These have included cryptography, optimization, elliptic curves, error detecting curves, statistics, non Euclidean geometry, number theory and mathematical biology. Speakers in the Lunchtime Mathematics Seminar include visitors from other institutions as well as Bowdoin's own faculty.

Monday, Sept. 17, 2007
7:30-8:30pm,
Prof. Nathan Dunfield, University of Illinois

Tuesday, Oct. 2, 2007
12:00-12:45pm
Prof. Adam Levy, Bowdoin College
Title: Numerical Analysis for Dummies (and smarties)
Lunchtime Seminar

Speaker: James Cannon, BYUOctober 12, 2007
CBB Algebra-Topology Colloquium Series
Speaker: James Cannon, BYU
4:30 in Searles 217. Reception at 4:00.
Title: Random 3-Manifolds

Abstract:
Every 3-manifold can be obtained by identifying faces in pairs on the boundary of a 3-cell with cellulated boundary. However, the probability of obtaining a closed 3-manifold by such a face-pairing, chosen randomly, is 0, according to a theorem of Dunfield and Thurston. Typically, one obtains instead a 3-dimensional pseudo-manifold having at least one vertex whose link is a closed 2-manifold that is not a 2-sphere.

I will outline a proof of the Dunfield and Thurston theorem, then describe the simple bitwist operation which starts with a random face-pairing and mechanically yields a parametrized, infinite collection of closed 3-manifolds. (The construction generalizes our earlier twisted-face-pairing construction.)

The advantages of the bitwist operation are these: (1) One obtains every closed, orientable 3-manifold in this manner. (2) If the original face-pairing is simple, even trivial, the resultant face-pairings are also relatively simple. (3) The bitwist face-pairings yield elegant presentations for the fundamental groups involved. (4) The parametrized fundamental groups yield beautiful families for study by the methods of geometric group theory.

Tuesday, Oct. 16, 2007
12:00-12:45pm
Prof. Jennifer Taback, Bowdoin College

Tuesday, Oct 23, 2007
4:15 in Searles 217
Mary Lou Zeeman, Bowdoin College
Department Seminar
Title: The State of the Planet: How can we help?

Abstract: This seminar is aimed at a very broad audience. There are, of course, many ways to answer the question posed in the title. For those of us who enjoy solving quantitative problems, ranging from pure mathematics to computer science, economics, biology, etc., I will discuss some of the mathematical challenges facing climate modeling, and report on a recent white paper on this topic produced at MSRI (the Mathematical Sciences Research Institute, in Berkeley). For those of us who are educators, I will describe a course that I have helped to develop and run at Cornell University called, simply, The State of the Planet. The theme of the course is: Whatever your talent, whatever your passion, you can use them to help the planet; Student feedback has been extremely positive, and the course has been written about in Nature, the Sierra Club, and elsewhere. It would be easy to run a similar course at any school.

Friday, Oct. 26, 2007
CBB Algebra-Topology Colloquium Series
There will be a reception at 4:00 in Mudd 412A.
Prof. Michael Hopkins, Harvard University
Time: 4:30pm
Location: Mudd 405, Colby College

Abstract:  I'll discuss the notion of a topological field theory and some of the many ways that it forces topologist to re-examine some of the oldest assumptions in topology. I'll also discuss recent joint work with Jacob Lurie giving a complete characterization of topological field theories in (very) low dimensions.

Tuesday, Oct. 30, 2007
7:30-8:30 pm
Prof. Adam Piggott, Tufts University
How Michael met Jessica: romance and error detecting codes
Lunchtime Seminar*
and he will present a Department Seminar
Automorphisms of graph products of abelian groups
4:15 in Searles 217

Thursday, Nov. 8, 2007
4:00-5:00 in Druckenmiller 20
3:30 Refreshments in Druckenmiller 110
CBB Mathematical Biology Seminar Series
Prof. Liam O'Brien, Colby College
Title: The Ins and Outs of Diagnostic and Screening Tests

Abstract: Not all diagnostic or screening tests are created equally. We will discuss how the basic properties of these tests tell us how well they perform in certain circumstances.  We will also describe what the differences are between a test designed to diagnose a condition versus one that designed to screen for a condition. Lastly, some new methods for choosing the best single screening test out of several candidate tests will be shown.

Tuesday, Nov. 13, 2007

12:00-12:45,
Prof. Helen Wong, Bowdoin College
Lunchtime Seminar*

Tuesday November 13, 2007

4:15 - 5:15 in Searles 217
4:00 Reception in Searles 214
Prof. Tom Pfaff, Ithaca College
Department Seminar
Title: Peak Oil, CAFE Standards, & a Modeling Problem

Come and hear Tom Pfaff talk about the simple ways he has brought real data about the planet into his calculus classroom, and the positive impact it has had on the depth of understanding and the motivation to learn about math and about sustainability. All you need are some data sets (available on Tom’s website at www.ithaca.edu/tpfaff/sustainability.htm) and excel.

Abstract:   This talk will begin with a brief look at peak oil (the point at which the amount of oil that can be extracted from the earth begins to decline) and CAFE (Corporate Average Fuel Economy) Standards.  Given this background we then work towards creating models to assess the impact of raising CAFE Standards.  In particular, we are interested in what would be needed to reduce the overall fuel consumption of our vehicle fleet as opposed to simply slowing the increase of our fuel consumption.  The simpler models that we will study in some detail will use curve fitting and maximization of functions.


Wednesday November 14, 2006
6:30 -7:30 in Druckenmiller 016
6:00 Reception in Druckenmiller Atrium
Prof. Tom Pfaff, Ithaca College

Charles F. Adams Lecture
Title:  Education about Sustainability while Enhancing Calculus

Abstract:  The Joint Science Academies and the United Nations have called for increased education in sustainability.  After an overview on sustainability,  we will discuss ways of achieving this sustainability education in a calculus course.  As we go through some examples we will also learn about some of the issues facing our society (Note: Knowledge of calculus while helpful is not necessary to gain from this portion of the talk.).   These examples will not only show how to incorporate sustainability into calculus, but also how we can get students to think about larger systems and improve quantitative literacy.  Further, we will see how it can become natural for calculus courses to work in an interdisciplinary way making calculus more relevant to the number of non-majors taking the course. Finally, we end by providing evidence from some assessment showing that these examples improve student engagement and learning.