Calendar of Events
Calendar of Events
Spring 2008 Events
Tuesday 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.
Friday, February 1
David Vogan, Massachusetts Institute of Technology, speaking at Bowdoin College
CBB Algebra-Topology Colloquium Series
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
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