MONDAY, November 14, 2005

GEOMETRY/TOPOLOGY SEMINAR 667

TIME: 12:20 p.m. – 1:20 p.m.
ROOM: 209A Ayres Hall
SPEAKER: Dr. Valeriy Berestovskiy, Visiting Faculty
TITLES: Riemannian manifolds

DIFFERENTIAL EQUATIONS/APPLIED AND COMPUTATIONAL MATH SEMINAR

TIME: 3:35 p.m. – 4:25 p.m.
ROOM: 104 Ayres Hall
SPEAKER: Rachael Miller
TITLE: Weed Invasions: To Control or not to Control
(summary of a paper by Cacho, Wise, Hester, and Sinden)

SPEAKER: Carrie Eaton
TITLE: The new classics: current approaches to modeling mutualistic interactions leading to speciation.
ABSTRACT: Last talk, I introduced a classic model by Kiester, et.al. (1984) that modeled plant-pollinator mutualisms leading to the differentiation and potential speciation of geographically separated populations. This talk will take a brief look at two currently popular approaches, Adaptive Dynamics and Tangled Nature, for modeling the effect of ecological interactions on population genetics. Both models predict that differentiation can occur within a population and can lead to sympatric speciation.

WEDNESDAY, NOVEMBER 16, 2005

GEOMETRY/TOPOLOGY SEMINAR 667

TIME: 12:20 p.m. – 1:20 p.m.
ROOM: 209A Ayres Hall
SPEAKER: Dr. Valeriy Berestovskiy, Visiting Faculty
TITLE: Curvature tensor of Riemannian manifold

ALGEBRA SEMINAR

TIME: 3:30 p.m.
ROOM: 214 Ayres Hall
SPEAKER: John LaGrange
TITLE: Kaplansky’s Theorem on Projective Modules
ABSTRACT: We’ll show that a direct summand of a direct sum of countably generated R-modules is again a direct sum of countably generated R-modules. Applications of this result to projective R-modules will also be discussed. (Beware: this does use the Axiom of Choice!)

ANALYSIS SEMINAR

TIME: 3:35 – 4:25 p.m.
ROOM: 309B Ayres Hall
SPEAKER: Dr. Brett Wick, Vanderbilt University
TITLE: Bounded Analytic Projections and The Corona Problem
ABSTRACT: In this talk, I will discuss the connection between bounded analytic projection valued functions and solutions to the Corona Problem. In particular, under some additional hypotheses, we obtain necessary and sufficient conditions to solve the Corona Problem in terms of bounded analytic projections.

THURSDAY, NOVEMBER 17, 2005

JUNIOR COLLOQUIUM

TIME: 3:30 p.m.
ROOM: 214 Ayres Hall
SPEAKER: Dr. Don Hinton, UT
TITLE: The Brachistochrone Problem
ABSTRACT: In 1696 Johann Bernoulli issued the following challenge to the world’s mathematicians. “Given two points A and B in a vertical plane, what is the curve traced out by a point acted on only by gravity, which starts at A and reaches B in the shortest time.” We will examine Bernoulli’s solution which is based on Fermat’s principle of least time. Other problems stated by Bernoulli will be considered as well as other least time problems. As Bernoulli pointed out, his solution was the same as the tautochrone which is the curve of constant time investigated by Huygens. (Huygens was interesting in building a perfect clock, i.e., a pendulum clock whose period is independent of its amplitude). In conclusion we will connect Bernoulli’s differential equation with the Euler-Lagrange equation developed some time later.

Pizza will be served at 3:30 p.m.

FRIDAY, NOVEMBER 18, 2005

COLLOQUIUM

TIME: 3:35 p.m. – 4:25 p.m.
ROOM: 214 Ayres Hall
SPEAKER: Dr. Nikolay Brodskiy
TITLE: Asymptotic topology: dimension and embeddings
ABSTRACT: It is suggested by Gormov to study the geometry of finitely generated groups, and their global properties where small (bounded) details can be disregarded. One investigates the properties which are defined by taking the limit at infinity. This provides an analogy between the large scale world and the small scale world, where one takes the limit at 0. The importance of large scale versions of concepts of local topology has been firmly established by now. The most influential result is due to G. Yu and it says that the Novikov higher signature conjecture holds for geometrically finite groups with a finite large scale dimension.

REFRESHMENTS WILL BE SERVED IN AYRES HALL ROOM 119 AT 3:00 P.M.