Unless stated otherwise, colloquia are scheduled for Thursdays 4:30-5:30pm in LN 2205 with refreshments served from 4:00-4:25 pm in the Anderson Memorial Reading Room.
Here you find some directions to Binghamton University and the Department of Mathematical Sciences.
Thursday, October 31st, 2013
Speaker:
Jim Davis (Indiana University)
Title:
Rigidity
Time:
4:30 - 5:30 pm
Room: LN-2205
Abstract: This is a largely expository talk on known topological obstructions to nonpositive curvature. We shall first explore geometric meaning of nonpositive curvature and explain why it forces the manifold to be covered by a Euclidean space. We also discuss the uniformization of surfaces, and significance of metric completeness, after which we move to more delicate obstructions coming from harmonic map superrigidity, random groups with fixed point properties, and elementary group actions.
Friday, November 8th, 2013
Speaker:
Benson Farb (Chicago University)
Title:
Braids, Homology and Polynomials : an Emerging Pattern in Algebra
and Topology
Time:
4:30 - 5:30 pm
Room: SW 323 (NOTE UNUSUAL ROOM!)
Abstract: Natural mathematical objects often occur in families parametrized by the natural numbers. Examples include the group of invertible n by n integer matrices (and its congruence subgroups), spaces of configurations of n distinct points on a manifold, and various spaces of polynomials in n variables. It was recently discovered that certain numerical invariants attached to these sequences, such as Betti numbers and dimensions, actually "stabilize" to a polynomial in n once n is big enough. In this talk I will try to explain what is happening here, tell the story of how it was discovered, and expose a single mechanism responsible for the common behavior in these very different examples. Along the way we will see this stability phenomenon reflected in the combinatorial stability of counts of degree n polynomials over finite fields. This is joint work with (various linear combinations of ) Tom Church, Jordan Ellenberg and Rohit Nagpal.
Thursday, November 21st, 2013
Speaker:
Toke Knudsen (SUNY Oneonta)
Title:
Mathematical Methods in Ancient Indian Ritual
Time:
4:30 - 5:30 pm
Room: UU 102 (NOTE UNUSUAL ROOM!)
Abstract: The earliest systematic textual presentation of mathematical knowledge in India appears within the context of ritual practices. Known as the rules of the cord -- a reference to the fact that cords, together with pegs and bamboo rods, are used for the practical constructions -- the texts give the mathematical rules necessary for measuring out and constructing the arenas and altars used in ancient Indian rituals in the period 800 to 200 BCE. A major portion of these rules is devoted to plane geometry, and they are by no means trivial as they include fundamental elements of the geometry: the Pythagorean theorem, the construction of geometrical figures, the combination of geometrical figures, and the transformation of geometrical figures, such as the quadrature of the circle and the circulature of the square; they also contain a very good approximation to the square root of 2. In addition to results from geometry, the rules of the cord also provide directions for covering various altars with bricks according to certain rules laid down by the ritual texts.
The talk will explain and demonstrate some of the mathematical rules, and will also discuss the social context of the rituals and their execution.