Seminar Schedule
February 11 - February 15, 2008
All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.
VIGRE – Algebraic Geometry
2:15pm, Room 222
Topology
2:30pm, Room 303
Speaker: Sa'ar Hersonsky, Unviersity of Georgia
Title of talk: On the Cannon Conjecture
Abstract: This will be a survey talk on the combinatorial approach to the Cannon Conjecture. The conjecture asserts that a neg. curved group $G$ (in the sense of Gromov) with $\partial G$ home to $S2$ acts geometrically on Hyperbolic $3$-space. The conjecture is a main step towards Thurston's geometrization conjecture (that seems to be proved by Perelman using Ricci flow techniques) but is logically independent of it.
TUESDAY, February 12, 2008
Colloquium – Note the Day
3:30pm, Room 304
Speaker: Adrian Butscher, Stanford University
Title of talk: Gluing Constructions for Constant Mean Curvature Surfaces.
Abstract: I will review the now classical Kapouleas gluing construction for CMC surfaces in Euclidean space and present some results and work in progress concerning the extensions of this theory to general ambient manifolds. An important feature which emerges is that the ambient Riemannian curvature seems to play a significant role in the existence of such surfaces; and exploiting this, it seems possible to construct examples of CMC surfaces having properties very different from their Euclidean analogues.
Mathematical Physics
3:30pm, Room 303
Speaker: Emily Pritchett, University of Georgia
Title of talk: Entropy in statistical mechanics and the 2nd law in thermodynamics
WEDNESDAY, February 13, 2008
Algebraic Geometry
2:30pm, Room 410
No meeting this week
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Tea, Cookies
Number Theory/Arithmetic Geometry
3:30pm, Room 304
No meeting this week
THURSDAY, February 14, 2008
VIGRE – Tropical Geometry
2:00pm, Room 304
VIGRE – Circle Packing
2:00pm, Room 326
VIGRE – Number Theory
3:30pm, Room 303
FRIDAY, February 15, 2008
VIGRE-Algebra
2:30pm, Room 322
Applied Math
2:30pm, Room 302
Speaker: Tom Lyche, Dept. of Computer Science, University of Oslo, Norway
Title of talk: New Formulas for Divided Differences and Partitions of a Convex Polygon
Abstract: Divided differences are a basic tool in approximation theory and numerical analysis: they play an important role in interpolation and approximation by polynomials and in spline theory. So it is worth while to look for identities that are analogous to identities for derivatives. An example is the Leibniz rule for differentiating products of functions. This rule was generalized to divided differences by Popoviciu and Steffensen 70 years ago. To our surprise it was discovered that there were no analog of a 150 year old formula for differentiating composite functions (Faa di Bruno's formula) and for differentiating the inverse of a function. In this talk I will discuss chain rules and inverse rules for divided differences. The inverse rule turns out to have a surprising and beautiful structure: it is a sum over partitions of a convex polygon into smaller polygons using only non-intersecting diagonals. This provides a new way of enumerating all partitions of a convex polygon with a specified number of triangles, quadrilaterals, and so on. The talk is based on joint work with Michael Floater. 1
Topology/Geometry
2:30pm, Room 303
Speaker: Sa’ar Hersonsky, University of Georgia
Title of talk: On the Cannon Conjecture, continuation
Abstract: This will be the second part of survey talk on the combinatorial approach to the Cannon Conjecture. The conjecture asserts that a neg. curved group $G$ (in the sense of Gromov) with $\partial G$ home to $S2$ acts geometrically on Hyperbolic $3$-space. The conjecture is a main step towards Thurston's geometrization conjecture (that seems to be proved by Perelman using Ricci flow techniques) but is logically independent of it.