The Simons Center for Geometry and Physics is pleased to announce the following talks during the week of Monday, September 29th - Saturday, October 4th

G2 Manifolds Program: Informal Discussion

Monday, September 29th at 2:00pm in Simons Donaldson's Office, 514

Special Tea in Honor of Professor Alexander Zamolodchikov

Monday, September 29th at 3:30pm in SCGP Lobby

Gauge Theory Program Seminar: Chris Hull, "The geometry of double field theory"

Tuesday, September 30th at 11:00am in SCGP 313

Speaker: Chris Hull

Title: "The geometry of double field theory"

G2 Manifolds Program Seminar: Robert Bryant, "Riemannian manifolds with special holonomy and special curvature"

Tuesday, September 30th at 2:00pm in SCGP 313

Speaker: Robert Bryant

Title: Riemannian manifolds with special holonomy and special curvature

Abstract: While the local generality of metrics with special holonomy is now well-understood and the existence of complete or even compact examples is well-established, the construction of explicit examples remains a challenge. An approach that has been followed with great success is to look for examples with large symmetry groups, for this often reduces the problem to studying systems of ordinary differential equations. A different approach is to look for examples whose curvature tensors satisfy some algebraically natural conditions, for this imposes higher order (partial) differential equations on the solutions, and so the methods of exterior differential systems can be brought to bear to analyze the resulting overdetermined systems of equations. This can sometimes yield solutions with relatively high cohomogeneity and may be expected to provide interesting characterizations of some of the known solutions as well. In this talk, I will report on work in progress along these lines, particularly in the low dimensions, in which the holonomy can be either $SU(2)$, $SU(3)$, or $G_2$. I will also show how these methods can be used to study similar problems in certain geometries with torsion.

Gauge Theory Program Seminar: Matthias Staudacher, "Deformed Graßmannians, N=4 Scattering Amplitudes, and Integrable Spin Chains"

Thursday, October 2nd at 11:00am in SCGP 313

Speaker: Matthias Staudacher

Title: "Deformed Graßmannians, N=4 Scattering Amplitudes, and Integrable Spin Chains"

G2 Manifolds Program Seminar: Lorenzo Foscolo, "Compact nearly Kahler 6-manifolds"

Friday, October 3rd at 1:15pm in SCGP 313

Speaker: Lorenzo Foscolo

Title: "Compact nearly Kahler 6-manifolds"

Abstract: Compact six dimensional nearly Kähler manifolds are the cross-sections of Riemannian cones with holonomy G2. Currently there are only four known examples, which are all homogeneous. In this talk I will report on joint work in progress with Mark Haskins to the effect of which there exists at least one non-homogeneous nearly Kähler structure both on S^3xS^3 and S^6 beside the known one.

Program Seminar: John Morgan, "A Topologist looks at Sheaf Theory"

Friday, October 3rd at 2:45pm in SCGP 313

Title: A Topologist looks at Sheaf Theory

Abstract: Sheaf theory has long been an essential tool in algebraic geometry, algebraic number theory, and complex analysis, but its inspiration comes directly from topology. This lecture course will emphasize these roots, hopefully making sheaf theory seem natural to those with a topological bent. The course will begin by covering the basic topics in sheaf theory describing the objects and the four basic maps of the theory and then will culminate with a discussion of Verdier duality, which generalizes Poincare duality. This theory will then be applied to define a bordism theory, called duality bordism, whose coefficient group agrees with the Grothendieck group of chain complexes satisfying Poincare duality modulo those that sit as the boundary term in an exact sequence satisfying Lefschetz duality. This bordism group is the Pontryjagin dual homology theory to the cohomology theory associated with surgery theory. This means that a surgery problem is completely classified by evaluating surgery obstructions (signatures, and Arf invariants) of its restrictions to all possible duality bordism elements. Direct analysis of this bordism theory allows one to identify it at odd primes with real K-theory and at the prime 2 with ordinary homology.