SGGTC this Friday: Chris Gerig and Allen David Boozer
Oleg Lazarev
Dear all,
This Friday we have two speakers. Chris Gerig from Harvard will give a talk at 10:30 am in Math 520. Allen David Boozer from UCLA will give a talk at 1:00 pm in Math 407. We will meet at 11:35 in the lobby and go out for lunch.
Best, Oleg
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Chris Gerig: Probing 4-manifolds with near-symplectic forms
Abstract: Most closed 4-manifolds don't admit symplectic forms, but most admit "near-symplectic" forms that are symplectic away from some embedded circles. This provides a gateway from the symplectic world to the non-symplectic world, and just like the Seiberg-Witten invariants there are counts of J-holomorphic curves that are compatible with the near-symplectic form. Although (potentially exotic) 4-spheres don't even admit near-symplectic forms, there is still a way to bring in near-symplectic techniques, and I will describe my attempt(s) to probe them using J-holomorphic curves.
Abstract: Most closed 4-manifolds don't admit symplectic forms, but most admit "near-symplectic" forms that are symplectic away from some embedded circles. This provides a gateway from the symplectic world to the non-symplectic world, and just like the Seiberg-Witten invariants there are counts of J-holomorphic curves that are compatible with the near-symplectic form. Although (potentially exotic) 4-spheres don't even admit near-symplectic forms, there is still a way to bring in near-symplectic techniques, and I will describe my attempt(s) to probe them using J-holomorphic curves.
Allen David Boozer: Computer Bounds for Kronheimer-Mrowka Foam Evaluation
Abstract: Kronheimer and Mrowka recently suggested a possible approach towards a new proof of the four color theorem that does not rely on computer calculations. One outgrowth of their approach is the definition of a functor J^flat from the category of webs and foams to the category of integer-graded vector spaces over the field of two elements. Of particular interest is the relationship between the dimension of J^flat(K) for a web K and the number of Tait colorings Tait(K) of K. I describe a computer program that strongly constrains the possibilities for the dimension and graded dimension of J^flat(K) for a given web K, in many cases determining these quantities uniquely.
Abstract: Kronheimer and Mrowka recently suggested a possible approach towards a new proof of the four color theorem that does not rely on computer calculations. One outgrowth of their approach is the definition of a functor J^flat from the category of webs and foams to the category of integer-graded vector spaces over the field of two elements. Of particular interest is the relationship between the dimension of J^flat(K) for a web K and the number of Tait colorings Tait(K) of K. I describe a computer program that strongly constrains the possibilities for the dimension and graded dimension of J^flat(K) for a given web K, in many cases determining these quantities uniquely.