Friday September 01, 2017 11:00 AM  12:20 AM 5127
 JeanFrancois Arbour,
Introduction to minimal models

Friday September 08, 2017 11:00 AM  12:20 AM Math Tower 5127
 Tobias Shin, Stony Brook University
Introduction to minimal models (cont'd)  Construction, formality, examples

Friday September 15, 2017 11:00 AM  12:20 AM 5127
 Ying Hong Tham, Stony Brook University
Construction of the algebra of rational forms and the model of the free loop space

Friday September 22, 2017 10:40 AM  12:00 AM 5127
 Alexandra Viktorova, Stony Brook University
The correspondence between generators in the minimal model and higher homotopy groups

Friday September 29, 2017 11:00 AM  12:20 AM 5127
 Michael Albanese, Stony Brook University
Minimal model of the free loop space of a manifoldWe will construct the minimal model of the free loop space of a manifold. This will be an important step on the way to proving the existence of infinitely many geodesics on a Riemannian manifold.

Friday October 06, 2017 11:00 AM  12:20 AM 5127
 Aleksandar Milivojevic, Stony Brook
Generators of the cohomology ring and Betti numbers of the free loop spaceWe will show that the cohomology ring of a simply connected manifold is not generated by a single element if and only if the free loop space of the manifold has unbounded Betti numbers.

Friday October 13, 2017 11:00 AM  12:20 AM Math 5127
 JeanFrancois Arbour, Stony Brook University
The GromollMeyer theoremLast time, we discussed the equivalence between the following two properties for a smooth manifold : (i) Its cohomology ring is not singly generated; (ii) The Betti numbers of its free loop space form an unbounded sequence. This time, I will discuss Gromoll and Meyer's theorem which says that if (ii) is satisfied, then for any choice of Riemannian metric, the manifold will necessarily admit infinitely many distinct closed geodesics. The proof goes by doing Morse theory on the free loop space.

