Algebraic models in geometry seminar

from Thursday
June 01, 2017 to Sunday
December 31, 2017
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Instructions for subscribing to Stony Brook Math Department Calendars

Friday
September 01, 2017

11:00 AM - 12:20 AM
5-127
Jean-Francois Arbour,
Introduction to minimal models


Friday
September 08, 2017

11:00 AM - 12:20 AM
Math Tower 5-127
Tobias Shin, Stony Brook University
Introduction to minimal models (cont'd) - Construction, formality, examples


Friday
September 15, 2017

11:00 AM - 12:20 AM
5-127
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
5-127
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
5-127
Michael Albanese, Stony Brook University
Minimal model of the free loop space of a manifold

We 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
5-127
Aleksandar Milivojevic, Stony Brook
Generators of the cohomology ring and Betti numbers of the free loop space

We 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 5-127
Jean-Francois Arbour, Stony Brook University
The Gromoll-Meyer theorem

Last 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.


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