Fall 2023 Algebraic topology seminar
Where:
622 Mathematics
When:
Fridays 10-11am
Date | Speaker (affiliation) | Title & Abstract |
September 15 | Søren Galatius (Copenhagen University) | Graph complexes in topology and algebraic geometryIn the 1990s, Kontsevich introduced certain rational chain complexes by an explicit presentation, known as graph complexes. The come in a few flavors and have shown up in different parts of mathematics. I will recall these chain complexes and explain how they showed up in joint work with Chan and Payne on the cohomology of moduli spaces of complex curves. |
September 22 | Jeremy Hahn (MIT) | Telescopes, prismatization, and exotic spheresAbstract: A smooth, oriented n-manifold is called a homotopy sphere if it is homeomorphic, but not necessarily diffeomorphic, to the standard n-sphere. In dimensions n>4, one often studies the group $\Theta_n$ of homotopy spheres up to orientation-preserving diffeomorphism, with group operation given by connected sum. I will give a leisurely introduction to the telescope conjecture in stable homotopy theory, and explain how its failure gives new lower bounds on the complexity of $\Theta_n$. To disprove the telescope conjecture, we construct invariants capable of distinguishing many diffeomorphism classes of exotic spheres: interestingly, key finiteness properties of these invariants are proved in part using intuitions and ideas from prismatic cohomology in p-adic algebraic geometry. The talk is based on joint projects with Burklund, Carmeli, Levy, Raksit, Schlank, Wilson, and Yanovski. |
October 13 | Noah Riggenbach (Northwestern University) | TitleAbstract: |
October 20 | Anh Hoang (University of Minnesota) | TitleAbstract: |
November 10 | J.D. Quigley (University of Virginia) | TitleAbstract: |
November 17 | Piotr Pstrągowski (Harvard University) | TitleAbstract: |
December 1 | Liam Keenan (University of Minnesota) | TitleAbstract: |
December 8 | Doosung Park (University of Wuppertal) | TitleAbstract: |