Geometry/Topology Seminar

Monday, October 18, 2021 at 3:00pm to 4:00pm

Building 2, 2-449
182 MEMORIAL DR, Cambridge, MA 02139

Featured Speaker: Robert Burklund (MIT)

Title: A classification of metastable manifolds.

Abstract:
A basic goal in differential topology is to classify all smooth, closed, oriented n-manifolds up to diffeomorphism. As stated, this goal is too ambitious. However, for large n and with strong restrictions on the topology of the manifold progress becomes possible. In this talk, I will begin by discussing the classification of simply-connected manifolds whose only nonzero homology groups are H_0, H_{n/2}, and H_n, from the seminal work of Wall to its final resolution by the speaker and his collaborators. Then, I will discuss the extension of this classification into the metastable range, where the condition on the homology groups is relaxed so that H_0, H_{n/3 + e}, ..., H_{2n/3 -e} and H_n may be nonzero ( e is an error term growing sublinearly in n ). These manifolds are distinguished by the feature that the ring structure on their cohomology groups is entirely recorded by Poincare duality. Time permitting, I'll indicate how modern homotopy-theoretic methods can exploit metastability. This talk represents joint works with Andy Senger and Jeremy Hahn.

Seminar Covid Statement
A notice to non-MIT seminar participants: at this time, not all seminars are open to the general public, and access to the MIT campus is highly regulated. Please check the seminar webpage or with the event organizer and confirm whether the seminar you'd like to attend is open to non-MIT (i.e. without CovidPass) attendees.
Some seminars may offer a Zoom option for off-campus participants.
To access MIT buildings for a math seminar without MIT's CovidPass, you must be invited via a Tim Ticket ahead of time. There are no exceptions; please make sure to plan accordingly before coming to campus. To be able to activate the Tim Ticket, the attendee will need to submit an attestation about vaccination and health status and provide contact info.
Finally, a reminder to all in-person participants. MIT Covid policies must be adhered to: remember to keep your mask on while inside buildings, eating food is not allowed within lecture rooms, and if you are feeling sick on the day of the talk, please stay home!

Event Type

Conferences/Seminars/Lectures

Events By Interest

Academic

Events By Audience

MIT Community

Events By School

School of Science

Website

https://sites.google.com/view/anthony...

Department
Department of Mathematics
Contact Email

sherport@mit.edu

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