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Geometry and Topology Seminar

Friday, January 8, 2021
3:00pm to 4:00pm
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Online Event
Orthogonal group and higher categorical adjoints
David Ayala, Department of Mathematical Sciences, Montana State University,

In this talk I will articulate and contextualize the following sequence of results.

  • The Bruhat decomposition of the general linear group defines a stratification of the orthogonal group.
  • Matrix multiplication defines an algebra structure on its exit-path category in a certain Morita category of categories.
  • In this Morita category, this algebra acts on the categeory of n-categories -- this action is given by adjoining adjoints to n-categories.

This result is extracted from a larger program -- entirely joint with John Francis, some parts joint with Nick Rozenblyum -- which proves the cobordism hypothesis.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected] or visit