This Week in Mathematics


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Today:

Homotopy Theory [url]
Cubical models of (infinity,1)-categories
- Brandon Doherty, University of Western Ontario
Time: 5pm Room: Zoom
More Information
Abstract/Desc: We describe a new model structure on the category of cubical sets with connections whose cofibrations are the monomorphisms and whose fibrant objects are defined by the right lifting property with respect to inner open boxes, the cubical analogue of inner horns. We discuss the proof that this model structure is Quillen equivalent to the Joyal model structure on simplicial sets via the triangulation functor, and a new theory of cones in cubical sets which is used in this proof. We also introduce the homotopy category and mapping spaces of a fibrant cubical set, and characterize weak equivalences between fibrant cubical sets in terms of these concepts. This talk is based on joint work with Chris Kapulkin, Zachery Lindsey, and Christian Sattler, arXiv:2005.04853.

Entries for this week: 4

Tuesday December 01, 2020

Homotopy Theory [url]
Cubical models of (infinity,1)-categories
- Brandon Doherty, University of Western Ontario
Time: 5pm Room: Zoom
More Information
Abstract/Desc: We describe a new model structure on the category of cubical sets with connections whose cofibrations are the monomorphisms and whose fibrant objects are defined by the right lifting property with respect to inner open boxes, the cubical analogue of inner horns. We discuss the proof that this model structure is Quillen equivalent to the Joyal model structure on simplicial sets via the triangulation functor, and a new theory of cones in cubical sets which is used in this proof. We also introduce the homotopy category and mapping spaces of a fibrant cubical set, and characterize weak equivalences between fibrant cubical sets in terms of these concepts. This talk is based on joint work with Chris Kapulkin, Zachery Lindsey, and Christian Sattler, arXiv:2005.04853.

Wednesday December 02, 2020

Departmental Tea Time
C is for cookie, and shorthand for C[0,1] w/the sup norm
Time: 3: Room: 204 LOV

Thursday December 03, 2020

Financial Math Seminar
Deep PDE Solutions of BSDEs
- Maxim Bichuch, Johns Hopkins University
Time: 4:35pm Room: Zoom
Abstract/Desc: We investigate the numerical convergence of a deep learning method of a solution to a PDE to that of a BSDE. We transform the BSDE to a coupled PDE, and find the relationship between the solutions to the two problems. We find sufficient conditions for the solution to be coupled PDE to be classical, and use a deep Galerkin method to obtain an approximation to the solution of the BSDE. We illustrate this with a numerical example.

Friday December 04, 2020

Colloquium Tea
Time: 3:00 pm Room: 204 LOV

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Department of Mathematics

This Week in Mathematics