Mathematical Institute Calendar

Tuesday, October 19, 2021

17:00-18:00

HFG611 and Zoom

Title: From K-theory to calculus

Abstract: Topological K-theory is an extension of algebraic K-theory to the world of geometry. Building from vector spaces (say over the real or complex numbers) Atiyah constructed an invariant of topological spaces which behaves similarly to how algebraic K-theory behaves as an invariant of rings. Depending on one's choice of the base field we obtain different invariants which are intricately related.

Also starting with real or complex vector spaces as the foundations, one can describe a categorification of differential calculus which studies functors from your category of vector spaces to the category of topological spaces. This calculus has much in common with differential calculus including the ability to examine the rate-of-change of a functor and a version of Taylor’s Theorem which provides a filtration of a topological space by “polynomial” parts.

In this talk, I will aim to provide some intuition behind these two seemingly unrelated constructions and discuss how the intricate relationship between real and complex K-theory offers deep insight into the calculus. If time permits I will discuss some other categorifications of calculus and how they relate to each other.

Website of the seminar: http://utrechtgeometrycentre.nl/ugc-seminar/

Practical details will be sent by email to the staff and student mailing lists a few days before the event.

Abstract: Topological K-theory is an extension of algebraic K-theory to the world of geometry. Building from vector spaces (say over the real or complex numbers) Atiyah constructed an invariant of topological spaces which behaves similarly to how algebraic K-theory behaves as an invariant of rings. Depending on one's choice of the base field we obtain different invariants which are intricately related.

Also starting with real or complex vector spaces as the foundations, one can describe a categorification of differential calculus which studies functors from your category of vector spaces to the category of topological spaces. This calculus has much in common with differential calculus including the ability to examine the rate-of-change of a functor and a version of Taylor’s Theorem which provides a filtration of a topological space by “polynomial” parts.

In this talk, I will aim to provide some intuition behind these two seemingly unrelated constructions and discuss how the intricate relationship between real and complex K-theory offers deep insight into the calculus. If time permits I will discuss some other categorifications of calculus and how they relate to each other.

Website of the seminar: http://utrechtgeometrycentre.nl/ugc-seminar/

Practical details will be sent by email to the staff and student mailing lists a few days before the event.

Thursday, October 21, 2021

09:00-10:30

Zoom

Guest presentation (2nd talk) by Hyeonjun Park (Seoul National University) - Virtual pullbacks in Donaldson-Thomas theory of Calabi-Yau 4-folds

see description

2nd Presentation,

Interested people can e-mail Martijn Kool (m.kool1@uu.nl) for Zoom details.

Abstract:In this second talk, I will introduce a virtual pullback formula for Oh-Thomasvirtual cycles. As applications, I will discuss the Lefschetz principle inDonaldson-Thomas theory and the Pairs/Sheaves correspondence. I will alsoexplain how they are related to the conjectures of Cao-Kool, Cao-Kool-Monavari,Cao-Maulik-Toda, and Cao-Toda. This is based on arXiv:2110.03631**.**

Thursday, October 28, 2021

16:00-17:00

Library

MI-Talks

Jason Frank -- How to solve a partial differential equation given nothing but data

see description

Using the solutions of certain Dirichlet problems one can gain information about the escape/transition times between equilibria of metastable stochastic differential equations. We show how to construct numerical approximations of these solutions directly from time series data taken from sample paths of the SDE.

(joint work with Francesca Cavallini)

(joint work with Francesca Cavallini)

Tuesday, November 2, 2021

16:00-17:00

Library and Zoom

TBA

Website of the UGC seminar: http://utrechtgeometrycentre.nl/ugc-seminar/

Practical details will be sent by email to the staff and student mailing lists a few days before the event.

Website of the UGC seminar: http://utrechtgeometrycentre.nl/ugc-seminar/

Practical details will be sent by email to the staff and student mailing lists a few days before the event.

Tuesday, November 16, 2021

17:00-18:00

Zoom and HFG611

TBA

Website of the seminar: http://utrechtgeometrycentre.nl/ugc-seminar/

Practical details will be sent by email to the staff and student mailing lists a few days before the event.

Website of the seminar: http://utrechtgeometrycentre.nl/ugc-seminar/

Practical details will be sent by email to the staff and student mailing lists a few days before the event.

Thursday, November 25, 2021

Thursday, December 2, 2021

16:00-17:00

BBG-112

Thursday, December 9, 2021

Tuesday, December 14, 2021

17:00-18:00

HFG 611 and Zoom

Website of the seminar: http://utrechtgeometrycentre.nl/ugc-seminar/

Practical details will be sent by email to the staff and student mailing lists a few days before the event.

Wednesday, December 22, 2021