[Turkmath:6698] FGC-Higher Structures Seminars::David Ayala [12 November, 2024 at 16:00 Istanbul time]

[kazimilhan.ikeda]

Değerli Matematikçiler,

Aşağıda bu Salı saat 16:00'da Zoom üzerinden gerçekleşecek Feza Gürsey 
Fizik ve Matematik UygAr Merkezi Yüksek Yapılar Seminer Dizimizin 
detaylarını bulacaksınız.

İyi çalışmalar dilerim,
ilhan ikeda

-------- Özgün ileti --------

Dear friends,

I hope you are all doing fine... After a long break, on the 12th of 
November 2024 Tuesday at 16:00 Istanbul local time, David Ayala from 
Montana State University will be the speaker of Feza Gursey Center for 
Physics and Mathematics Higher Structure Research Group Seminars.

The details of David's seminar talk are as follows:

Speaker: David Ayala (Montana State University).

Date: November 12, 2024, Tuesday.

Time: 16:00 Istanbul local time / 06:00 Bozeman local time.

Title:_ Factorization homology of higher categories_

Abstract:
The "alpha" version of factorization homology pairs (framed) n-manifolds 
with En-algebras.  This construction generalizes classical homology of a 
manifold, yields novel results concerning configuration spaces of points 
in a manifold, and supplies a sort of state-sum model for sigma-models 
(ie, mapping spaces) to (n-1)-connected targets.  This "alpha" version 
of factorization homology novelly extends Poincaré duality, shedding 
light on deformation theory and dualities among field theories.  Being 
defined  using homotopical
mathematical foundations, "alpha" factorization homology is manifestly 
functorial and continuous in all arguments, notably in moduli of 
manifolds and embeddings between them, and it satisfies a 
local-to-global expression that is inherently homotopical in nature.   
Now, En-algebras can be characterized as (∞,n)-categories equipped with 
an (n-1)-connected functor from a point.  The (full) "beta" version
of factorization homology pairs (framed) n-manifolds with pointed 
(∞,n)-categories (with adjoints).  Applying 0th homology, or π0,
recovers a version of the String Net construction of surfaces, as well 
as of Skein modules of 3-manifolds.  In some sense, the inherently
homotopical nature of (full) "beta" factorization homology affords 
otherwise unforeseen continuity in all arguments, and local-to-global
expressions.
In this talk, I will outline a definition of "beta" factorization 
homology, focusing on low-dimensions and on suitably reduced 
(∞,n)-categories (specifically, braided monoidal categories).  I will 
outline some examples, and demonstrate some operational practice of 
factorization homology.  Some of this material is established in 
literature, some a work in progress, and some conjectural -- the status
of each assertion will be made clear.  I will be especially interested 
in targeting this talk wot those present, and so will welcome comments 
and questions.
All of this work is joint with John Francis.

Zoom uygulaması Bilim Akademisi tarafından sağlanmaktadır./Zoom link is 
provided by The Science Academy.

Zoom link details:
(As usual the Zoom link will be active 30 minutes before the seminar 
time; that is at 15:30 Istanbul time.)

Topic: FGC-Higher Structures Seminars

Date and Time: Nov 12, 2024 active at 15:30 Istanbul

Join Zoom Meeting
https://us02web.zoom.us/j/81515082956?pwd=3GFxY9q3pp9jNXAA3E7qI2Ya8DItA8.1

Meeting ID: 815 1508 2956
Passcode: 613918

Best regards,
Ilhan

Organized by Feza Gürsey Center for Physics and Mathematics
Supported by Bilim Akademisi - The Science Academy
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://yunus.listweb.bilkent.edu.tr/pipermail/turkmath/attachments/20241109/0bec4c6d/attachment-0001.html>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: feza-logo.jpg
Type: image/jpeg
Size: 104962 bytes
Desc: not available
URL: <http://yunus.listweb.bilkent.edu.tr/pipermail/turkmath/attachments/20241109/0bec4c6d/attachment-0002.jpg>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: BilimAkademisiLogo11.jpg
Type: image/jpeg
Size: 36661 bytes
Desc: not available
URL: <http://yunus.listweb.bilkent.edu.tr/pipermail/turkmath/attachments/20241109/0bec4c6d/attachment-0003.jpg>