[Turkmath:6448] FGC-Higher Structures Seminars::Elena Caviglia [April 23, 2024 at 18:00 Istanbul time]

Thu Apr 18 17:30:08 UTC 2024

Sayın matematikçiler,

Aşağıda 23 Nisan 2024 saat 18:00'da yapılacak Feza Gürsey Fizik ve 
Matematik UygAr Merkezi Yüksek Yapılar Seminerleri konuşması ile ilgili 
detayları bulacaksınız.

Saygılarımla,

ilhan ikeda

--------------

Dear friends,

On April 23, 2024 Tuesday at 18:00 Istanbul local time (16:00 Leichester 
local time), Elena Caviglia from the University of Leichester will be 
the speaker of Feza Gursey Center for Physics and Mathematics Higher 
Structure Research Group Seminars.

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

Speaker: Elena Caviglia (University of Leichester)

Date: April 23, 2024, Tuesday

Time: 18:00 Istanbul local time (16:00 Leichester local time)

Title: _2-stacks and quotient 2-stacks_

Abstract:
Stacks generalize one dimension higher the fundamental concept of sheaf. 
They are pseudofunctors that are able to glue together weakly compatible 
local data into global data. Stacks are a very important concept in 
geometry, due to their ability to take into account automorphisms of 
objects. While many classification problems do not have a moduli space 
as solution because of the presence of automorphisms, it is often 
nonetheless possible to construct a moduli stack. In recent years, the 
research community has begun generalizing the notion of stack one 
dimension higher. Lurie studied a notion of (∞, 1)-stack, that yields a 
notion of (2, 1)- stack for a trihomomorphism that takes values in (2, 
1)-categories, when truncated to dimension 3. And Campbell introduced a 
notion of 2-stack that involves a trihomomorphism from a one-dimensional 
category into the tricategory of bicategories. In this talk, we will 
introduce a notion of 2-stack that is suitable for a trihomomorphism 
from a 2-category endowed with a bitopology into the tricategory of 
bicategories. The notion of bitopology that we consider is the one 
introduced by Street for bicategories. We achieve our definition of 
2-stack by generalizing a characterization of stack due to Street. Since 
our definition of 2-stack is quite abstract, we will also present a 
useful characterization in terms of explicit gluing conditions that can 
be checked more easily in practice. These explicit conditions generalize 
to one dimension higher the usual stacky gluing conditions. A key idea 
behind our characterization is to use the tricategorical Yoneda Lemma to 
translate the biequivalences required by the definition of 2-stack into 
effectiveness conditions of appropriate data of descent. As a 
biequivalence is equivalently a pseudofunctor which is surjective on 
equivalence classes of objects, essentially surjective on morphisms and 
fully faithful on 2-cells, we obtain effectiveness conditions for data 
of descent on objects, morphisms and 2-cells. It would have been hard to 
give the definition of 2-stack in these explicit terms from the 
beginning, as we would not have known the correct coherences to ask in 
the various gluing conditions. Our natural implicit definition is 
instead able to guide us in finding the right coherence conditions. 
Finally, we will present the motivating example for our notion of 
2-stack, which is the one of quotient 2-stack. After having generalized 
principal bundles and quotient stacks to the categorical context of 
sites, we aimed at a generalization of our theory one dimension higher, 
to the context of bisites, motivated by promising applications of 
principal 2- bundles to higher gauge theory. But there was no notion of 
higher dimensional stack suitable for the produced analogues of quotient 
prestacks in the two-categorical context. Our notion of 2-stack is able 
to fill this gap. Indeed, we have proven that, if the bisite satisfies 
some mild conditions, our analogues of quotient stacks one dimension 
higher are 2-stacks.

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.)

Topic: FG seminer
Time: Apr 23, 2024 17:30 Istanbul

Join Zoom Meeting
https://us02web.zoom.us/j/83285391847?pwd=ZnpoTkdxa3p6cnVwRi9JSXE0WmtPZz09 
[1]

Meeting ID: 832 8539 1847
Passcode: 167146

Best Regards,
Ilhan

Organized by Feza Gürsey Center for Physics and Mathematics
Supported by Bilim Akademisi - The Science Academy

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Links:
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[1] 
https://us02web.zoom.us/j/83285391847?pwd=ZnpoTkdxa3p6cnVwRi9JSXE0WmtPZz09
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