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AKSZ Construction for Shifted Contact Structures
Efe İzbudak, Kadri İlker Berktav
This paper establishes the AKSZ theorem for shifted contact structures and its applications. In brief, to resolve certain obstructions, we first define the quotient mapping stack a…
A Derived Legendrian Category for Shifted Contact Stacks
Efe İzbudak, Kadri İlker Berktav
For every integer and every , we construct a symmetric monoidal -category whose objects are -shifted contact derived Artin stacks an…
Equivariant Quotients of Derived Symplectic Spaces and Legendrian Intersection Theorem
Efe İzbudak, Kadri İlker Berktav
The classical transversality lemma of contact geometry constructs a contact structure on a hypersurface transverse to a Liouville vector field using point-set topology and local fl…
On Shifted Contact Derived Artin Stacks
Kadri İlker Berktav
This is a sequel of our previous work, arXiv:2209.09686, on the development of derived contact geometry, in which we formally introduced shifted contact structures on derived stack…
Shifted Contact Structures and Their Local Theory
Kadri İlker Berktav
In this paper, we formally define the concept of shifted contact structures on derived (Artin) stacks and study their local properties in the context of derived algebraic geometry.…
Notes on Moduli theory, Stacks and 2-Yoneda's Lemma
Kadri İlker Berktav
This note is a survey on the basic aspects of moduli theory along with some examples. In that respect, one of the purposes of this current document is to understand how the introdu…
Stacks in Einstein Gravity and a Stacky Equivalence of 3D Quantum Gravity with Gauge Theory
Kadri İlker Berktav
In this paper, we examine stacky structures in Einstein's theory of gravity. In brief, we first give a construction of the moduli stack of solutions to (vacuum) Einstein field equa…
Notes on Derived Geometric Formulations in Physics
Kadri İlker Berktav
This is an overview of higher structural constructions in physics. The main motivations of our current attempt are as follows: (i) to provide a brief introduction to derived algebr…