1 citations · 2 across the 13 of their papers we have counts for
13 papers
Shifted Contact Structures on Exact Symplectic Fibrations
Mehmet Fırat Arıkan, Kadri İlker Berktav, Efe İzbudak
Within the framework of classical contact geometry, the first author introduced the notion of contact symplectic structure --the data of an exact symplectic fibration with a contac…
Shifted Symplectic Fibrations and Derived Thurston Theorem
Mehmet Fırat Arıkan, Kadri İlker Berktav, Efe İzbudak
In classical symplectic geometry, under mild conditions, Thurston proved that one can construct a compatible symplectic form on the total space of a symplectic fibration with a con…
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…
A Mathematical Introduction to Geometric Quantization
Kadri İlker Berktav, Burak Oğuz, Ömer Önder +3
These notes are based on a series of lectures by Kadri İlker Berktav from May 2024 to November 2024, providing a detailed exposition of geometric quantization formalism and its ess…
Legendrian Structures in Derived Geometry
Kadri İlker Berktav
This is the third installment in a series of papers on the subject of derived contact structures. In this paper, we formally introduce the notion of a Legendrian structure in the d…
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…
An Introduction to Geometric Quantization and Witten's Quantum Invariant
Kadri İlker Berktav
This note, in a rather expository manner, serves as a conceptional introduction to the certain underlying mathematical structures encoding the geometric quantization formalism and…