Related papers: Geometric Quantization with Applications to Gromov…
This text introduces geometric quantization on orbifolds. After reviewing the necessary background, it develops new treatments of prequantization, polarizations, and metaplectic correction for symplectic orbifolds.
We establish Gromov's celebrated reconstruction theorem in Lorentzian geometry. Alongside this result, we introduce and study a natural concept of isomorphy of normalized bounded Lorentzian metric measure spaces. We outline applications to…
The basic elements of the geometric approach to a consistent quantization formalism are summarized, with reference to the methods of the old quantum mechanics and the induced representations theory of Lie groups. A possible relationship…
This expository article introduces the Kapustin-Witten equations to mathematicians. We discuss the connections between the Complex Yang-Mills equations and the Kapustin-Witten equations. In addition, we show the relation between the…
Geometric complexity theory (GCT) is an approach to the P vs. NP and related problems. This article gives its complexity theoretic overview without assuming any background in algebraic geometry or representation theory.
This is a review of the aspirations and disappointments of the canonical quantization of geometry. I compare the two chief ways of looking at canonical gravity, geometrodynamics and connection dynamics. I capture as much of the classical…
This article describes recent applications of algebraic geometry to noncommutative algebra. These techniques have been particularly successful in describing graded algebras of small dimension.
An analogue of geometric quantization of Poisson algebras obtained by algebraic reduction of symmetries is developed. Interpretation of the obtained results and their application to the problem of commutativity of quantization and reduction…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
We define a formal Gromov-Witten theory of the quintic 3-fold via localization on CP4. Our main result is a direct geometric proof of holomorphic anomaly equations for the formal quintic in precisely the same form as predicted by B-model…
Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to…
We compute the Gromov-Witten potential at all genera of target smooth Riemann surfaces using Symplectic Field Theory techniques and establish differential equations for the full descendant potential. This amounts to impose (and possibly…
The study of open/closed string duality and large $N$ duality suggests a Gromov-Witten theory for conifolds that sits on the border of both a closed Gromov-Witten theory and an open Gromov-Witten theory. In this work we employ the result of…
In this paper we introduce invariants of semi-free Hamiltonian actions of $S\sp 1$ on compact symplectic manifolds (which satisfy some technical conditions related to positivity) using the space of solutions to certain gauge theoretical…
The metric known to be relevant for standard quantization procedures receives a natural interpretation and its explicit use simultaneously gives both physical and mathematical meaning to a (coherent-state) phase-space path integral, and at…
We discuss the deformation quantization approach for the teaching of quantum mechanics. This approach has certain conceptual advantages which make its consideration worthwhile. In particular, it sheds new light on the relation between…
We discuss some questions about Gromov-Witten classes of target stacks.
Quantization of gravitation theory as gauge theory of general covariant transformations in the framework of Batalin-Vilkoviski (BV) formalism is considered. Its gauge-fixed Lagrangian is constructed.
These are expanded notes of author's talk at the ECM 2008 attempting to give an elementary introduction into the main ideas of the theory of wheeled props for beginners, and also a survey of its most recent major applications (ranging from…
The paper presents shortly the geometric approach to the problem of a general quantization formalism, both physically meaningful and mathematically consistent.