Related papers: Variations on the theme of quantum Lefschetz
This thesis start by a review of different approaches to classical and quantum gravity. The main theme is Lorentzian Gromov Hausdorff theory which is an active diffeomorphism invariant theory on the space of Lorentz spaces (think about…
Givental's $K$-theoretical $J$-function can be used to reconstruct genus zero $K$-theoretical Gromov--Witten invariants. We view this function as a fundamental solution of a $q$-difference system. In the case of projective spaces, we show…
Graphical functions have emerged as a powerful framework for evaluating multi-loop Feynman integrals in perturbative quantum field theory. Defined as massless three-point position-space integrals, they reveal rich analytic structures and…
We use Noether-Lefschetz theory to study the reduced Gromov--Witten invariants of a holomorphic-symplectic variety of $K3^{[n]}$-type. This yields strong evidence for a new conjectural formula that expresses Gromov-Witten invariants of this…
We study certain aspects of the recently proposed notion of nonrelativistic diffeomorphism invariance. In particular, we consider specific examples of invariant actions, extended gauge symmetry as well as an application to the theory of…
We prove two general factorization theorems for fixed-point invariants of fibrations: one for the Lefschetz number and one for the Reidemeister trace. These theorems imply the familiar multiplicativity results for the Lefschetz and Nielsen…
We adapt the definition of the Vietoris map to the framework of finite topological spaces and we prove some coincidence theorems. From them, we deduce a Lefschetz fixed point theorem for multivalued maps that improves recent results in the…
The paper aims at giving an introduction to the notion of quantum curves. The main purpose is to describe the new discovery of the relation between the following two disparate subjects: one is the topological recursion, that has its origin…
Electromagnetic and gravitational central-field problems are studied with relativistic quantum mechanics on curved space-time backgrounds. Corrections to the transition current are identified. Analogies of the gravitational and…
Let X be a locally compact space with a continuous proper action of a locally compact group G. Assuming that X satisfies a certain kind of duality in equivariant bivariant Kasparov theory, we can enrich the classical construction of…
This review is an extended version of the Seoul ICM 2014 proceedings.It is a short overview of the "topological recursion", a relation appearing in the asymptotic expansion of many integrable systems and in enumerative problems. We recall…
In algebraic geometry, Gromov--Witten invariants are enumerative invariants that count the number of complex curves in a smooth projective variety satisfying some incidence conditions. In 2001, A. Givental and Y.P. Lee defined new…
We compare the recently formulated multifractional spacetimes with field theories of quantum gravity based on the renormalization group (RG), such as asymptotic safety and Ho\v{r}ava--Lifshitz gravity. The change of spacetime dimensionality…
Quantization of diffeomorphism invariant theories of connections is studied. A solutions of the diffeomorphism constraints is found. The space of solutions is equipped with an inner product that is shown to satisfy the physical reality…
We describe the combinatorics that arise in summing a double recursion formula for the enumeration of connected Feynman graphs in quantum field theory. In one index the problem is more tractable and yields concise formulas which are…
Recent work in gravitational lensing and catastrophe theory has shown that the sum of the signed magnifications of images near folds, cusps and also higher catastrophes is zero. Here, it is discussed how Lefschetz fixed point theory can be…
The status of multifractional theories is reviewed using comparative tables. Theoretical foundations, classical matter and gravity dynamics, cosmology and experimental constraints are summarized and the application of the multifractional…
We develop further the approach to derived differential geometry introduced in Costello's work on the Witten genus. In particular, we introduce several new examples of L-infinity spaces, discuss vector bundles and shifted symplectic…
We examine a number of results of infinite combinatorics using the techniques of reverse mathematics. Our results are inspired by similar results in recursive combinatorics. Theorems included concern colorings of graphs and bounded graphs,…
Let $X$ be any smooth Deligne-Mumford stack with projective coarse moduli, and $Y$ be a smooth complete intersection in $X$ associated with a direct sum of semi-positive line bundles. We will introduce a useful and broad class known as…