Related papers: Dual Feynman transform for modular operads

We show that Rabinowitz Floer homology and cohomology carry the structure of a graded Frobenius algebra for both closed and open strings. We prove a Poincar\'e duality theorem between homology and cohomology that preserves this structure.…

Let $V$ be a rational, selfdual, $C_2$-cofinite vertex operator algebra of CFT type, and $G$ a finite automorphism group of $V.$ It is proved that the kernel of the representation of the modular group on twisted conformal blocks associated…

We introduce a cohomology theory of grading-restricted vertex algebras. To construct the {\it correct} cohomologies, we consider linear maps from tensor powers of a grading-restricted vertex algebra to "rational functions valued in the…

We develop a notion of a dual of a graph, generalizing the definition of Goulden and Yong (which only applied to trees), and reproving their main result using our new notion. We in fact give three definitions of the dual: a graph-theoretic…

We show that sums over graphs such as appear in the theory of Feynman diagrams can be seen as integrals over discrete groupoids. From this point of view, basic combinatorial formulas of the theory of Feynman diagrams can be interpreted as…

The R*-operation by Chetyrkin, Tkachov, and Smirnov is a generalisation of the BPHZ R-operation, which subtracts both ultraviolet and infrared divergences of euclidean Feynman graphs with non-exceptional external momenta. It can be used to…

For operads with a map from the curved homotopy Lie operad, we introduce a corresponding curved variant `cTw' of Willwacher's operadic twisting comonad `Tw'. We show that cTw-coalgebra structures on such an operad are in bijection with…

We give a new proof of the non-triviality of wheel graph homology classes using higher operations on Lie graph homology and a derived version of Koszul duality for modular operads.

There are two approaches to projective representation theory of symmetric and alternating groups, which are powerful enough to work for modular representations. One is based on Sergeev duality, which connects projective representation…

We prove several claims made by Kontsevich about the orbifold Euler characteristic of the three types of graph homology introduced by him. For this purpose, first we develop a simplified version of the Feynman diagram method, which requires…

There are known two different constructions of contractible dg 2-operads, providing a weak 2-category structure on the following dg 2-quiver of small dg 2-categories. Its vertices are small dg 2-categories over a given field, arrows are dg…

This contribution is mainly based on joint papers with Lepowsky and Milas, and some parts of these papers are reproduced here. These papers further extended works by Lepowsky and by Milas. Following our joint papers, I explain the general…

Some equivalence classes in symmetric group lead to an interesting class of noncommutive and associative algebras. From these algebras we construct noncommutative Frobenius algebras. Based on the correspondence between Frobenius algebras…

This work presents a detailed analysis of the combinatorics of modular operads. These are operad-like structures that admit a contraction operation as well as an operadic multiplication. Their combinatorics are governed by graphs that admit…

Certain Feynman integrals can be expressed as periods of differential forms on Calabi--Yau manifolds. We provide a mathematical proof of a result of Duhr and Maggio on the modularity of the two-dimensional conformal traintrack integral. Our…

This thesis studies Frobenius manifolds arising from extended deformations of complex structures on compact Calabi-Yau manifolds, following the construction by Sergey Barannikov and Maxim Kontsevich. The work is based on the investigation…

Every unital nonselfadjoint operator algebra possesses canonical and functorial classes of faithful (even completely isometric) Hilbert space representations satisfying a double commutant theorem generalizing von Neumann's classical result.…

The purpose of this paper is to show that, under certain combinatorial conditions on the graph, parametric Feynman integrals can be realized as periods on the complement of the determinant hypersurface in an affine space depending on the…

The Connes-Kreimer Hopf algebra of rooted trees, its dual, and the Foissy Hopf algebra of of planar rooted trees are related to each other and to the well-known Hopf algebras of symmetric and quasi-symmetric functions via a pair of…

For each commutative, graded algebra with finite dimension in each degree, we construct a graded cohomology theory for graphs whose graded Euler characteristic is the chromatic polynomial of the graph. This extends our previous work which…