Related papers: Homotopy Transfer and Effective Field Theory I: Tr…
The text contains introduction and preliminary definitions and results to my talk on category theory description of supersymmetries and integrability in string theory. In the talk I plan to present homological and homotopical algebra…
In this review we study quantum field theories and conformal field theories with global symmetries in the limit of large charge for some of the generators of the symmetry group. At low energy the sectors of the theory with large charge are…
We define and develop two-level type theory (2LTT), a version of Martin-L\"of type theory which combines two different type theories. We refer to them as the inner and the outer type theory. In our case of interest, the inner theory is…
The purpose of this paper is to explain how the identities of various fundamental lemmas fall within the scope of the transfer principle, a general result that allows to transfer theorems about identities of p-adic integrals from one…
In this paper we describe explicit $L_\infty$ algebras modeling the rational homotopy type of any component of the spaces $\map(X,Y)$ and $\map^*(X,Y)$ of free and pointed maps between the finite nilpotent CW-complex $X$ and the finite type…
We show that an A-infinity algebra structure can be transferred to a projective resolution of the complex underlying any A-infinity algebra. Under certain connectedness assumptions, this transferred structure is unique up to homotopy. In…
On-shell amplitudes are invariant under field redefinitions. Nonderivative field redefinitions have a natural interpretation as coordinate transformations on the target manifold. General field redefinitions, which may involve derivatives,…
We classify the homotopy classes of proper Fredholm maps from an infinite dimensional Hilbert manifold into its model space in terms of a suitable version of framed cobordism. Our construction is an alternative approach to the…
Homotopy links have proven to be one of the most powerful tools of stratified homotopy theory. In previous work, we described combinatorial models for the generalized homotopy links of a stratified simplicial set. For many purposes, in…
In these lecture notes we discuss a body of work in which Morse theory is used to construct various homology and cohomology operations. In the classical setting of algebraic topology this is done by constructing a moduli space of graph…
A general framework for effective theories propagating two tensor and one scalar degrees of freedom is investigated. Geometrically, it describes dynamical foliation of spacelike hypersurfaces coupled to a general background, in which the…
This Ph.D. thesis investigates effective field and string theories in which supersymmetry is realized and broken in various ways. Chapter 1 addresses effective theories with nonlinearly realized supersymmetry, constructed using the…
In this article, we establish the compatibility between norms and transfers in motivic homotopy theory. More precisely, we construct norm functors for motivic spaces equipped with various flavours of transfer. This yields a norm monoidal…
Inducing latent tree structures from sequential data is an emerging trend in the NLP research landscape today, largely popularized by recent methods such as Gumbel LSTM and Ordered Neurons (ON-LSTM). This paper proposes FASTTREES, a new…
The Hopf theorem states that homotopy classes of continuous maps from a closed connected oriented smooth $n$-manifold $M$ to the $n$-sphere are classified by their degree. Such a map is equivalent to a section of the trivial $n$-sphere…
We analyze the gauge structure of a recently proposed superconformal field theory in six dimensions. We find that this structure amounts to a weak Courant-Dorfman algebra, which, in turn, can be interpreted as a strong homotopy Lie algebra.…
We calculate the higher homotopy groups of the Deligne-Getzler infinity-groupoid associated to a nilpotent L-infinity algebra. As an application, we present a new approach to the rational homotopy theory of mapping spaces.
The geometry-dependent energy transfer rate from an electrically pumped inorganic semiconductor quantum well into an organic molecular layer is studied theoretically. We focus on F\"orster-type nonradiative excitation transfer between the…
We study properties of differential graded (dg) operads modulo weak equivalences, that is, modulo the relation given by the existence of a chain of dg operad maps inducing a homology isomorphism. This approach, naturally arising in string…
We study the connection between the Goodwillie tower of the identity and the lower central series of the loop group on connected spaces. We define the simplicial theory of homotopy n-nilpotent groups. This notion interpolates between…