Related papers: Non-absolute integration and application to Young …
Generalized Functions play a central role in the understanding of differential equations containing singularities and nonlinearities. Introducing infinitesimals and infinities to deal with these obstructions leads to controversies…
We explore the idea to bootstrap Feynman integrals using integrability. In particular, we put the recently discovered Yangian symmetry of conformal Feynman integrals to work. As a prototypical example we demonstrate that the D-dimensional…
Relations between triple Jordan systems and integrable multi-component models of the modified Korteveg--de Vries type are established. The most general model is related to a pair consisting of a triple Jordan system and a skew-symmetric…
Additional integral inequalities are obtained for integrals of the differences of subharmonic functions by Borel measures on balls in a multidimensional Euclidean space. These integrals are still estimated from above through the Nevanlinna…
We give a general criterion for conformal embeddings of vertex operator algebras associated to affine Lie algebras at arbitrary levels. Using that criterion, we construct new conformal embeddings at admissible rational and negative integer…
In this work, families of kinks are analytically identified in multifield theories with either polynomial or deformed sine-Gordon-type potentials. The underlying procedure not only allows us to obtain analytical solutions for these models,…
This paper studies random lozenge tilings of general non-convex polygonal regions. We show that the pairwise interaction of the non-convexities leads asymptotically to new kernels and thus to new statistics for the tiling fluctuations. The…
The Jacobian conjecture over a field of characteristic zero is considered directly in view of the nonlinear partial differential equations it is associated with. Exploring the integrals of such partial differential equations, this work…
Universal Drinfeld twists are inner automorphisms which relate the coproduct of a quantum enveloping algebra to the coproduct of the undeformed enveloping algebra. Even though they govern the deformation theory of classical symmetries and…
We establish a weighted simultaneous Khintchine-type theorem, both convergence and divergence, for all nondegenerate manifolds, which answers a problem posed in [Math. Ann., 337(4):769-796, 2007]. This extends the main results of [Acta…
This survey paper explains how one can attach geometric invariants to semialgebraic sets defined over non-archimedean fields, using the theory of motivic integration of Hrushovski and Kazhdan. It also discusses tropical methods to compute…
We discuss no-dimensional (approximate) versions of Carath\'eodory's and Helly's theorems. Our goal is to draw attention to open problems and potential applications related to these results. We survey recent progress and pose several…
A new (in)finite dimensional algebra which is a fundamental dynamical symmetry of a large class of (continuum or lattice) quantum integrable models is introduced and studied in details. Finite dimensional representations are constructed and…
We derive a new expression for the q-analogue of the Young symmetrizer which generate irreducible representations of the Hecke algebra. We obtain this new expression using Cherednik's fusion procedure. However, instead of splitting Young…
Intersection distribution and non-hitting index are concepts introduced recently by Li and Pott as a new way to view the behaviour of a collection of finite field polynomials. With both an algebraic interpretation via the intersection of a…
In the article we discuss the notion of the generalized invariant manifold introduced in our previous study. In the literature the method of the differential constraints is well known as a tool for constructing particular solutions for the…
In this thesis, we describe some recent results obtained in the analysis of two-dimensional quantum field theories by means of semiclassical techniques. These achievements represent a natural development of the non-perturbative studies…
Several studies have exploited the integrable structure of central spin models to deepen understanding of these fundamental systems. In recent years, an underlying supersymmetry for systems with XX interactions has been uncovered. Here we…
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear integrable systems is obtained, and the integration scheme for such equations is proposed.
Integral properties of multifunctions determined by vector valued functions are presented. Such multifunctions quite often serve as examples and counterexamples. In particular it can be observed that the properties of being integrable in…