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We prove a H\"older-type inequality for Hamiltonian diffeomorphisms relating the $C^0$ norm, the $C^0$ norm of the derivative, and the Hofer/spectral norm. We obtain as a consequence that sufficiently fast convergence in Hofer/spectral…

In this short note we prove an equivariant version of the formality of multidiffirential operators for a proper Lie group action. More precisely, we show that the equivariant Hochschild-Kostant-Rosenberg quasi-isomorphism between the…

I briefly review the properties of classical affine Toda field theories and indicate how some of this features survive in the quantum theory on-shell. I demonstrate how this knowledge can be extended off-shell, i.e. how to compute…

We prove the classical Riemann-Roch theorems for the Adams operations $\,\psi^j\,$ on $K$-theory: a statement with coefficients on $\mathbb{Z}[j^{-1}]$, that holds for arbitrary projective morphisms, as well as another one with integral…

We prove an inverse theorem for the Gowers $U^2$-norm for maps $G\to\mathcal M$ from an countable, discrete, amenable group $G$ into a von Neumann algebra $\mathcal M$ equipped with an ultraweakly lower semi-continuous, unitarily invariant…

We develop the notion of a (pro-) conformal pseudo operad and apply it to the construction of the basic cohomology complex of a vertex algebra. The paper heavily uses the ideas and constructions of the work of Tamarkin [Tam02]

In [S\'eries Gevrey de type arithm\'etique I Th\'eor\'emes de puret\'e et de dualit\'e, Annals of Math. 151 (2000), 705--740], Andr\'e has introduced E-operators, a class of differential operators intimately related to E-functions, and…

The Holant theorem is a powerful tool for studying the computational complexity of counting problems in the Holant framework. Due to the great expressiveness of the Holant framework, a converse to the Holant theorem would itself be a very…

Let K(n) be the nth Morava K--theory at a prime p. This paper is a thorough study of questions like the following: to what extent does the K(n)--localization, or the K(n)--homology, of a spectrum X determine the K(n)--homology of its 0th…

$\mathcal{O}$-operators are important in broad areas in mathematics and physics, such as integrable systems, the classical Yang-Baxter equation, pre-Lie algebras and splitting of operads. In this paper, a deformation theory of…

We establish a new and surprisingly strong link between two previously unrelated theories: the theory of moduli spaces of curves ${\mathcal M}_{g,n}$ (which, according to Penner, is controlled by the ribbon graph complex) and the homotopy…

We develop a general obstruction theory to the formality of algebraic structures over any commutative ground ring. It relies on the construction of Kaledin obstruction classes that faithfully detect the formality of differential graded…

We present a formal model developed to reason about topologies created by sensor ranges. This model is used to formalise the topological aspects of an existing counting algorithm to estimate the number of targets in the area covered by the…

We prove a simple criterion for essential normality of composition operators on the Hardy space induced by maps in a reasonably large class of analytic self-maps of the unit disk. By combining this criterion with boundary…

We discuss various aspects concerning transformations of local analytic, or formal, vector fields to Poincare-Dulac normal form, and the convergence of such transformations. We first review A.D. Bruno's approach to formal normalization, as…

Let $K$ be a field complete with respect to a nonarchimedean real-valued norm, and let $L/K$ be an algebraic extension. We show that there is a unique norm on $L$ extending the given norm on $K$, with an explicit description. As an…

We use induction and interpolation techniques to prove that a composition operator induced by a map $\phi$ is bounded on the weighted Bergman space $\A^2_\alpha(\mathbb{H})$ of the right half-plane if and only if $\phi$ fixes $\infty$…

We study the local preservation of Birkhoff-James orthogonality by linear operators between normed linear spaces, at a point and in a particular direction. We obtain a complete characterization of the same, which allows us to present…

We study the Toda field theory with finite Lie algebras using an extension of the Goulian-Li technique. In this way, we show that, after integrating over the zero mode in the correlation functions of the exponential fields, the resulting…

Recently, Connelly and Gortler gave a novel proof of the circle packing theorem for tangency packings by introducing a hybrid combinatorial-geometric operation, flip-and-flow, that allows two tangency packings whose contact graphs differ by…