Related papers: Hirzebruch-Riemann-Roch for complex analytic infin…

Model checking properties are often described by means of finite automata. Any particular such automaton divides the set of infinite trees into finitely many classes, according to which state has an infinite run. Building the full type…

We establish a general Kronecker limit formula of arbitrary rank over global function fields with Drinfeld period domains playing the role of upper-half plane. The Drinfeld-Siegel units come up as equal characteristic modular forms…

Let $(1) Rh=f$, $0\leq x\leq L$, $Rh=\int^L_0 R(x,y)h(y) dy$, where the kernel $R(x,y)$ satisfies the equation $QR=P\delta(x-y)$. Here $Q$ and $P$ are formal differential operators of order $n$ and $m<n$, respectively, $n$ and $m$ are…

We classify transcendental entire functions that are compositions of a polynomial and the exponential for which all singular values escape on disjoint rays. The construction involves an iteration procedure on an infinite-dimensional…

We give an overview of our formalizations in the proof assistant Isabelle/HOL of certain irrationality and transcendence criteria for infinite series from three different research papers: by Erd\H{o}s and Straus (1974), Han\v{c}l (2002),…

We define a higher analogue of Dirac structures on a manifold M. Under a regularity assumption, higher Dirac structures can be described by a foliation and a (not necessarily closed, non-unique) differential form on M, and are equivalent to…

We review some basic facts on vector fields, in the complex-analytic setting, thus, obtaining a rationality result and an extension of the Birkhoff-Grothendieck theorem, as follows: (1) Let $Z$ be a compact complex manifold endowed with a…

Atiyah and Hirzebruch gave examples ofeven degree torsion classes in the singularcohomology of a smooth complex projective manifold, which arenot Poincar\'{e} dual to an algebraiccycle. We notice that the order ofthese classes are small…

In finite graphs, finite-order tangles offer an abstract description of highly connected substructures. In infinite graphs, infinite-order tangles compactify the graphs in the same way the ends compactify connected locally finite graphs.…

We are concerned with rigid analytic geometry in the general setting of Henselian fields $K$ with separated analytic structure, whose theory was developed by Cluckers--Lipshitz--Robinson. It unifies earlier work and approaches of numerous…

A concept of randomness for infinite time register machines (ITRMs) is defined and studied. In particular, we show that for this notion of randomness, computability from mutually random reals implies computability and that an analogue of…

We derive explicit formulae for the subalgebra zeta functions of all higher Heisenberg Lie algebras over an arbitrary compact discrete valuation ring $\mathfrak{o}$. To this end, we develop Hecke-theoretic techniques for the enumeration, by…

We discuss resent developments in the problem of description of finite rank Toeplitz operators in different Bergman spaces and give some applications in analysis and mathematical physics

Classical computations can not capture the essence of infinite computations very well. This paper will focus on a class of infinite computations called convergent infinite computations}. A logic for convergent infinite computations is…

We introduce a new class of automata on infinite trees called \emph{alternating nonzero automata}, which extends the class of non-deterministic nonzero automata. We reduce the emptiness problem for alternating nonzero automata to the same…

There is a way of assigning a realizability notion to each degree of incomputability. In our setting, we make use of Weihrauch degrees (degrees of incomputability/discontinuity of partial multi-valued functions) to obtain Lifschitz-like…

We employ Hirzebruch-type invariants obtained from iterated p-covers to investigate concordance of links and string links. We show that the invariants naturally give various group homomorphisms of the string link concordance group into…

In this paper we study some new theories of characteristic homology classes for singular complex algebraic varieties. First we introduce a natural transformation T_{y}: K_{0}(var/X) -> H_{*}(X,Q)[y] commuting with proper pushdown, which…

Chung and Jiang showed that, if a one ended group contains an infinite order element, then every continuous cocycle over the full shift on that group, taking values in a discrete group, must be cohomologous to a homomorphism. We show that…

In this paper we obtain asymptotic formulas of arbitrary order for the Bloch eigenvalue and the Bloch function of the periodic Schrodinger operator of arbitrary dimension, when corresponding quasimomentum lies near a diffraction hyperplane.…