Related papers: The norm map on the Bloch group for quadratic exte…
We obtain the sharp estimates on the growth of the uniform norm of orthonormal polynomials for measures satisfying the Steklov condition. This improves the earlier results by Rakhmanov and completely settles a problem by Steklov. The sharp…
We study central extensions E of elementary abelian 2-groups by elementary abelian 2-groups. Associated to such an extension is a quadratic map which determines the extension uniquely. The components of the map determine a quadratic ideal…
The Grothendieck ring of varieties has well-known realization maps to, say, mixed Hodge structures or compactly supported $\ell$-adic cohomology. Zakharevich and\ Campbell have developed {a spectral refinement} of the Grothendieck ring of…
Let M be a monoidal category endowed with a distinguished class of weak equivalences and with appropriately compatible classifying bundles for monoids and comonoids. We define and study homotopy-invariant notions of normality for maps of…
In this paper we give some results concerning Frechet differentiable mappings between domains in normed spaces with controlled growth. The results are mainly motivated by Pavlovic's equality for the Bloch semi-norm of continuously…
We associate to each non-degenerate smooth interval map a number measuring its global asymptotic expansion. We show that this number can be calculated in various different ways. A consequence is that several natural notions of nonuniform…
In this note we prove a generalization of the flat extension theorem of Curto and Fialkow for truncated moment matrices. It applies to moment matrices indexed by an arbitrary set of monomials and its border, assuming that this set is…
For an algebraic family $(f_t)$ of regular quadratic polynomial endomorphisms of $\mathbb{C}^2$ parametrized by $\mathbb{D}^*$ and degenerating to a H\'enon map at $t=0$, we study the continuous (and indeed harmonic) extendibility across…
In \cite{Mil}, Milnor posed the {\em Monotonicity Conjecture} that the set of parameters within a family of real multimodal polynomial interval maps, for which the topological entropy is constant, is connected. This conjecture was proved…
We prove that for any two closed Riemannian manifolds $M^{2m}$ ($m\geq 1$) and $N$, there exists a minimizing (extrinsic) $m$-polyharmonic map for every free homotopy class in $[M^{2m}, N]$, provided that the homotopy group $\pi_{2m}(N)$ is…
We prove that the entropy function on the moduli space of real quadratic rational maps is not monotonic by exhibiting a continuum of disconnected level sets. This entropy behavior is in stark contrast with the case of polynomial maps, and…
In this paper we extend recent results of Fiorini et al. on the extension complexity of the cut polytope and related polyhedra. We first describe a lifting argument to show exponential extension complexity for a number of NP-complete…
M. Beck, J. De Loera, M. Develin, J. Pfeifle and R. Stanley found that the roots of the Ehrhart polynomial of a d-dimensional lattice polytope are bounded above in norm by 1+(d+1)!. We provide an improved bound which is quadratic in d and…
In this paper we continue Prasma's homotopical group theory program by considering homotopy normal maps in arbitrary $\infty$-topoi. We show that maps of group objects equipped with normality data, in Prasma's sense, are algebras for a…
Gowers and Hatami initiated the inverse theory for the uniformity norms $U^k$ of matrix-valued functions on non-abelian groups by proving a $1\%$-inverse theorem for the $U^2$-norm and relating it to stability questions for almost…
We prove that all injective maps on positive complex matrices which preserve order and shrink spectrum are implemented by unitary or antiunitary conjugations. We show by counterexamples that all assumptions are indispensable. The result…
The estimates of the uniform norm of the Chebyshev polynomials associated with a compact set $K$ in the complex plane are established. These estimates are exact (up to a constant factor) in the case where $K$ consists of a finite number of…
We establish basic facts about the varieties of homogeneous polynomials divisible by powers of linear forms, and explain consequences for geometric complexity theory. This includes quadratic set-theoretic equations, a description of the…
The article focuses on three different notions of polynomiality for maps of modules. In addition to the polynomial maps studied by Eilenberg and Mac Lane and the strict polynomial maps ("lois polynomes") considered by Roby, we introduce…
A family of non-conjugate chaotic maps generalizing the well-known logistic function is defined, and some of its basic properties studied. A simple formula for the Lyapunov exponents of all the maps contained in this family is given based…