Related papers: Sharp volume and multiplicity bounds for Fano simp…
We show the relevance of a multifractal-type analysis for pointwise convergence and divergence properties of wavelet series: Depending on the sequence space which the wavelet coefficients sequence belongs to, we obtain deterministic upper…
In his paper "On the Schlafli differential equality", J. Milnor conjectured that the volume of n-dimensional hyperbolic and spherical simplices, as a function of the dihedral angles, extends continuously to the closure of the space of…
Littlewood polynomials are polynomials with each of their coefficients in {-1,1}. A sequence of Littlewood polynomials that satisfies a remarkable flatness property on the unit circle of the complex plane is given by the Rudin-Shapiro…
We study Fano threefolds with~terminal singularities admitting a "minimal" action of a finite group. We prove that under certain additional assumptions such a variety does not contain planes. We also obtain an upper bounds of the number of…
New selected values of odd random simplex volumetric moments (moments of the volume of a random simplex picked from a given body) are derived in an exact form in various bodies in dimensions three, four, five, and six. In three dimensions,…
We study affine osp(1|2) fusion, the fusion in osp(1|2) conformal field theory, for example. Higher-point and higher-genus fusion is discussed. The fusion multiplicities are characterized as discretized volumes of certain convex polytopes,…
We prove non-trivial upper and lower bounds for the "Spectrum of Singularities" of Fourier Series with polynomial frequencies. The Spectrum of Singularities of a function f gives the Hausdorff dimension of the set of points with a given…
We introduce a theory of volume polynomials and corresponding duality algebras of multi-fans. Any complete simplicial multi-fan $\Delta$ determines a volume polynomial $V_\Delta$ whose values are the volumes of multi-polytopes based on…
In 2003, Atserias and Dalmau resolved a major open question about the resolution proof system by establishing that the space complexity of CNF formulas is always an upper bound on the width needed to refute them. Their proof is beautiful…
We prove a compactness result for minimal hypersurfaces with bounded index and volume, which can be thought of as an extension of the compactness theorem of Choi-Schoen (Invent. Math. 1985) to higher dimensions.
We prove the Shafarevich conjecture for Fano threefolds of Picard rank 1, index 1 and degree 4.
In this paper, we prove new upper bounds for sums of reciprocals of fractional parts over general aligned boxes, thus extending a previous result of the author concerning bounds for sums of reciprocals over symmetric boxes. These new upper…
We present two identities (contiguity relation and variation formula) concerning the volume of a spherically faced simplex in the Euclidean space. These identities are described in terms of Cayley-Menger determinants and their differentials…
We study congruences of lines $X_\omega$ defined by a sufficiently general choice of an alternating 3-form $\omega$ in $n+1$ dimensions, as Fano manifolds of index $3$ and dimension $n-1$. These congruences include the…
Let $A$ be a simple algebra over a field $F$. Under a mild cardinality assumption on $F$, we determine the greatest possible dimension for an $F$-affine subspace of $A$ that is included in the group of units $A^\times$, and we describe the…
We introduce a concept of minimality for Fano polygons. We show that, up to mutation, there are only finitely many Fano polygons with given singularity content, and give an algorithm to determine the mutation-equivalence classes of such…
Under a hypothesis on $k$, $d$ and $n$ that is almost the best possible, we prove that for every smooth degree $d$ hypersurface in $P^n$, the $k$-plane sections dominate the moduli space of degree $d$ hypersurface in $P^k$. Using this we…
The purpose of this paper is to investigate finite-dimensional superbialgebras and Hopf superalgebras. We study connected superbialgebras and provide a classification of non-trivial superbialgebras and Hopf superalgebras in dimension $n$…
We provide the first known upper bounds for the packing dimension of weighted singular and weighted $\omega$-singular matrices. We also prove upper bounds for these sets when intersected with fractal subsets. The latter results, even in the…
We exhibit a large class of quiver moduli spaces which are Fano varieties, by studying line bundles on quiver moduli and their global sections in general, and work out several classes of examples, comprising moduli spaces of point…