Related papers: Computing the 4D Geode

We exploit the presence of moduli fields in the ${\rm AdS}_3\times { S}^3\times CY_2$, where $CY_2=T^4$ or $K3$, solution to Type IIB superstring theory, to construct a U-fold solution with geometry ${\rm AdS}_2\times S^1\times {\rm…

The superconformal index of a 4d gauge theory is computed by a matrix integral arising from localization of the supersymmetric path integral on S^3 x S^1 to the saddle point. As the radius of the circle goes to zero, it is natural to expect…

Let H be the hyperbolic space of dimension n+1. A geodesic foliation of H is given by a smooth unit vector field on H all of whose integral curves are geodesics. Each geodesic foliation of H determines an n-dimensional submanifold M of the…

Finding the so-called characteristic numbers of the complex projective plane ${\mathbb C}P^2$ is a classical problem of enumerative geometry posed by Zeuthen more than a century ago. For a given $d$ and $g$ one has to find the number of…

We obtain algorithms for computing Tverberg partitions based on centerpoint approximations. This applies to a wide range of convexity spaces, from the classic Euclidean setting to geodetic convexity in graphs. In the Euclidean setting, we…

Using equivariant geometry, we find a universal formula that computes the number of times a general cubic surface arises in a family. As applications, we show that the PGL(4) orbit closure of a generic cubic surface has degree 96120, and…

We study the L-series of cubic fourfolds. Our main result is that, if X/C is a special cubic fourfold associated to some polarized K3 surface $S$, defined over a number field K such that S^[2](K) is not empty, then X has a model over K such…

We present exponential and super factorial lower bounds on the number of Hamiltonian cycles passing through any edge of the basis graphs of a graphic, generalized Catalan and uniform matroids. All lower bounds were obtained by a common…

We study the field isomorphism problem of cubic generic polynomial $X^3+sX+s$ over the field of rational numbers with the specialization of the parameter $s$ to nonzero rational integers $m$ via primitive solutions to the family of cubic…

For an infinite family of monogenic trinomials $P(X) = X^3\pm 3rbX-b$ in $\mathbb{Z}\lbrack X\rbrack$, arithmetical invariants of the cubic number field $L = \mathbb{Q}(\theta)$, generated by a zero $\theta$ of $P(X)$, and of its Galois…

The strong geodetic problem is a recent variation of the classical geodetic problem. For a graph $G$, its strong geodetic number ${\rm sg}(G)$ is the cardinality of a smallest vertex subset $S$, such that each vertex of $G$ lies on one…

A real form $G_0$ of a complex semisimple Lie group $G$ has only finitely many orbits in any given compact $G$-homogeneous projective algebraic manifold $Z=G/Q$. A maximal compact subgroup $K_0$ of $G_0$ has special orbits $C$ which are…

This paper provides a characterization and examples of homogeneous geodesics on full $G/T$ and $G_{2}$ flag manifolds. We discuss for generalized root systems the property of sum-zero triple of $T$-roots and give several applications of…

We define a weighted multiplicity function for closed geodesics of given length on a finite area Riemann surface. These weighted multiplicities appear naturally in the Selberg trace formula, and in particular their mean square plays an…

We study solutions of a homogeneous quadratic equation $q(x_0,\dots, x_n)=0$, defined over a field $K$, where the $x_i$ are themselves homogeneous polynomials of some degree $d$ in $r+1$ variables. Equivalently, we are looking at rational…

In 2015, Guth proved that if $S$ is a collection of $n$ $g$-dimensional semi-algebraic sets in $\mathbb{R}^d$ and if $D\geq 1$ is an integer, then there is a $d$-variate polynomial $P$ of degree at most $D$ so that each connected component…

We investigate S^3/Z_n partition function of 3d N = 2 supersymmetric field theories. In a gauge theory the partition function is the sum of the contributions of sectors specified by holonomies, and we should carefully choose the relative…

We compute the prepotential of N=2 supersymmetric gauge theories in four dimensions obtained by toroidal compactifications of gauge theories from 6 dimensions, as a function of Kahler and complex moduli of T^2. We use three different…

A general class of Lorentzian metrics, $M_0 x R^2$, $ds^2 = <.,.> + 2 du dv + H(x,u) du^2$, with $(M_0, <.,.>$ any Riemannian manifold, is introduced in order to generalize classical exact plane fronted waves. Here, we start a systematic…

This paper examines the issues involved with concretely implementing a sum over conifolds in the formulation of Euclidean sums over histories for gravity. The first step in precisely formulating any sum over topological spaces is that one…