Related papers: On the singular points approached by the medial ax…
We write supersymmetry preserving conditions for infinite M5-branes intersecting on a (3+1)-dimensional space. In contrast to previously known solutions, these intersections are completely localized. We solve the equations for a particular…
This paper provides a non-standard analogue of Bezout's theorem. This is acheived by showing that, in all characteristics, the notion of Zariski multiplicity coincides with intersection multiplicity when we consider the full families of…
In this note we study IR limits of pure two-dimensional supersymmetric gauge theories with semisimple non-simply-connected gauge groups including SU(k)/Z_k, SO(2k)/Z_2, Sp(2k)/Z_2, E_6/Z_3, and E_7/Z_2 for various discrete theta angles,…
We give an estimate of the mean curvature of a complete submanifold lying inside a closed cylinder $B(r)\times\R^{\ell}$ in a product Riemannian manifold $N^{n-\ell}\times\R^{\ell}$. It follows that a complete hypersurface of given constant…
The centralized circumcentered-reflection method (\cCRM) of~\cite{Behling:2024} converges superlinearly to a solution of $\operatorname{find}\;z\in X\cap Y$ when $\inte(X\cap Y)\neq\emptyset$ and the boundaries of $X$ and $Y$ are…
Let X be a projective cubic hypersurface of dimension 11 or more, which is defined over the rationals. In this paper it is shown that X contains rational points provided that the cubic form defining X can be written as the sum of two forms…
The $r$-uniform linear $k$-cycle $C^r_k$ is the $r$-uniform hypergraph on $k(r-1)$ vertices whose edges are sets of $r$ consecutive vertices in a cyclic ordering of the vertex set chosen in such a way that every pair of consecutive edges…
For a connected $n$-dimensional compact smooth hypersurface $M$ without boundary embedded in $\mathbb{R}^{n+1}$, a classical result of Aleksandrov shows that it must be a sphere if it has constant mean curvature. Li and Nirenberg studied a…
We reformulate superalgebra and supergeometry in completely categorical terms by a consequent use of the functor of points. The increased abstraction of this approach is rewarded by a number of great advantages. First, we show that one can…
The aim of this fisrt part is to introduce, for a rather large class of hypersurface singularities with 1 dimensionnal locus, the analog of the Brieskorn lattice at the origin (the singular point of the singular locus). The main results are…
Let $k$ be a field of characteristic not 2 or 3. We establish polynomial lower bounds on the ambient dimension $N$ for an intersection $X\subset\mathbb{P}^N$ of quadrics, cubics and quartics to have a dense collection of solvable points,…
It is known that, in string sigma-model metric, the `extreme' fivebrane solution of D=10 supergravity interpolates between D=10 Minkowski spacetime and a supersymmetric $S^3$ compactification to a linear dilaton vacuum. We show here that,…
We study anti-de Sitter black holes in 2+1 dimensions in terms of Chern Simons gauge theory of the anti-de Sitter group coupled to a Source. Taking the source to be an anti-de Sitter state specified by its Casimir invariants, we show how…
We prove a new formula for the Hirzebruch-Milnor classes of global complete intersections with arbitrary singularities describing the difference between the Hirzebruch classes and the virtual ones. This generalizes a formula for the…
Zarankiewicz's problem asks for the largest possible number of edges in a graph that does not contain a $K_{u,u}$ subgraph for a fixed positive integer $u$. Recently, Fox, Pach, Sheffer, Sulk and Zahl considered this problem for…
We investigate the nature of subsets of spheres which satisfy a tameness condition associated with the Bieri-Groves conjecture on cohomological finiteness conditions for metabelian groups. We find that there is a natural polyhedrality in a…
We discuss the non-perturbative behavior of the U(1)_R symmetry in N=2 superconformal Chern-Simons theories coupled to matter in the (anti)fundamental and adjoint representations of the gauge group, which we take to be U(N). Inequalities…
The first part of this review tries to provide a self-contained view of supersymmetry breaking from the bottom-up perspective. We thus describe N=1 supersymmetry in four dimensions, the Standard Model and the MSSM, with emphasis on the…
We discuss questions of isospectrality for hyperbolic orbisurfaces, examining the relationship between the geometry of an orbisurface and its Laplace spectrum. We show that certain hyperbolic orbisurfaces cannot be isospectral, where the…
We give sharp lower bounds for the degree of the syzygies involving the partial derivatives of a homogeneous polynomial defining an even dimensional nodal hypersurface. This implies the validity of formulas due to M. Saito, L. Wotzlaw and…