Related papers: On the Sector Counting Lemma
Chisini's conjecture asserts that for a cuspidal curve $B\subset \mathbb P^2$ a generic morphism $f$ of a smooth projective surface onto $\mathbb P^2$ of degree $\geq 5$, branched along $B$, is unique up to isomorphism. We prove that if…
We present a predictive scheme for fermion masses and mixings based on supersymmetric SO(10) which provides an understanding of the observed hierarchies in the charged fermion sector including CKM mixings. In the neutrino sector bi-large…
Graphs embedded into surfaces have many important applications, in particular, in combinatorics, geometry, and physics. For example, ribbon graphs and their counting is of great interest in string theory and quantum field theory (QFT).…
Conformal field theory (CFT) has become an active area of research beyond its origins in statistical physics and attracted much attention due to its intrinsic mathematical interest, which reveals deep connections with other diverse branches…
An interesting problem in classical differential geometry is to find methods to prove that two surfaces defined by different charts actually coincide up to position in space. In a previous paper we proposed a method in this direction for…
With the help of Van der Corput lemmas, decay estimates are proven for Fourier transforms of mixed homogeneous hypersurface measures with densities that can be quite irregular. The primary results are local in nature, but can be extended to…
Regularity of the deformation of the Fermi surface under short-range interactions is established to all orders in perturbation theory. The proofs are based on a new classification of all graphs that are not doubly overlapping. They turn out…
Over a global field any finite number of central simple algebras of exponent dividing $m$ is split by a common cyclic field extension of degree $m$. We show that the same property holds for function fields of two-dimensional excellent…
We report on our project to find explicit examples of $K3$ surfaces having real or complex multiplication. Our strategy is to search through the arithmetic consequences of RM and CM. In order to do this, an efficient method is needed for…
We present simulations of 2-d site animals on square and triangular lattices in non-trivial geomeLattice animals are one of the few critical models in statistical mechanics violating conformal invariance. We present here simulations of 2-d…
Let M be a Q-divisor on a smooth surface over C. In this paper we give criteria for very ampleness of the adjoint of the round-up of M. (Similar results for global generation were given by Ein and Lazarsfeld and used in their proof of…
Let $X$ be a smooth irreducible projective variety of dimension at least 2 over an algebraically closed field of characteristic 0 in the projective space ${\mathbb{P}}^n$. Bertini's Theorem states that a general hyperplane $H$ intersects…
We introduce the effective field theory of two different light dark particles interacting with the standard model (SM) light states in a single vertex, termed dark sector effective field theory (DSEFT). We focus on the new light particles…
We prove several sharp distortion and monotonicity theorems for spherically convex functions defined on the unit disk involving geometric quantities such as spherical length, spherical area and total spherical curvature. These results can…
We introduce a new multiscale decomposition of the Fermi propagator based on its parametric representation. We prove that the corresponding sliced propagator obeys the same direct space bounds than the previous decomposition used by the…
The numerical range of a matrix is studied geometrically via the cone of positive semidefinite matrices (or semidefinite cone for short). In particular it is shown that the feasible set of a two-dimensional linear matrix inequality (LMI),…
The numerical range of a matrix is studied geometrically via the cone of positive semidefinite matrices (or semidefinite cone for short). In particular it is shown that the feasible set of a two-dimensional linear matrix inequality (LMI),…
Block copolymers provide a wonderful platform in studying the soft condensed matter systems. Many fascinating ordered structures have been discovered in bulk and confined systems. Among various theories, the self-consistent field theory…
We calculate the Fermi surface of electrons in hole-doped, extended t-J models on a square lattice in a regime where no long-range antiferromagnetic order is present, and no symmetries are broken. Using the "spinon-dopon" formalism of…
We establish half-space type results for a class of height-dependent weighted minimal surfaces in $\mathbb{R}^3$, namely critical points of a weighted area functional whose weight depends on the height. When the weight has at most quadratic…