Related papers: Computing Moment Maps of Hypersurfaces using MAXIM…
In this article we suggest a new approach to the systematic, computer-aided construction and to the classification of product-quotient surfaces, introducing a new invariant, the integer gamma, which depends only on the singularities of the…
We characterize homogeneous hypersurfaces in complex space forms which arise as critical points of a higher order energy functional. As a consequence, we obtain existence and non-existence results for $\mathbb{CP}^n$ and $\mathbb{CH}^n$,…
A program to calculate the three-particle hyperspherical brackets is presented. Test results are listed and it is seen that the program is well applicable up to very high values of the hypermomentum and orbital momenta. The listed runs show…
This paper studies the application of multimomentum maps to the constraint analysis of general relativity on null hypersurfaces. It is shown that, unlike the case of spacelike hypersurfaces, some constraints which are second class in the…
Subtraction schemes provide a systematic way to compute fully-differential cross sections beyond the leading order in the strong coupling constant. These methods make singular real-emission corrections integrable in phase space by the…
We give a bijection between a quotient space of the parameters and the space of moments for any $A$-hypergeometric distribution. An algorithmic method to compute the inverse image of the map is proposed utilizing the holonomic gradient…
We illustrate the typical usage of Bayer and Macr\`{i}'s Positivity Lemma to compute the nef cones of the Hilbert schemes $X^{[n]}$ by combining the Bridgeland stability methods (for large $n$) and classical methods (for small $n$). We use…
The surface properties of solid-state materials often dictate their functionality, especially for applications where nanoscale effects become important. The relevant surface(s) and their properties are determined, in large part, by the…
We use moment techniques to construct a converging hierarchy of optimization problems to lower bound the ground state energy of interacting particle systems. We approximate (from below) the infinite dimensional optimization problems in this…
We describe a new relation between the topology of hypersurface complements, Milnor fibers and degree of gradient mappings. In particular we show that any projective hypersurface has affine parts which are bouquets of spheres. The main…
We apply the technique of jet differentials to establish a Gauss curvature estimate for an open Riemann surface $M$, equipped with a conformal metric induced from a nonconstant holomorphic map that is highly ramified over a generic…
We study the space of smooth marked hypersurfaces in a given linear system. Specifically, we prove a homology h-principle to compare it with a space of sections of an appropriate jet bundle. Using rational models, we compute its rational…
We use the transport methods developped in [3] to obtain universality results for local statistics of eigenvalues in the bulk and at the edge for $\beta$-matrix models in the multi-cut regime. We construct an approximate transport map…
We describe a procedure for constructing formal normal forms of holomorphic maps with a hypersurface of fixed points, and we apply it to obtain a complete list of formal normal forms for 2-dimensional holomorphic maps tangential to a curve…
A curve of genus g is maximal Mumford (MM) if it has g+1 ovals and g tropical cycles. We construct full-dimensional families of MM curves in the Hilbert scheme of canonical curves. This rests on first-order deformations of graph curves…
This paper studies geometric properties of the Iterated Matrix Multiplication polynomial and the hypersurface that it defines. We focus on geometric aspects that may be relevant for complexity theory such as the symmetry group of the…
We obtain estimates on both size and dimensions of the singular set at the first blow-up time of the mean curvature flow of hypersurfaces whose initial data is $\sigma_k$-convex.
This paper employs the method of moments (MOM) to calculate the capacitances of a cube and a hollow cylinder. For the cube, each face was divided into a maximum of 600 x 600 sub-areas. By fully exploiting the geometric symmetry between…
Let $X$ be a hypersurface in $\mathbb{P}^N$ with $N\geq 3$ defined over a finite field. The main result of this note is the classification, up to projective equivalence, of hypersurfaces $X$ as above without a linear component when the…
We combine two important recent advancements of MCMC algorithms: first, methods utilizing the intrinsic manifold structure of the parameter space; then, algorithms effective for targets in infinite-dimensions with the critical property that…