Related papers: Characterization of SDP Designs That Yield Certain…
In this paper branching rules for the fundamental representations of the symplectic groups in positive characteristic are found. The submodule structure of the restrictions of the fundamental modules for the group $Sp_{2n}(K)$ to the…
A pseudo $(v,\, k,\, \la)$-design is a pair $(X, {\cal B})$ where $X$ is a $v$-set and ${\cal B}=\{B_1,...,B_{v-1}\}$ is a collection of $k$-subsets (blocks) of $X$ such that each two distinct $B_i, B_j$ intersect in $\la$ elements; and…
We develop a basic theory for divisible design graphs with possible selfloops (LDDG's), and describe two infinite families of such graphs, some members of which are also classical examples of divisible design graphs without loops (DDG's).…
Semidefinite programs (SDPs) -- some of the most useful and versatile optimization problems of the last few decades -- are often pathological: the optimal values of the primal and dual problems may differ and may not be attained. Such SDPs…
Cyclicity of a convolutional code (CC) is relying on a nontrivial automorphism of the algebra F[x]/(x^n-1), where F is a finite field. If this automorphism itself has certain specific cyclicity properties one is lead to the class of…
We classify bireflectional elements (products of 2 involutions) in symplectic groups Sp$(2n, K)$ over a field $K$. We also classify rev ersible elements (elements conjugate to their inverses) and bireflectional elements in finite projective…
We study the geometry of manifolds carrying symplectic pairs consisting of two closed 2-forms of constant ranks, whose kernel foliations are complementary. Using a variation of the construction of Boothby and Wang we build…
In this paper we make a comparison between certain probabilistic and deterministic point sets and show that some deterministic constructions (spherical $t$-designs) are better or as good as probabilistic ones. We find asymptotic equalities…
We present a 2D lattice model of self-propelled spins that can only change direction upon collision with another spin. We show that even with ballistic motion and minimal cooperativity, these spins display robust flocking behavior at nearly…
We study two-dimensional subshifts whose horizontal trace (a.k.a. projective subdynamics) contains only points of finite support. Our main result is a classification result for such subshifts satisfying a minimality property. As…
We give a characterization of irreducible symplectic fourfolds which are given as Hilbert scheme of points on a K3 surface.
We show there is a class of symplectic Lie algebra representations over any field of characteristic not 2 or 3 that have many of the exceptional algebraic and geometric properties of both symmetric three forms in two dimensions and…
We perform a systematic classification of scalar field theories whose amplitudes admit a double copy formulation and identify two building blocks at 4-point and 13 at 5-point. Using the 4-point blocks as bootstrap seeds, this naturally…
Spin systems with hyperbolic symmetry originated as simplified models for the Anderson metal--insulator transition, and were subsequently found to exactly describe probabilistic models of linearly reinforced walks and random forests. In…
Cluster varieties are geometric objects that have recently found applications in several areas of mathematics and mathematical physics. This thesis studies the geometry of a large class of cluster varieties associated to compact oriented…
We study the birational geometry of irreducible holomorphic symplectic varieties arising as varieties of lines of general cubic fourfolds containing a cubic scroll. We compute the ample and moving cones, and exhibit a birational…
An arithmetical structure on a graph is given by a labeling of the vertices which satisfies certain divisibility properties. In this note, we look at several families of graphs and attempt to give counts on the number of arithmetical…
Spherical Designs are finite sets of points on the sphere $\mathbb{S}^{d}$ with the property that the average of certain (low-degree) polynomials in these points coincides with the global average of the polynomial on $\mathbb{S}^{d}$. They…
Block character of a finite symmetric group S(n) is a positive definite function which depends only on the number of cycles in permutation. We describe the cone of block characters by identifying its extreme rays, and find relations of the…
The low-energy properties of the SU(4) spin-orbital model on a two-leg ladder are studied by a variety of analytical and numerical techniques. Like in the case of SU(2) models, there is a singlet-multiplet gap in the spectrum, but the…