• Publications
  • Influence
Trees, parking functions, syzygies, and deformations of monomial ideals
For a graph G, we construct two algebras whose dimensions are both equal to the number of spanning trees of G. One of these algebras is the quotient of the polynomial ring modulo certain monomialExpand
Algebras of Curvature Forms on Homogeneous Manifolds
Let C(X) be the algebra generated by the curvature two-forms of standard holomorphic hermitian line bundles over the complex homogeneous manifold X = G=B. The cohomology ring of X is a quotient ofExpand
Mystery of point charges
We discuss the problem of finding an upper bound for the number of equilibrium points of a potential of several fixed point charges in Rn. This question goes back to J. C. Maxwell [10] and M. MorseExpand
ON THE NUMBER OF CONNECTED COMPONENTS IN THE SPACE OF CLOSED NONDEGENERATE CURVES ON S n
The main definition. A parametrized curve γ : I → R is called nondegenerate if for any t ∈ I the vectors γ′(t), . . . , γ(t) are linearly independent. Analogously γ : I → S is called nondegenerate ifExpand
On ring generated by Chern 2-forms on %plane1D;54A;%plane1D;543;n/B
Abstract In this short Note we give an explicit presentation of the ring A n generated by the curvature 2-forms of the standard Hermitian linear bundles over %plane1D;54A;%plane1D;543; n / B as theExpand
Homotopy classification of nondegenerate quasiperiodic curves on the 2-sphere
We classify the curves on S with fixed monodromy operator and nowhere vanishing geodesic curvature. The number of connected components of the space of such curves turns out to be 2 or 3 depending onExpand
On the Waring problem for polynomial rings
In this note we discuss an analog of the classical Waring problem for . Namely, we show that a general homogeneous polynomial of degree divisible by k≥2 can be represented as a sum of at most kn k-thExpand
On Spectral Polynomials of the Heun Equation. II
AbstractThe well-known Heun equation has the form $$\begin{array}{ll}\left\{Q(z)\frac {d^2}{dz^2}+P(z)\frac{d}{dz}+V(z)\right\}S(z)=0,\end{array}$$where Q(z) is a cubic complex polynomial, P(z) andExpand
Ramified coverings of S^2 with one degenerate branching point and enumeration of edge-ordered graphs
Ramified coverings of S^2 with one degenerate branching point and enumeration of edge-ordered graphs
Root Asymptotics of Spectral Polynomials for the Lamé Operator
The study of polynomial solutions to the classical Lamé equation in its algebraic form, or equivalently, of double-periodic solutions of its Weierstrass form has a long history. Such solutions appearExpand
...
1
2
3
4
5
...