Mathematics and crystallography.
Mather measures and the Bowen–Series transformation
Matrix coefficients, counting and primes for orbits of geometrically finite groups
Let and for and when for , we obtain an effective archimedean counting result for a discrete orbit of in a homogeneous space where is the trivial group, a symmetric subgroup or a horospherical subgroup. More precisely, we show that for any effectively well-rounded family of compact subsets, there exists such that for an explicit measure on which depends on . We also apply the affine sieve and describe the distribution of almost primes on orbits of in arithmetic settings....
Maximal groups of automorphisms of compact Riemann surfaces in various classes of finite groups.
Maximal Nonparabolic Subgroups of the Modular Group.
Methods of Perfect Coloring
Metric rigidity of crystallographic groups.
Minimal dimensions for flat manifolds with prescribed holonomy.
Minimum of quadratic forms with respect to Fuchsian groups. II.
Minimum of quadratic forms with respect to Fuchsian groups. I.
Modular embeddings and rigidity for Fuchsian groups
We prove a rigidity theorem for semiarithmetic Fuchsian groups: If Γ₁, Γ₂ are two semiarithmetic lattices in PSL(2,ℝ ) virtually admitting modular embeddings, and f: Γ₁ → Γ₂ is a group isomorphism that respects the notion of congruence subgroups, then f is induced by an inner automorphism of PGL(2,ℝ ).
Modular embeddings for some non-arithmetic Fuchsian groups
Modularity in Science and Art
Modules over group rings of soluble groups with a certain condition of maximality
Let A be an R G-module, where R is an integral domain and G is a soluble group. Suppose that C G(A) = 1 and A/C A(G) is not a noetherian R-module. Let L nnd(G) be the family of all subgroups H of G such that A/C A(H) is not a noetherian R-module. In this paper we study the structure of those G for which L nnd(G) satisfies the maximal condition.
Monodromy for the hypergeometric function nFn-1.