We show that the least genus of any compact Riemann surface S, admitting a simple Suzuki group G = Sz(^) as a group of automorphisms, is equal to 1 +|G|/40. We compute the number of such surfaces S as the number of normal subgroups of the triangle group A(2,4,5) with quotient-group G, and investigate the associated regular maps of type {4,5}.

The theory of complex hyperbolic discrete groups is still in its childhood but promises to grow into a rich subfield of geometry. In this paper I will discuss some recent progress that has been made on complex hyperbolic deformations of the modular group and, more generally, triangle groups. These are some of the simplest nontrivial complex hyperbolic discrete groups. In particular, I will talk...

We present a new method for performing Boolean operations on volumes represented as triangle meshes. In contrast to existing methods which treat meshes as 3D polyhedra and try to partition the faces at their exact intersection curves, we treat meshes as adaptive surfaces which can be arbitrarily refined. Rather than depending on computing precise face intersections, our approach refines the inp...

Let C(Γ) be the set of isomorphism classes of the finite groups that are quotients (homomorphic images) of Γ. We investigate the extent to which C(Γ) determines Γ when Γ is a group of geometric interest. If Γ1 is a lattice in PSL(2,R) and Γ2 is a lattice in any connected Lie group, then C(Γ1) = C(Γ2) implies that Γ1 ∼= Γ2. If F is a free group and Γ is a right-angled Artin group or a residually...

The most recent results from the B-factories on the time-dependent CP asymmetries measured in B -decays mediated by b → cc̄s quark-transitions are reviewed. The Standard Model interpretation of the results in terms of the parameter sin 2β leads to a four-fold ambiguity on the unitarity triangle β which can be reduced to a two-fold ambiguity by measuring the sign of the parameter cos 2β. The resu...

The goal of this paper is to give a conjectural census of complex hyperbolic sporadic triangle groups. We prove that only finitely many of these sporadic groups are lattices. We also give a conjectural list of all lattices among sporadic groups, and for each group in the list we give a conjectural group presentation, as well as a list of cusps and generators for their stabilisers. We describe s...

A latin bitrade (T , T⊗) is a pair of partial latin squares that define the difference between two arbitrary latin squares L ⊇ T and L⊗ ⊇ T⊗ of the same order. A 3-homogeneous bitrade (T , T⊗) has three entries in each row, three entries in each column, and each symbol appears three times in T . Cavenagh [2] showed that any 3-homogeneous bitrade may be partitioned into three transversals. In th...

We study the number of connected spanning subgraphs fd,b(n) on the generalized Sierpinski gasket SGd,b(n) at stage n with dimension d equal to two, three and four for b = 2, and layer b equal to three and four for d = 2. The upper and lower bounds for the asymptotic growth constant, defined as zSGd,b = limv→∞ ln fd,b(n)/v where v is the number of vertices, on SG2,b(n) with b = 2, 3, 4 are deriv...

In an Apollonian circle packing, the curvatures a, b, c, d of any four mutually tangent circles satisfy Descartes’ equation, 2(a + b + c + d) = (a+ b+ c+ d). For an equilateral triangle and a point P , if a, b, c, d denote the squares of the lengths of the sides of the triangle and the distances from P to the vertices of the triangle, then a, b, c, d, satisfy 3(a+ b+ c+d) = (a+ b+ c+d). Define ...

We present a new method for simulating volume conserving deformable bodies using an impulse-based approach. In order to simulate a deformable body a tetrahedral model is generated from an arbitrary triangle mesh. All resulting tetrahedrons are assigned to volume constraints which ensure the conservation of the total volume. For the simulation of such a constraint impulses are computed and appli...