Moonshine Elements in Elliptic Cohomology
نویسندگان
چکیده
This is a historical talk about the recent confluence of two lines of research in equivariant elliptic cohomology, one concerned with connected Lie groups, the other with the finite case. These themes come together in (what seems to me remarkable) work of N. Ganter, relating replicability of McKay-Thompson series to the theory of exponential cohomology operations.
منابع مشابه
Classifying Spaces, Virasoro Equivariant Bundles, Elliptic Cohomology and Moonshine
This work explores some connections between the elliptic cohomology of classifying spaces for finite groups, Virasoro equivariant bundles over their loop spaces and Moonshine for finite groups. Our motivation is as follows: up to homotopy we can replace the loop group LBG by the disjoint union ⨿ [γ]BCG(γ) of classifying spaces of centralizers of elements γ representing conjugacy classes of elem...
متن کاملConformal field theory and elliptic cohomology
In this paper, we use conformal field theory to construct a generalized cohomology theory which has some properties of elliptic cohomology theory which was some properties of elliptic cohomology. A part of our presentation is a rigorous definition of conformal field theory following Segal’s axioms, and some examples, such as lattice theories associated with a unimodular even lattice. We also in...
متن کاملModular Forms and Topology
We want to discuss various applications of modular forms in topology. The starting point is elliptic genus and its generalizations. The main techniques are the Atiyah-Singer index theorem, the Atiyah-Bott-Segal-Singer Lefschetz fixed point formula, Kac-Moody Lie algebras, modular forms and theta-functions. Just as the representations theory of classical Lie groups has close connections with the...
متن کاملQuasi-quadratic elliptic curve point counting using rigid cohomology
We present a deterministic algorithm that computes the zeta function of a nonsupersingular elliptic curve E over a finite field with p elements in time quasi-quadratic in n. An older algorithm having the same time complexity uses the canonical lift of E, whereas our algorithm uses rigid cohomology combined with a deformation approach. An implementation in small odd characteristic turns out to g...
متن کاملCoset Graphs and Modular Surfaces
We establish a correspondence between generalized quiver gauge theories in four dimensions and congruence subgroups of the modular group, hinging upon the trivalent graphs which arise in both. The gauge theories and the graphs are enumerated and their numbers are compared. The correspondence is particularly striking for genus zero torsion-free congruence subgroups as exemplified by those which ...
متن کامل