相关论文: Some Irrational Generalised Moonshine from Orbifol…

Let $V$ be a rational, selfdual, $C_2$-cofinite vertex operator algebra of CFT type, and $G$ a finite automorphism group of $V.$ It is proved that the kernel of the representation of the modular group on twisted conformal blocks associated…

The commencement of monstrous moonshine is a connection between the largest sporadic simple group---the monster---and complex elliptic curves. Here we explain how a closer look at this connection leads, via the Thompson group, to recently…

In earlier work we initiated a program to study relationships between finite groups and arithmetic geometric invariants of modular curves in a systematic way. In the present work we continue this program, with a focus on the two smallest…

We construct a non-normal affine monoid together with its modules associated with a negative definite plumbed $3$-manifold $M$. In terms of their structure, we describe the $H_1(M,\mathbb{Z})$-equivariant parts of the topological Poincar\'e…

Generating functions of BPS indices, counting states of D4-D2-D0 black holes in Calabi-Yau compactifications of type IIA string theory and identified with rank 0 Donaldson- Thomas invariants, are examples of mock modular forms. They have a…

In this note, we provide evidence for new (super) moonshines relating the Monster and the Baby monster to some weakly holomorphic weight 1/2 modular forms defined by Zagier in his work on traces of singular moduli. They are similar in…

We study normal reflection subgroups of complex reflection groups. Our point of view leads to a refinement of a theorem of Orlik and Solomon to the effect that the generating function for fixed-space dimension over a reflection group is a…

For a non-isotrivial family of surfaces of general type over a complex projective curve, we give upper bounds for the degree of the direct images of powers of the relative dualizing sheaf. They imply that, fixing the curve and the possible…

The pattern of duality symmetries acting on the states of compactified superstring models reinforces an earlier suggestion that the Monster sporadic group is a hidden symmetry for superstring models. This in turn points to a supersymmetric…

Using the Luthar--Passi method, we investigate the Zassenhaus and Kimmerle conjectures for normalized unit groups of integral group rings of the Held and O'Nan sporadic simple groups. We confirm the Kimmerle conjecture for the Held simple…

The theory of topological modular forms (TMF) predicts that elliptic genera of physical theories satisfy a certain divisibility property, determined by the theory's gravitational anomaly. In this note we verify this prediction in Duncan's…

In an article in the Pure and Applied Mathematics Quarterly in 2008, Duke and Jenkins investigated a certain natural basis of the space of weakly holomorphic modular forms for the full modular group $SL_2({\bf Z})$. We show here that their…

We introduce a category of possibly irregular holonomic D-modules which can be endowed in a canonical way with an irregular Hodge filtration. Mixed Hodge modules with their Hodge filtration naturally belong to this category, as well as…

We prove the Noether-Lefschetz conjecture on the moduli space of quasi-polarized K3 surfaces. This is deduced as a particular case of a general theorem that states that low degree cohomology classes of arithmetic manifolds of orthogonal…

By enforcing invariance under S-duality in type IIB string theory compactified on a Calabi-Yau threefold, we derive modular properties of the generating function of BPS degeneracies of D4-D2-D0 black holes in type IIA string theory…

We exhibit geometric conditions on a family of toric hypersurfaces under which the value of a canonical normal function at a point of maximal unipotent monodromy is irrational.

The Thompson sporadic group admits special relationships to modular forms of two kinds. On the one hand, last century's generalized moonshine for the monster equipped the Thompson group with a module for which the associated McKay-Thompson…

We construct a model of moonshine phenomenon based on the use of N=2 superconformal algebra. We consider an extremal Jacobi form of weight 0 and index 2, and expand it in terms of N=2 massless and massive representations. We find the…

A log generic hypersurface in $\mathbb{P}^n$ with respect to a birational modification of $\mathbb{P}^n$ is by definition the image of a generic element of a high power of an ample linear series on the modification. A log very-generic…

We prove a generalization of the Conley conjecture: Every Hamiltonian diffeomorphism of a closed symplectic manifold has infinitely many periodic orbits if the first Chern class vanishes over the second fundamental group. In particular, we…