We derive the potential modular symmetries of heterotic string theory. For a toroidal compactification with Wilson line modulus, we obtain Siegel group Sp(4,Z) that includes SL(2,Z)T and SL(2,Z)U (of “geometric” moduli T U) as well mirror symmetry. In addition, theory provides candidate for CP -like symmetry enhances to GSp(4,Z).

This article is an expository paper. We first survey developments over the past three decades in the theory of harmonic analysis on reductive symmetric spaces. Next we deal with the particular homogeneous space of non-reductive type, the so called Siegel-Jacobi space that is important arithmetically and geometrically. We present some new results on the Siegel-Jacobi space.

We study the Masur-Veech volumes $MV_{g,n}$ of principal stratum moduli space quadratic differentials unit area on curves genus $g$ with $n$ punctures. show that are constant terms a family polynomials in variables governed by topological recursion/Virasoro constraints. This is equivalent to formula giving these as sum over stable graphs, and retrieves result \cite{Delecroix} proved combinatori...

The kinematic separation of size, shape, and orientation of n-body systems is investigated together with specific issues concerning the dynamics of classical n-body motions. A central topic is the asymptotic behavior of general collisions, extending the early work of Siegel, Wintner, and more recently Saari. In particular, asymptotic formulas for the derivatives of any order of the basic kinema...

In general, it is difficult to determine the dimension of the space of Siegel modular forms of low weights. In particular, the dimension of the space of cusp forms are known in only a few cases. In this paper, we calculate the dimension of the space of Siegel Eisenstein series of weight 1, which is a certain subspace of a complement of the space of cusp forms.

We construct the genus two (or two loop) partition function for meromorphic bosonic conformal field theories. We use a sewing procedure involving two genus one tori by exploiting an explicit relationship between the genus two period matrix and pinching modular parameters. We obtain expressions for the partition function for the chiral bosonic string, even rank lattice theories and self-dual mer...

In this paper, we decompose the space of nearly holomorphic Hilbert-Siegel automorphic forms as representations adele group under certain assumptions. We also give an application for classical modular forms. particular, show surjectivity global Siegel operator congruence subgroups with large weights.

Recent work on the log-minimal model program for the moduli space of curves, as well as past results of Caporaso, Pandharipande, and Simpson motivate an investigation of compactifications of the universal moduli space of slope semi-stable vector bundles over moduli spaces of curves arising in the Hassett–Keel program. Our main result is the construction of a universal moduli space of slope semi...