Related papers: $\Gamma^{0}(2)$ modular forms and anomaly cancella…

We apply differential operators to modular forms on orthogonal groups $\mathrm{O}(2, \ell)$ to construct infinite families of modular forms on special cycles. These operators generalize the quasi-pullback. The subspaces of theta lifts are…

We study modular transformation of holomorphic Yukawa couplings in magnetized D-brane models. It is found that their products are modular forms, which are non-trivial representations of finite modular subgroups, e.g. $S_3$, $S_4$,…

We give necessary conditions for perfection of some families of odd numbers with special multiplicative forms. Extending earlier work of Steuerwald, Kanold, McDaniel et al.

We present a concise review of the recent theoretical progress concerning the standard model calculation of the inclusive radiative anti-B --> X(s) gamma decay. Particular attention is thereby devoted to the calculations of the…

We study the arithmetic aspects of the finite group of extensions of abelian varieties defined over a number field. In particular, we establish relations with special values of L-functions and congruences between modular forms.

We give an informal survey, emphasizing examples and open problems, of two interconnected research programs in moduli of curves: the systematic classification of modular compactifications of $M_{g,n}$, and the study of Mori chamber…

In this note, we describe several new examples of holomorphic modular forms on the group SU(2,1). These forms are distinguished by having weight $\frac{1}{3}$. We also describe a method for determining the levels at which one should expect…

We study a twisted version of module algebras called module Hom-algebras. It is shown that module algebras deform into module Hom-algebras via endomorphisms. As an example, we construct certain q-deformations of the usual sl(2)-action on…

We consider the functional inverse of the Gamma function in the complex plane, where it is multi-valued, and define a set of suitable branches by proposing a natural extension from the real case.

Changes of variables giving the dual model are constructed explicitly for sigma-models without isotropy. In particular, the jacobian is calculated to give the known results. The global aspects of the abelian case as well as some of those of…

We prove a vanishing theorem for one forms on the moduli stack of principally polarized abelian varieties of genus g>1 with level structure N over fields of characteristic p different from two. This is used to compute the Picard groups of…

In this paper, we will introduce two generalizations of second submodules of a module over a commutative ring and explore some basic properties of these classes of modules.

The problem of normalisation of the modular forms in modular invariant lepton and quark flavour models is discussed. Modular invariant normalisations of the modular forms are proposed.

In this paper, we first discuss the structure of the Ramond N=2 superconformal algebras. Then we also classify the modules of the intermediate series over Ramond N=2 superconformal algebra.

We carefully review the basic examples of anomaly cancellation in M-theory: the 5-brane anomalies and the anomalies on S^1/Z_2. This involves cancellation between quantum anomalies and classical inflow from topological terms. To correctly…

In this paper we expand on previous results, studying the extent to which one can detect fusion in certain finite groups $\Gamma$, from information about the universal deformation rings of absolutely irreducible…

Let $\Lambda$ be a radical square zero Nakayama algebra with $n$ simple modules and let $\Gamma$ be the Auslander algebra of $\Lambda$. Then every indecomposable direct summand of a tilting $\Gamma$-module is either simple or projective.…

We have one more look at the (homological) perturbation lemma and we point out some non-standard consequences, including the relevance to deformations.

We explain the basic ideas, describe with proofs the main results, and demonstrate the effectiveness, of an evolving theory of vector-valued modular forms (vvmf). To keep the exposition concrete, we restrict here to the special case of the…

This is a survey based on the construction of Siegel modular forms of degree 2 and 3 using invariant theory in joint work with Fabien Cl\'ery and Carel Faber.