Reflection algebras is a class of algebras associated with integrable models with boundaries. The coefficients of Sklyanin determinant generate the center of the reflection algebra. We give a combinatorial description of Sklyanin determinant suitable for explicit computations.

The structures and distributions of light nuclei are investigated within a microscopic correlation model. Two particle correlations are responsible for the scattering of model particles either to low momentum-or to high momentum-states. The low momentum states form the model space while the high momentum states are used to calculate the G-matrix. The three and higher order particle correlations...

2 Faltings’ theorem 15 2.1 Prelude: the Shafarevich problem . . . . . . . . . . . . . . . . 15 2.2 First reduction: the Kodaira–Parshin trick . . . . . . . . . . . 17 2.3 Second reduction: passing to the jacobian . . . . . . . . . . . 19 2.4 Third reduction: passing to isogeny classes . . . . . . . . . . . 19 2.5 Fourth reduction: from isogeny classes to `-adic representations 21 2.6 The isogen...

We prove three conjectures concerning the evaluation of determinants, which are related to the counting of plane partitions and rhombus tilings. One of them has been posed by George Andrews in 1980, the other two are by Guoce Xin and Christian Krattenthaler. Our proofs employ computer algebra methods, namely the holonomic ansatz proposed by Doron Zeilberger and variations thereof. These variati...

We confirm a conjecture of Merel describing a certain relation between the jacobians of various quotients of X(p) in terms of specific correspondences.

We prove non-vanishing results for the central value of high derivatives of the complete L-function Λ(f, s) attached to primitive forms of weight 2 and prime level q. For fixed k ≥ 0 the proportion of primitive forms f such that Λ(f, 1/2) 6= 0 is ≥ pk +o(1) with pk > 0 and pk = 1/2 + O(k−2), as the level q goes to infinity. This result is (asymptotically in k) optimal and analogous to a result ...

Because QCD in four dimensions is renormalizable, not super-renormalizable, the fluctuations of the fermion determinant are significant at all physical scales. Fortunately the short distance behaviour of QCD is very well understood. In particular, we know that for sufficiently high momentum scales this physics should be accurately described by an improved gauge action. In the truncated determin...