. A G ] 6 M ar 2 00 3 RECONSTRUCTION OF FUNCTION FIELDS

. A G ] 1 6 O ct 2 00 3 RECONSTRUCTION OF FUNCTION FIELDS

— We study the structure of abelian subgroups of Galois groups of function fields of surfaces.

ar X iv : m at h / 06 08 07 1 v 1 [ m at h . C O ] 3 A ug 2 00 6 G - reconstruction of graphs ∗

Let G be a group of permutations acting on an n-vertex set V , and X and Y be two simple graphs on V . We say that X and Y are Gisomorphic if Y belongs to the orbit of X under the action of G. One can naturally generalize the reconstruction problems so that when G is Sn, the symmetric group, we have the usual reconstruction problems. In this paper, we study G-edge reconstructibility of graphs. ...

ar X iv : m at h - ph / 0 60 20 16 v 2 3 A pr 2 00 6 Magnetic Geodesic Flows on Coadjoint Orbits ∗ † ‡

We describe a class of completely integrable G-invariant magnetic geodesic flows on (co)adjoint orbits of a compact connected Lie group G with magnetic field given by the Kirillov-Konstant 2-form.

ar X iv : m at h / 06 09 42 6 v 3 [ m at h . C O ] 1 5 O ct 2 00 6 SUM - PRODUCT ESTIMATES IN FINITE FIELDS VIA KLOOSTERMAN

We establish improved sum-product bounds in finite fields using incidence theorems based on bounds for classical Kloosterman and related sums.

ar X iv : 0 71 2 . 22 30 v 3 [ m at h . D G ] 6 M ar 2 00 8 η Forms and Determinant Lines