An infinite family of hyperovals of Q+(5,q)Q^+(5,q), qq even

We construct an infinite family of hyperovals on the Klein quadric $Q^+(5,q)$, $q$ even. The construction makes use of ovoids of the symplectic generalized quadrangle $W(q)$ that is associated with an elliptic quadric which arises as solid intersection with $Q^+(5,q)$. We also solve the isomorphism problem: we determine necessary and sufficient conditions for two hyperovals arising from the construction to be isomorphic

The homogeneous pseudo-embeddings and hyperovals of the generalized quadrangle H(3,4)

In this paper, we determine all homogeneous pseudo-embeddings of the generalized quadrangle H(3, 4) and give a description of all its even sets. Using this description, we subsequently compute all hyperovals of H(3, 4), up to isomorphism, and give computer free descriptions of them. Several of these hyperovals, but not all of them, have already been described before in the literature. (C) 2020 Elsevier Inc. All rights reserved

Q(sqrt(-3))-Integral Points on a Mordell Curve

We use an extension of quadratic Chabauty to number fields,recently developed by the author with Balakrishnan, Besser and M ̈uller,combined with a sieving technique, to determine the integral points overQ(√−3) on the Mordell curve y2 = x3 − 4