Sunday 13 October 2024 |

Events for day: Tuesday 21 December 2021 |

14:00 - 15:00 Weekly SeminarHEPCo Group Higher-derivative field redefinitions in the presence of boundary School PHYSICS Abstract: Recently it has been proposed that the consistency with T-duality requires the effective action of string theory at order $alpha'^n$ satisfies the least action principle provided that the values of the massless fields and their derivatives up to order $n$ are known on the boundary. In this lecture, I speculate that this boundary condition constrains the field redefinitions and the corrections to the T-duality transformations in the presence of the boundary, e.g. at order, $alpha'$, the metric does not change and all other massless fields should change to include only the first derivative of the massless fields. Using these ... 17:30 - 19:30 Number Theory WebinarIntegral Points on Mordell Curves of Rank 1 School MATHEMATICS A well-known theorem of Siegel states that any elliptic curve $E/mathbb{Q}$ has only finitely many integral points. Lang conjectured that the number of integral points on a quasi-minimal model of an elliptic curve should be bounded solely in terms of the rank of the group of rational points. Silverman proved Lang's conjecture for the curves with at most a fixed number of primes dividing the denominator of the $j$-invariant. Using more explicit methods, Silverman and Gross compute the dependence of the bounds on the various constants. In the case of curves of rank 1, techniques of Ingram on multiples of integral points enable one to prove much ... |