Naslov
Practical computation with indefinite forms

Autori
Dutour Sikirić, Mathieu

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, pp prezentacija, znanstveni

Skup
Algebraic Geometry seminar of the University of Hannover

Mjesto i datum
Hannover, Njemačka, 06.09.2022

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Lattice ; Indefinite Forms ; Groups

Sažetak
An indefinite lattice is an integral valued quadratic form on Z^n of signature (p, q) with p, q>0. We consider the following problems for them: - Compute a generating set of the group of invertible integral transformations preserving q. - Given two forms A and B test if there is an invertible integral transformation f such that B[x] = A[f(x)]. - Given C is not 0 find the orbit representatives of solutions of A[x] = C. - Find the orbit representatives of solutions of A[x] = 0 with x primitive. - Find the orbit representatives of k-dimensional totally isotropic planes. We provide some methods that allow resolving such questions. This is based on polyhedral, lattice, and group theoretic techniques. If time allows I will also explain how the edgewalk algorithm of Allcock gives a subgroup of Aut(L) / Cox(L).

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA