Naslov
Lattices and perfect form theory

Autori
Dutour Sikirić, Mathieu

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

Izvornik
Algebraic Geometry Seminar of the Institute for Algebraic Geometry / - , 2014

Skup
Algebraic Geometry Seminar of the Institute for Algebraic Geometry

Mjesto i datum
Hannover, Njemačka, 27.02.2014

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Perfect Form; cohomology; enumeration

Sažetak
Lattices are discrete subgroups of R^n and they have interest in geometry of numbers, algebra (root lattices), number theory (mass formulas), and algebraic geometry. I will explain the basics of lattice theory, the classical examples and how to compute with them. Then I will explain the perfect form theory, which is the simplest example of a reduction theory and gives a tessellation of the space of positive definite quadratic forms. Finally, if time allows, I will try to give some other reduction theories (i.e. tessellation of the space of quadratic forms): The L-type reduction theory and the central cone compactification. Within the limits of my knowledge, I will present the relation between such tessellations and the corresponding toroidal compactification of the moduli space Ag of principally polarized abelian varieties. Again if time allows, I will present the possible applications of the tesselations to cohomology computations.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA