Colóquio de Geometria e Aritmética
Rio de Janeiro


Descrição:

Colóquio rotativo entre IMPA, UFRJ e UFF. Acontecerá toda última sexta feira do mês, contando com duas palestras, uma de 10:30 as 11:30 e outra de 12:00 as 13:00. As palestras serão ministradas por pesquisadores locais e do exterior das áreas de geometria algébrica e aritmética.

O objetivo principal é estimular a troca de ideias e a colaboração entre as instituições do Rio de Janeiro. A pausa para o café e o almoço após o colóquio darão oportunidade para discussões entre os participantes e interação com os palestrantes.

Esperamos uma grande participação dos pesquisadores da área. Estudantes de mestrado e doutorado são encorajados a participar.

Programa: 2018.2

24/8, UFF. Campus do Gragoatá, Bloco H, sala 407.

10:30-11:30 Misha Verbitsky (IMPA), Transcendental Hodge algebra
Resumo. Let M be a projective manifold. Transcendental Hodge lattice of weight p is the smallest rational Hodge substructure in Hp(M) containing Hp,0(M). Transcendental Hodge lattice is a birational invariant of M. Yu. Zarhin computed the transcendental Hodge lattice for a K3 surface, and proved that it is an irreducible representation of a unitary or orthogonal group over a number field. I will prove that the direct sum of all transcendental Hodge lattices for any projective manifold is an algebra, and compute it (using Zarhin's theorem) explicitly for all hyperkahler manifolds in terms of irreducible representations of unitary or orthogonal groups over number fields.
12:00-13:00 Omid Amini (ENS, Paris), Trees in algebraic geometry
Resumo. The aim of the talk is to show through examples of recent results how combinatorial objects called trees naturally arise and play a role in understanding the geometry of algebraic varieties and their asymptotics. The results themselves are motivated by arithmetic geometry and mathematical physics.

28/9, IMPA.

10:30-11:30 Luciane Quoos (UFRJ), tba
Resumo. tba
12:00-13:00 Kostiantyn Iusenko (USP), Stable representations of posets.
Resumo. Representations of finite dimensional algebras can be approached combinatorially via representations of posets (due to L.A. Nazarova and A.V. Roiter) and representations of quivers (due to P. Gabriel). The problem of classifying representations of "most" algebras is wild in a sense that it is as difficult as the problem of classifying representations of free algebras. Nevertheless, one can use geometrical approach by considering the spaces whose points correspond naturally to isomorphism classes of representations. Using standard GIT methods A. King defined the moduli spaces of quiver representations. In this talk we will discuss certain aspects related to study of moduli space of poset representations. We will see that the Euler quadratic form associated with a poset plays significant role here: for calculation of dimension of moduli space and for canonical choice of stability (which is certain analogue of Schofield's characterization of Schurian roots for quiver). Also we plan to discuss the behavior of Coxeter transformations on stable representations.

26/10, UFRJ.

10:30-11:30 tba, tba
Resumo. tba
12:00-13:00 Edgar Costa (MIT), tba
Resumo. tba


Semestres anteriores: 2012.2 2013.1 2013.2 2014.1 2014.2 2015.1 2015.2 2016.1 2016.2 2017.1 2017.2 2018.1


Comite Organizador:
Carolina Araujo (IMPA)
Cecília Salgado (UFRJ)
Eduardo Esteves (IMPA)
Marco Pacini (UFF)
Oliver Lorscheid (IMPA)

Past Organizers: Nivaldo Medeiros (UFF)

Apoio: CNPq, Capes, Faperj

Contato: colga at impa.br