This mini workshop is funded by Research Council of Norway.
The workshop includes 3 talks by researchers in the fields of Dynamical Systems and Geometry.
Place: Niels Henrik Abels hus Undervisningsrom 723, University of Oslo
Date: 28 June 2023
Schedule:
Talk 1 from 11:00-12:00: Thuy Nguyen,
Lunch: 12:00-13:30,
Talk 2 from 13:30-14:30: Fei Hu,
Talk 3 from 15:00-16:00: Thang Nguyen,
Dinner: 17:30-21:00.
Speakers:
Fei Hu, Nanjing University, China. Webpage
Title: Polynomial volume growth of automorphisms of zero entropy on abelian varieties.
Abstract: Given a holomorphic dynamical system (X,f), Gromov introduced in 1977 the notion called volume growth lov(f) of iterated graphs. Mimicking this construction, Cantat and Paris-Romaskevich introduced in 2020 the polynomial volume growth plov(f) of an automorphism f of zero entropy.
Soon afterward, in 2021, Lin, Oguiso, and Zhang observed that according to Keeler's earlier work on noncommutative algebraic geometry, the above algebraic dynamical invariant is equivalent to the Gelfand--Kirillov dimension of the twisted homogeneous coordinate ring associated with (X,f).
I will provide an explicit formula calculating plov in the case of abelian varieties in arbitrary characteristic, which generalizes a result of Lin--Oguiso--Zhang for complex tori..
Thang Nguyen, Florida State University, USA. Webpage
Title: Local rigidity of boundary actions
Abstract: We consider the question how hard/easy it is to perturb a nice action of a group on a manifold. In general, when the group is ``large'', it is a general belief that the only way to perturb actions is by conjugating the actions by a map close to identity. This is indeed true in many situations, even perturbations are allowed to have low regularity. On the other hand, there are also cases, perturbations are flexible to obtain. In this talk, we'll mostly look at actions of uniform lattices in semisimple Lie groups or more generally fundamental groups of nonpositively curved closed manifolds on geodesic boundaries and Furstenberg boundaries.
Thuy Nguyen, University of Estadual Paulista, Brazil. [Webpage] bv.fapesp.br/en/pesquisador/672376/nguyen-thi-bich-thuy
Title: Geometry of polynomial maps at infinity
Abstract: We present some recent results on polynomial maps approached by intersection homology, asymptotic sets and Newton polygons.
Organiser: Tuyen Trung Truong (University of Oslo, Norway, website)
