# Seminários

## PRÓXIMOS

On secant defectivity of homogeneous varieties

Expositor: Alex Massarenti - UFF
Qua 14 Nov 2018, 15:30 - Room 228Álgebra

Resumo: Most of the seminar will be a basic introduction to classical concepts in algebraic geometry such assecant defectivity, dimension of linear systems, and existence of special subvarieties of a given projective variety.I will then comment on Terracini's lemma and explain how it has been used to attack the problem of secant defectivity ofcertain homogeneous varieties.Finally, I will give an idea of a new method, based on degenerations techniques, I recently introduced with Rick Rischterto tackle secant defectivity problems. Such method allowed us to improve a result on non secant defectivity of Grassmanniansdue to Abo, Ottaviani and Peterson.

Bernoulli Numbers and the Riemann Zeta Function

Expositor: Santiago Arango - IMPA
Sex 16 Nov 2018, 15:30 - Room 349Colóquio dos Alunos

Resumo: Jakob Bernoulli was studying sums of the sequance of $k$-th powers when he discovered an interestig sequence of rational numbers, which turned out to beclosely related with several important problems in arithmetic;like Fermat's last theorem andthe Riemann Hypothesis.

A question of Norton-Sullivan and the rigidity of pseudo-rotations on the two-torus

Expositor: Jian Wang - IMPA
Ter 20 Nov 2018, 15:30 - Room 228Teoria Ergódica

Resumo: In 1996,A. Norton and D. Sullivan asked the following question: If $f : \mathbb{T}^2 \rightarrow \mathbb{T}^2$ is a diffeomorphism,$h : \mathbb{T}^2\rightarrow\mathbb{T}^2$ is a continuous map homotopic to the identity,and $hf = T_{\rho}h$ where $\rho \in \mathbb{R}^2$ is a totally irrational vector and $T_{\rho} : \mathbb{T}^2 \rightarrow \mathbb{T}^2,z \mapsto z + \rho$ is a translation,are there natural geometric conditions(e.g. smoothness)on $f$ that force $h$ to be a homeomorphism? In this talk,we give a negative answer to this question with respect to the regularity.We also show that under certain boundedness condition,a $C^r$(resp. Hölder)conservative irrational pseudo-rotation on $\mathbb{T}^2$ with a generic rotation vector is $C^{r-1}$-rigid(resp. $C^0$-rigid). These provide a partial generalization of the main results in[Bramham,Invent. Math. 199 (2), 561-580, 2015;A. Avila,B. Fayad,P. Le Calvez,D. Xu,Z. Zhang,arXiv: 1509.06906v1]. These are joint works with Zhiyuan Zhang and Hui Yang.

On SUSY curves and supervolumes over curves

Expositor: Ricardo J. Ramos Castillo - IMPA
Qua 21 Nov 2018, 15:30 - Room 228Álgebra

Resumo:

We start studying the known case of $N_k=N$ SUSY curves, after that we define anew type of supercurves with a trivial supervolume form. Such curves are amiddle point between oriented $N_k=2$ and $N_k=4$ SUSY curves, this fact is reflectin the clasification of conformal superalgebras.

Finally, we will try to give a wide family of new examples of such curves.