Venue

The conference talks and poster session will be hosted at Auditório Prof. Francisco Romeu Landi, which is located at Av. Prof. Luciano Gualberto, travessa 3, no. 380, on the campus of USP.

Program

Monday	Tuesday	Wednesday	Thursday	Friday
J. Perez Recent advances in minimal surface theory in R3 slide video	P. Pansu Large scale conformal geometry slide video	B. Wilking Torus actions on positively curved manifolds slide video	G. Tian Relative volume comparison along Ricci Flow slide video
POSTER SESSION Coffee-break
D. Maximo On Morse index estimates for minimal surfaces video	D. Hulin Harmonic maps in negative curvature video	B. Hanke Positive scalar curvature on manifolds with abelian fundamental groups slide video	M. Abreu A toric geometry road from Kaehler metrics to contact topology slide video	C. Olmos Submanifolds, holonomy and homogeneous geometry slide video
Lunch
R. L. Fernandes Bochner-K ̈ahler metrics (after R. Bryant) slide video	E. Falbel Flag structures on 3-manifolds video	W. Ziller Finsler metrics, closed geodesics and geodesic flows video	T. Rivière A proof of the multiplicity one conjecture for minmax minimal surfaces in arbitrary codimension	R. Miatello On the Hodge spectra of lens spaces video
Coffe-break
J. Lauret Homogeneous Ricci curvature and the beta operator slide	C. de Lellis Boundary regularity for area minimizing currents and a question of Almgren slide video	M. Radeschi Manifold submetries and polynomial algebras slide video	PROBLEM SESSION	F. Morgan Isoperimetric and partitioning problems slide video

Printable Version (PDF): Program, talks and abstracts

Preliminary Talks

The event will have preliminary talks that will be given on July 19-20.

July 19 14h	Cone structures and Finsler spacetimes Prof. Miguel Angel Javaloyes Abstract: We will introduce the notions of cone structures and Finsler spacetimes, establishing an explicit relation between both concepts and providing a good amount of examples. Indeed, we will give a characterization of all the possible Lorentz-Finsler metrics under some regularity conditions. Finally, we will explore some basic properties of Finsler spacetimes, which include maximizing properties of geodesics and basic results on Causality.
July 19 15h	Uma re-definição do conceito de buraco negro usando fronteiras causais Dr. Jonatan Herrera Abstract: A definiçao clasica de buraco negro [2,4] é apresentada em termos da denominada fronteira conforme. Para esta aproximaçao de buraco negro, define-se inicialmente o denominado "future null infinity" $\mathcal{J}^+$, um subconjunto da borda conforme que joga o role de "area de fuga" do buraco negro. Deste modo, um ponto está fora do buraco negro se pode ser conectado com $\mathcal{J}^+$ por meio de uma curva causal. A definiçao anterior apresenta porem um problema importante, a fronteira conforme nao pode ser obtida para todo modelo de espaço-tempo. Este é o caso, como foi observado por Marolf e Ross, das ondas planas [3]. Para evitar esse problema, nos apresentaremos uma nova definiçao de buraco negro com base na fronteira causal. Esta fronteira está definida para qualquer modelo de espaço tempo fortemente causal, incluindo modelos onde a fronteira conforme nao esta disponivel. Provaremos que a maioria das propriedades clasicas de buraco negro sao preservadas com esta definiçao, incluindo que as denominadas superficies atrapadas estao completamente cobertas por buracos negros se a condiçao de convergencia luminosa é satisfeita. Finalmente, mostraremos que as ondas planas generalizadas causalmente continuas nao admitem buracos negros. [1] José Luis Flores, Jónatan Herrera, and Miguel Sánchez, On the final definition of the causal boundary and its relation with the conformal boundary, Advances in Theoretical and Mathematical Physics 15 (2011), no. 4, 991–1057. [2] Stephen W. Hawking and George F. R. Ellis, The Large Scale Structure of Space-Time (Cambridge Monographs on Mathematical Physics), Cambridge University Press, 1975. [3] Donald Marolf and Simon F. Ross, Plane waves: To infinity and beyond!, Classical and Quantum Gravity 19 (2002), no. 24, 6289–6302. [4] R.M. Wald, General Relativity, University of Chicago Press, 1984.
July 19 16:30h	Geometry of null hypersurfaces Oscar Alfredo Palmas Velasco Abstract: In this talk I will review the techniques for studying null hypersurfaces in Lorentzian manifolds and give the characterization of them when adding the condition of being totally umbilical or isoparametric.
July 19 17:30h	On isoparametric surfaces in homogeneous 3-spaces Prof. Miguel Vazquez Abstract: A hypersurface of a Riemannian manifold is called isoparametric if it and its nearby equidistant hypersurfaces have constant mean curvature. In spaces of constant curvature, Cartan proved that a hypersurface is isoparametric if and only if has constant principal curvatures. However, this characterization does not necessarily hold in spaces of nonconstant curvature. In this talk I will present a recent joint work with José Miguel Manzano (ICMAT-CSIC, Madrid) where we initiated the study of isoparametric surfaces and surfaces with constant principal curvatures in homogenous 3-spaces, obtaining their classification in the homogeneous 3-spaces with 4-dimensional isometry group.
July 20 14:00h	Diameter of quotients of the sphere by isometric group actions Dr. Ricardo Mendes Abstract: (Joint with C. Gorodski, C. Lange, A. Lytchak) We show the existence of C>0 such that, for all n>1 and every closed non-transitive subgroup G of O(n+1), the diameter of the quotient of the unit sphere S^n by G is larger than C. The novelty is that C is independent of the dimension n. The classification of finite simple groups is used in the proof.
July 20 15:00h	Remarks on the abelian convexity theorem Prof. Leonardo Biliotti Abstract: in this seminar we discuss abelian convexity theorem. Convexity along an orbit is established in a very general setting using Kempf-Ness functions. This is applied to give short proofs of the Atiyah-Guillemin-Sternberg theorem and of abelian convexity for the gradient map in the case of a real analytic submanifold of complex projective space. Finally we give an application to the action on the probability measures. This is a joint work with Alessandro Ghigi that has been accepted for pubblication on PAMS.
July 20 16:30h	Extending a diffeomorphism finiteness theorem to dimension 4 Prof. Curtis Pro (California State University, Stanislaus) Abstract: In the early 90s, Grove, Petersen, and Wu, and independently Perelman, showed in dimensions different than 4, the conclusion of Cheeger's Finiteness Theorem still holds without the assumption of an upper curvature bound. Namely, given numbers $k\in\mathbb R, v, D>0$, if $n\neq 4$, there are at most finitely many differentiable structures on the class of $n$-manifolds $M$ that support metrics with $\sec M\geq k, \mathrm{vol}\,M\geq v,$ and $\mathrm{diam}\,M\leq D.$ In this talk, I'll present current joint work with Fred Wilhelm that shows, with a new approach, the same is also true in dimension 4.
July 20 17:30h	A Weitzenboeck viewpoint on sectional curvature and applications Prof. Renato G. Bettiol Abstract: In this talk, I will describe a new algebraic characterization of sectional curvature bounds that only involves curvature terms in the Weitzenb\"ock formulae for symmetric tensors. This characterization is further clarified by means of a symmetric analogue of the Kulkarni-Nomizu product, which renders it computationally amenable. Furthermore, a related application of the Bochner technique to closed 4-manifolds with indefinite intersection form and positive or nonnegative sectional curvature will be discussed, yielding some new insight about the Hopf Conjecture. This is based on joint work with R. Mendes (Univ. zu Koeln, Germany)