Seminars appear in decreasing order in relation to date. To find an activity of your interest just go down on the list. Normally seminars are given in english. If not, they will be marked as **Spanish Only.**

## Hidden Convexity in the l0 Pseudonorm and Lower Bound Convex Programs for Exact Sparse Optimization

Abstract: In sparse optimization problems, one looks for solution that have few nonzero components. We consider problems where sparsity is exactly measured by the l0 pseudonorm. We display a suitable conjugacy for which we show that the l0 pseudonorm is equal to its biconjugate. As a corollary, we obtain that the (nonconvex) l0 pseudonorm coincides, on the sphere, with a convex lsc function that we characterize. With this conjugacy, we display a lower bound for the original exact sparse optimization problem, which is a...

## Graph decompositions using group actions

Abstract: I will present some recent results on graph decompositions. To this end, we find a very `nice’ subgraph H in a host graph we would like to decompose into copies of H. Then we employ a group action to `rotate’ H. This rotation yields a decomposition of the host graph into copies of H. We construct this `nice’ subgraph using probabilistic tools, a well-known hypergraph matching theorem due to Pippenger and Spencer and an absorption method. This is joint work with Stefan Ehard and Stefan Glock.

## Farkas’ lemma: some extensions and applications

Abstract: The classical Farkas’ lemma characterizing the linear inequalities which are consequence of an ordinary linear system was proved in 1902 by this Hungarian Physicist to justify the first order necessary optimality condition for nonlinear programming problems stated by Ostrogradski in 1838. At present, any result characterizing the containment of the solution set of a given system in the sublevel sets of a given function is said to be a Farkas-type lemma. These results provide partial answers to the so-called containment problem,...

## Assouad dimension of planar self-affine sets

ABSTRACT: We consider planar self-affine sets X satisfying the strong separation condition and the projection condition. We show that any two points of X, which are generic with respect to a self-affine measure having simple Lyapunov spectrum, share the same collection of tangent sets. We also calculate the Assouad dimension of X. Finally, we prove that if X is dominated, then it is minimal for the conformal Assouad dimension. The talk is based on joint work with Balázs Bárány and Eino Rossi.

## Partially localized solutions of some elliptic equations on $R^{N+1}

Abstract: It is well known that, under quite general assumptions, fully localized solutions of a homogeneous semilinear elliptic equation must be radially symmetric. Many authors have exhibited the complexity of solutions which are only partially localized (that is, only decaying in some variables). In this talk I consider solutions which are quasiperiodic in one variable, decaying in all the others. In the first part of the talk I develop a framework for finding such solutions in the nonhomogeneous case; in the second part I show the...

## Uso de GIS en Plataformas Web

Seminarios de la Alianza Copernicus-Chile Titulo Uso de GIS en Plataformas Web Expositor Carlos Patillo CPRSIG Ltda. Fecha: Lunes 13 de Mayo de 2019 Hora inicio: 16:00 horas Lugar: Sala Multimedia, Centro de Modelamiento Matemático, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile. Beauchef 851, Santiago – Edificio Norte, Piso 6 Participación en Linea: http://vcespresso.redclara.net/@352109705c115cdd511fb968f9f4ff86# Use Explorer, Firefox o Safari. Debe tener instalado Flash Player en su...

## Generalizations of the geometric de Bruijn Erdős Theorem

Abstract: A classic Theorem of de Bruijn and Erdős states that every noncollinear set of n points in the plane determines at least n distinct lines. The line L(u, v) determined by two points u, v in the plane consists of all points p such that dist(p, u) + dist(u, v) = dist(p, v) (i.e. u is between p and v) or • dist(u, p) + dist(p, v) = dist(u, v) (i.e. p is between u and v) or • dist(u, v) + dist(v, p) = dist(u, p) (i.e. v is between u and p). With this definition of line L(uv) in an arbitrary metric space (V, dist), Chen and Chvátal...

## Decay of small odd solutions of the long range Schrödinger and Hartree equations in one dimension.

Abstract: We consider the long time asymptotics of (not necessarily small) odd solutions to the nonlinear Schrödinger equation with semilinear and nonlocal Hartree nonlinearities, in one dimension space. We assume data in the energy space only and we prove decay to zero in compact regions of space as time tends to infinity. We give three different results were decay holds: NLS without potential, NLS with potential and Hartree (defocusing case). The proof is based in the use of suitable virial identities and covers all range of scattering...

## Enhancing Mathematics Instruction to Facilitate Student Participation: Studying Elementary Classrooms Using Head-Mounted Cameras

Resumen: During the talk participants will view video clips filmed by third grade students who wore head-mounted cameras and discuss an intervention that helped teachers learn about how to support the development of mathematics and student interactions.