John Willard Milnor
6 de diciembre de 2017
Auditorio Alfonso Nápoles
Inauguración de la Conferencia Internacional “75 años de matemáticas en México” que se lleva a cabo del 4 al 7 de diciembre de 2017 en la Facultad de Ciencias y el Instituto de Matemáticas de la UNAM
Abstract: In the 70´s Coxeter considered the 4-dimensional regular convex polytopes and used the so-called Petrie Polygons to obtain quotients of the polytopes that while having all possible rotational symmetry, lack of reflectional symmetry. He called this objects Twisted Honeycombs. Now a days, objects with such symmetry properties are often called chiral. In this talk I will review Coxeter´s twisted honeycombs and will connect them to chiral maniplexes and chiral polytopes of full rank (objects that I will define). We will also see a natural way to extend Coxeter´s work.
Mónica Clapp (Instituto de Matemáticas-UNAM, Mexico)
New blow up profiles for Yamabe type problems
Abstract: Many problems in differential geometry are expressed in terms of an elliptic partial differential equation which is conformally invariant. Typical examples are the Yamabe problem or the prescribed scalar curvature problem.
The invariance of these equations under dilations gives rise to blow-up phenomena, which makes them hard to solve. It is, thus, important to understand these phenomena, in other words, to obtain information on energy level, the location and the limit profile of the blow-up.
A particular profile has been profusely studied: that given by the so-called standard bubble, i.e., the solution to the Yamabe problem on the round sphere. It has been successfully used to construct solutions of many different types of problems.
In this talk we will exhibit other blow-up profiles, which arise by considering special types of symmetries, and we will use them to produce solutions of some elliptic PDEs.
Abstract: We present several results about solenoidal manifolds motivated by results by Dennis Sullivan in  with commentaries developed in  and on a join project with Dennis Sullivan . Solenoidal manifolds of dimension n are topological spaces which are locally homeomorphic to the product of a Cantor set with an open subset of $R^n$. Geometric 3-dimensional solenoidal manifolds are the analog of geometric 3-manifolds in the sense of Thurston. We will give some results related to 3-dimensional geometric solenoidal manifolds.
 D. Sullivan, Solenoidal manifolds, J. Singul. 9 (2014), 203–205.
 A. Verjovsky, Commentaries on the paper “Solenoidal manifolds” by Dennis Sullivan. J. Singul. 9 (2014), 245–251.
 D. Sullivan, A. Verjovsky, Compact 3-dimensional geometric solenoidal manifolds. In preparation.