**Problem of the Week**

**Math Club**

**DST and GT Day**

**Number Theory Conf.**

**Zassenhaus Conference**

**Hilton Memorial Lecture**

seminars:topsem:topsem_spring2018

**February 15**

Speaker:**Carlos Vega**(Binghamton University)

Title:**Null Distance on a Spacetime***Abstract:*In contrast to the Riemannian setting, a Lorentzian manifold (M,g) is not known to possess any naturally induced distance function. I will first try to explain why that is, starting with some of the basics of spacetime (Lorentzian) geometry. We will then discuss a `null distance function' introduced in joint work with Christina Sormani, some of its properties, examples, and some open questions.

**February 8**

Speaker:**Russell Ricks**(Binghamton University)

Title:**A Rank Rigidity Result for Certain Nonpositively Curved Spaces via Spherical Geometry***Abstract:*To understand the geometry of nonpositively curved (NPC) spaces, it is natural to classify the various types of spaces that can occur. The Rank Rigidity Theorem for compact NPC manifolds separates the class of compact NPC manifolds into three very distinct types, and proves that nothing else can exist.A version of Rank Rigidity has been conjectured for more general NPC spaces (CAT(0) spaces). In this talk, we discuss some progress toward this general conjecture, by reducing the problem to looking at patterns on spheres. In particular, we prove the conjecture for certain NPC spaces with one-dimensional boundary. Unlike previous results in this area, there are no additional constraints on the CAT(0) space (such as a manifold or polyhedral structure).

**February 1**

Speaker:**Jonathan Williams**(Binghamton University)

Title:**Sewing a homotopy into pieces***Abstract:*In this talk, I will try to explain the title. There will be 4-manifolds, many pictures, and very little background needed.

**January 16**(algebra crosspost - meets in WH-100E at 2:50)

Speaker:**Jonas Deré**(KU Leuven Kulak)

Title:**Which manifolds admit expanding maps***Abstract:*In 1981, M. Gromov completed the proof that every manifold admitting an expanding map is, up to finite cover, homeomorphic to a nilmanifold. Since then it was an open question to give an algebraic characterization of the nilmanifolds admitting an expanding map. During my talk, I will start by introducing the basic notions of expanding maps and nilmanifolds. Then I explain how the existence of such an expanding map only depends on the covering Lie group and on the existence of certain gradings on the corresponding Lie algebra. One of the applications is the construction of a nilmanifold admitting an Anosov diffeomorphism but no expanding map, which is the first example of this type.

seminars/topsem/topsem_spring2018.txt · Last modified: 2018/02/18 12:46 by jwilliams

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