Galperin's Talk on Invisible Objects

Gregory Galperin recently gave a talk in the colloquium series about invisible objects. These objects are typically invisible in one direction in the sense that light flows around the object and not through it. We give here an example of such an invisible object.





Can you show that light from infinity (parallel rays) flow around the object as shown if the base angles of each isosceles triangle is 30 degrees?

Gordon to Speak on the Continuum Hypothesis

From the abstract:

In the middle of 60's P. Cohen proved the independence of CH. The method of forcing that he developed for this problem was later rewritten in terms of Boolean-valued models of set theory by D. Scott and R. Solovay. In the middle of 70's I proved that Boolean-valued models of the field of real numbers are exactly the universal K-spaces. This fact did not only give a rigorous mathematical formulation to the problem of Kantorovich, but also allowed to transfer many properties of real numbers to K-spaces. In particular, it allowed generalizing a lot of theorems about linear functionals on operators with the values in Kantorovich spaces.

Many results in this area were obtained by functional analysts from Novosibirsk. However, this method did not become popular among specialists in analysis, since it requires a deep knowledge of mathematical logic, especially of the axiomatic set theory.

Recently, I found an exposition of this method that seems to me quite accessible for non- specialists in mathematical logic. I will try to explain the basic ideas of this method (including the idea of the independence proof of CH) in two consecutive talks.

Galperin to Give Feb 4 Colloquium

Gregory Galperin is slated to give the Friday colloquium this week. His topic is

A Geometric Problem That Leads to the Billiard Law of Reflection

Abstract:I will show some examples of "invisible geometric objects." This means that light bends around an object, causing it to become as it were invisible. The Billiard Law of Reflection, which states that the angle of reflection equals the angle of incidence, will play a crucial role. The main examples will concern billiard reflection for ellipses and hyperbolas.