Kevin Beanland (VCU)
Constructions in Banach spaces
Abstract: In 1974 Boris Tsirelson constructed the first Banach space that contained no 'isomorphic copies' of $\ell_p$ for $1 \leq p < \infty$ or $c_0$. This solved an old problem in Banach space theory. Perhaps more interesting though is the method he developed to carry out the construction. The so-called saturation method was inspired by forcing from logic and is now the predominant way to construct Banach spaces with prescribed properties. This method has lead to numerous breakthroughs during the past 40 years, which I plan to discuss. In this talk I will describe this construction and explain its versatility. In the end I will state several open problems which I believe are accessible to masters students.