Mathematics | College of Science

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Mathematics

Completely coarse maps are real-linear

Event Date: 
Friday, July 17, 2020 - 9:00am

Abstract. In this talk I will present joint work with Bruno M. Braga, continuing the study of the nonlinear geometry of operator spaces that was recently started by Braga and Sinclair.

Operator spaces are Banach spaces with an extra "noncommutative" structure. Their theory sometimes resembles very closely the Banach space case, but other times is very different. Our main result is an instance of the latter: a completely coarse map between operator spaces (that is, a map such that the sequence of its amplifications is equi-coarse) has to be real-linear.

A C(K) space with few operators and few decompositions

Event Date: 
Friday, July 10, 2020 - 9:00am
Location: 
https://unt.zoom.us/j/512907580

Abstract. I shall report on joint work with Piotr Koszmider (IMPAN) concerning the closed subspace of $\ell_\infty$ generated by $c_0$ and the characteristic functions of elements of an uncountable, almost disjoint family $A$ of infinite subsets of the natural numbers. This Banach space has the form $C_0(K_A)$ for a locally compact Hausdorff space $K_A$ that is known under many names, including $\Psi$-space and Isbell--Mr\'ow\-ka space.

Kalton's interlacing graphs and embeddings into dual Banach spaces

Event Date: 
Friday, July 3, 2020 - 9:00am
Location: 
https://unt.zoom.us/j/512907580

Abstract. A fundamental theorem of Aharoni (1974) states that every separable metric spaces bi-Lipschitz embeds into $c_0$​. It is a major open question to know whether any Banach space containing a Lipschitz copy of $c_0$​ must contain a subspace linearly isomorphic to $c_0$​. In this talk, we will consider similar questions in relation with the weaker notion of coarse embeddings.

Bringing uniform Roe algebras to Banach space theory

Event Date: 
Friday, June 26, 2020 - 9:00am
Location: 
https://unt.zoom.us/j/512907580

Abstract. Given a metric space $X$, the uniform Roe algebra of $X$, denoted by $C^*_u(X)$, is a $C^*$-algebra which encodes many of $X$'s large scale geometric properties. In this talk, I will give an introduction on those objects and give an overview of the current state of the literature on questions related to rigidity of uniform Roe algebras (i.e., on how much of the large scale geometry of a metric space is encoded in its uniform Roe algebra). The second half of the talk will focus on bringing these mathematical objects to the context of Banach space/lattice theory.

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