We prove that a finite braided tensor category A is invertible in the Morita 4-category BrTens of categories if, and only it non-degenerate. This includes case semisimple modular categories, but also non-semisimple examples such as representations small quantum group at good roots unity. Via cobordism hypothesis, we obtain new 4-dimensional framed topological field theories, which regard versio...

We give a calculation of Picard groups Pic2 of K(2)-local invertible spectra and Pic(L2) of E(2)-local invertible spectra, both at the prime 3. The main contribution of this paper is to calculation the subgroup κ2 of invertible spectra X with (E2)∗X ∼= (E2)∗S as continuous modules over the Morava stabilizer group G2.

This talk discusses a conjecture of R. V. Kadison and myself. Our conjecture is that each one-to-one linear map of one unital C*-algebra onto another that preserves the identity is a Jordan isomorphism if it maps the invertible elements of the first C*-algebra onto the invertible elements of the other C*-algebra. Connections are shown between this conjecture and Cartan’s uniqueness theorem. 1. ...

Semi-invertible multiplicative ergodic theorems establish the existence of an Oseledets splitting for cocycles of non-invertible linear operators (such as transfer operators) over an invertible base. Using a constructive approach, we establish a semi-invertible multiplicative ergodic theorem that for the first time can be applied to the study of transfer operators associated to the composition ...

We consider certain decision problems for the free model of theory Cartesian monoids. introduce a computation based on notion single stack one-way PDA due to Ginsburg, Greibach and Harrison. This allows us solve such as (1) Given finite set B elements an element F, is F product members B? (2) Is submonoid generated by infinite? fragments monoid. These include right invertible so our results app...