Week starting Monday 16 September 2019
Preconditioning techniques form an crucial part of developing efficient solvers for saddle point problems, and are often conjugated with Krylov's subspace methods. One saddle point system can be arisen from discretisation of a thin plate spline which is a popular data fitting technique. Such a system is problematic with respect to its conditioning. Some common saddle point preconditioners are considered, and a note of finding preconditioner will be mentioned from Gergelits et.al. recent work.
We consider L^p boundedness of the Riesz transform on a class of non-doubling manifolds obtained by taking the connected sum of two Riemannian manifolds which are both a product of a Euclidean space and a closed manifold. We assume that one of the ends has Euclidean dimension equal to 2 which is a special case in which the L^p boundedness of the Riesz transform requires a delicate analysis.
We will watch a short talk given by Brooke Shipley followed by a talk given by Doug Ravenel. We might pause to discuss or discuss afterwards.
Abstract 1: An overview of the development of symmetric spectra, orthogonal spectra, and other monoidal model categories of spectra as well as some generalizations and applications.
The video and some notes are available here: https://www.msri.org/workshops/797/schedules/22698
Abstract 2: We will discuss methods for constructing a model structure on the category of orthogonal equivariant spectra for a finite group G. The most convenient one is two large steps away from the most obvious one.
The video is available here: https://www.newton.ac.uk/seminar/20180815090010001
Modal Type Theory and its Semantics
Dr. Ranald Clouston (RSCS)
Type theory offers an alternative foundation for mathematics, particularly suited to automated proof checking. This talk will discuss the design of a new type theory, introducing connectives from modal logic. In particular we will see how the mathematical notion of denotational semantics helps us to establish both the consistency and the expressive power of a type theory.
(Higher) category theory vs (Homotopy) type theory.
Martina Rovelli (MSI)
Given a category with adjectives, one can talk about its internal language, which is a formal system that encodes the syntax of that category. This construction generally induces a correspondence between the given flavour of category theory and a certain flavour of type theory. In this introductory talk, we will provide a basic dictionary on how to translate categorical information into type theoretical information. We will mention how the internal language of the category of sets can be expressed by means of traditional type theories, while the internal language of the (∞-)category of spaces is homotopy type theory.
This event is free and open to the public. It will be followed by drinks and nibbles on Level 3 of the Hanna Neumann Building (145).
The MSI/RSCS Seminar Series is supported by the Mathematical Sciences Institute at the College of Science and the Research School of Computer Science at the College of Engineering & Computer Science at ANU.