Math Colloquium

### Speaker: Daniel Friedan, Rutgers University and University of Iceland

Title: Quasi Riemann Surfaces

Location: TG-227 (Tæknigarður, 2nd floor)

Time: Friday, August 26 at 13:20.

### Abstract:

This will be a talk about some speculative mathematics (analysis) with

possible applications in quantum field theory. I will leave any mention

of quantum field theory to the end. I will try to define everything

from scratch, but it probably will help to have already seen the basics

of manifolds, differential forms, and Riemann surfaces.

The talk is taken from my recent paper

“Quantum field theories of extended objects”, arXiv:1605.03279 [hep-th]

which is a mixture of speculative quantum field theory and speculative

mathematics. In the talk, the speculative mathematics will be presented

on its own, without the motivations from quantum field theory.

Below is the abstract from a note I am presently writing to try to

interest mathematicians in looking at this structure:

Continue reading 'Daniel Friedan (26/08/16)'»

Math Colloquium

### Speaker: Eggert Briem

Title: Real Banach algebras and norms on real \(C(X)\) spaces.

Location: V-157, VRII.

Time: Friday, April 8 at 13:20.

### Abstract:

A commutative *complex* unital Banach algebra can be represented as a space of continuous functions on a compact Hausdorff space via the Gelfand transform. However, in general it is not possible to represent a commutative *real* unital Banach algebra as a space of continuous real-valued functions on some compact Hausdorff space, additional conditions are needed. We shall discuss conditions which imply isomorphic representations and also discuss various complete algebra norm on real \(C(X)\) spaces which arise from such representations.

Math Colloquium – BS project

### Speaker: Jón Áskell Þorbjarnarson.

Title: Distributions and fundamental solutions of partial differential equations

Location: V02-157 , VRII

Time: Friday, January 29, at 15:00-16:00.

### Abstract:

We discuss distributions, which are generalisations of integrable functions on Rn. We define them as linear functionals on the space of smooth functions with compact support. Distributions are infinitely differentiable in a weaker sense than in classical analysis and provide a larger space of solutions to differential equations. We discuss fundamental solutions of differential equations which enable us to find solutions to inhomogeneous equations using convolution. We calculate fundamental solutions for a few operators from mathematical physics and finally prove the existence theorem of Ehrenpreis & Malgrange which states that every partial differential operator with constant coefficients has a fundamental solution.

Math Colloquium

### Speaker: Patrice Lassère, Université Paul Sabatier, Toulouse

Title: When is \(L^r(\mathbb R)\) contained in \(L^p(\mathbb R) + L^q(\mathbb R)\)?

Location: V-157, VRII

Time: Monday, December 15 at **10:00-11:00**.