## Daniel Friedan (26/08/16)

Sigurður Örn Stefánsson, August 22, 2016

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:

## Eggert Briem (08/04/16)

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.

## Jón Áskell Þorbjarnarson (29/02/16)

Sigurður Örn Stefánsson, January 22, 2016

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.

## Patrice Lassère (15/12/14)

Benedikt Magnússon, December 11, 2014

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.