S�ren Fuglede J�rgensen

Contact information

Name: S�ren Fuglede J�rgensen, PhD fellow
Address: Centre for Quantum Geometry of Moduli Spaces,
Aarhus University, Ny Munkegade 118, 8000 Aarhus C
Office: A4.32 (1530-432)
Phone: +45 871 55 812
E-mail:

Teaching (all notes are in Danish)

Hold 2, Introduktion til matematisk analyse, E08

Forslag til l�sning af anden afleveringsopgave.*
Forslag til l�sning af f�rste afleveringsopgave.*

MA1, Calculus E08

Kommentarer til T� uge 40 (anvendelser af itererede integraler).
Kommentarer til T� uge 38 (linearisering og differentialer).
Kommentarer til T� uge 37 (mere om pol�re koordinater).
Kommentarer til T� uge 36 (grafer og pol�re koordinater).

*Jeg har af gode grunde valgt ikke at l�gge disse online. Skriv p� ovenst�ende adresse for at f� en kopi.

Research

My PhD project is concerned with the so-called quantum representations of mapping class groups. The representations are related to topological quantum field theory and arise in a wide variety of different mathematical fields. My work will be about combining techniques from the various fields in an attempt to investigate the properties of the representations. I have made a couple of write-ups on the subject:

Progress report: Quantum representations of mapping class groups – this is the report I wrote halfway through my PhD project. It contains an introduction to a selection of mathematical topics, relevant for understanding quantum representations, and gives a glimpse at where my own PhD studies are heading.
Quantum representations of mapping class groups and TQFTs for newcomers – these notes are actually notes for a talk, taking place on UC Berkeley, 2010. Huge parts of the notes should be readable for a reader with an understanding of undergraduate geometry (knowledge of homology probably also helps). However, most of the contents have been absorbed in revised and corrected form in my progress report.
Quantum representations for dummies (in preparation) – these I did mainly for people with a very basic understanding of math, trying to assume as little knowledge as possible, instead focusing on the ideas behind the concepts.

Class notes

More or less as an experiment, I decided to TeX my notes for classes and seminars on the fly. I mainly did them as a service to my self, obtaining a collection of non-chaotic notes. My notes will be available here more or less after each class, but should be taken for what they are: Not proof-read and ridden with typos. Nevertheless, someone might find use for them:

Spring 2012, Aarhus

Conformal field theory

Fall 2011, Aarhus

Introduction to gauge theory
Symplectic geometry, non-abelian localization and path integrals
Topics on K�hler Geometry and Hodge Theory

Spring 2011, Aarhus

Topological quantum field theories and moduli spaces

Fall 2010, UC Berkeley

256 – Algebraic Geometry
275 – Quantum Field Theory (discontinued early on due to time constraints)
276 – Topics in Topology

Other notes

Master class on TQFTs, Barcelona 2012

Talks

A list of all my seminars and talks is available on the university web page. The following are PDF slides, I have used for some of the talks. As they were meant to supplement my ramblings, as stand-alone objects they are probably not all that useful, but here they are anyway:

Witten–Reshetikhin–Turaev invariants of mapping tori and their asymptotics – slides for my talk at the Winter School in Mathematical Physics, Les Houches 2012
Witten–Reshetikhin–Turaev invariants of mapping tori via skein theory – slides for my talk at the QGM Nielsen retreat 2011 (essentially identical to the above).
Qualifying exam – Integral lattices in TQFT – not directly related to my own research, these I used for the talk I gave for my qualifying exam.

A bachelor's project (in Danish – English abstract included in the pdf)

I forbindelse med kurset Videreg�ende analyse skrev jeg i midten af 2008 et bachelorprojekt under titlen Stone-von Neumanns s�tning. I opgaven tager jeg et kig p� og beviser et repr�sentationsteoretisk resultat, der kendes som Stone-von Neumanns s�tning, og jeg betragter s�tningens anvendelse i kvantemekanikkens matematiske formalisme. Opgaven kan forst�s med kendskab til hvad der svarer til grundkurserne p� matematikstudiet sammen med kurset videreg�ende analyse. Hent projektet i pdf-format.

Other writings

Flader (in Danish) – these are notes aimed at high school students. I give the classification of triangulated surfaces using a number of examples.

Math related picture galleries

I usually make sure to take a lot of pictures at various special events. While previously made available on this page, I decided to take them down for a number of reasons. Feel very free to ask me for pictures from any events.

	Monday	Tuesday	Wednesday	Thursday	Friday
10:15–12.00		Gauge theory		Gauge theory	Symplectic geometry
12.15–14.00	Symplectic geometry	K�hler geometry
14.15–16.00	K�hler geometry