Jakob Blaavand

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Jakob Lindblad Blaavand
D.Phil-student, M.Sc. and B.Sc. in Mathematics

Mathematical Institute
Oxford University
24-29 St Giles'
Oxford, OX1 3LB, England

+44 (0) 7527116767
blaavand@maths.ox.ac.uk

www.lindbladblaavand.dk

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I'm a D.Phil student at the Mathematical Institute at Oxford Universtity, a member of Balliol College, and retained pure maths lecturer at Jesus College. I'm working with Higgs bundles on Riemann surfaces, and a type of Fourier transform for these. My supervisor is professor Nigel Hitchin. I did my B.Sc. and M.Sc. at Centre for Quantum Geometry of Moduli Spaces (QGM), at Aarhus University. My supervisor was professor Jørgen Ellegaard Andersen.

Publications

Asymptotics of Toeplitz operators and applications to TQFT With Jørgen Ellegaard Andersen in Travaux Mathematiques, University of Luxembourg, Vol. 19, Nr. Geometry and Quantization. Lectures of the GEOQUANT school, 2011, s. 167-201.

Outreach

QGM Hall of Fame I've had the opportunity to interview several high profile mathematicians about their views upon mathematics, and their entry into maths. The results can be viewed on the page in the link or by clicking on the names below.
RNA er jo bare matematik! in Aktuel Naturvidenskab, no. 6, 2011

Various mathematical writings

Derived categories of coherent sheaves This document is an assessment for a course on derived categories of coherent sheaves, in the fall of 2011, at Oxford University. The document is a review of aspects of derived categories of coherent sheaves. We review the definitions of derived categories and of coherent sheaves on a smooth projective variety. Following this we will discuss properties such as Serre duality and applications of Serre duality. Lastly we will discuss the Bondal–Orlov Reconstruction theorem.
Mirror symmetry and Gromov-Witten invariants This document is an assessment for a course on symplectic geometry, in the fall of 2011, at Oxford University. The document is a review of aspects of mirror symmetry with special attention to the predictions about the number of rational curves on a quintic threefold. The calculations leading to the predictions are reviewed, and afterwards Gromov–Witten invariants for quintic three-folds are defined and calculations are discussed.
Deformation quantization and geometric quantization of abelian varieties This is my progress report. It is written as the conclusion of my first 3 years as a PhD-student. It contains a chapter about complex geometry, quantization, the Hitchin connection, moduli spaces of flat connections, abelian varieties, Berezin-Topelitz deformation quantization, geometric quantization of abelian varieties.
Computations of moduli spaces We calculate the moduli space of flat SU(2) connections on several surfaces. The surfaces in question are the torus with zero and one puncture, and the sphere with one, two, three and four punctures. Included is also a chapter with serveral nice facts about SU(2) and its lie algebra. Besides all this is a chapter dedicated to the SU(2) representation variety, discussing its topology and the dimension in the case of a surface group.
3-manifold invariants derived from link invariants These notes were written for a talk I gave at University of California, Berkeley in November 2010. The talk was about a method of converting link invariants to 3-manifold invariants. The example in mind are the BHMV-invariants derived from skein theory and the Kauffman bracket.
Knot Theory and the Jones Polynomial

This is lecture notes written for the UNF Matematik Camp 2010, held at University of Copenhagen, July 2010. The document is written in Danish.

Denne note, om knudeteori og Jones-polynomiet, er skrevet i forbindelse med UNF Matematik Camp 2010, afholdt på Københavns Universitet, HC Ørsted Instituttet, Juli 2010. Noten kræver ingen forudsætninger, og er skrevet i et sprog, gymnasieelever kan læse og forstå.

The Mathematics behind Google This is a note on the mathematics behind Google.The first part of the note is mainly about the philosophy behind Google, and a small toy example of how it works. The last part is the mathematical part, where it is proven using basic linear algebra, how Google works. The paper is written in Danish.

Denne note handler om matematikken og filosofien bag Google. Første del er hovedsageligt om filosofien bag Google, som illustreres med et lille eksempel. Sidste del er rent matematisk, hvor alle påstandene fra første del bliver bevist. Beviserne laves med basal lineær algebra.
Properties of classical Lie Groups In this note we list a lot of facts about classical Lie groups. The focus will mainly be on dimension, compactness, connectedness and relationships between the classical Lie groups. Some basic principal bundles of the classical Lie groups will also be listed.
Homogeneous spaces

In this note we investigate the notion of a group action on a topological space. First of all what it is, but also see that almost all such spaces have the structure of a quotient space. The spaces which have a quotient space structure are called homogeneous spaces. Last but not least we will be dealing with some examples of homogeneous spaces.

This note is part of the evaluation in the course Unitary group representations.

Poincaré models for the hyperbolic plane I have written a note on two representations of the hyperbolic plane: The disc model and the Upper Half-plane model. In particular we will look at the geodesics in the two representations, and especially discuss the distance between two arbitrary points in the disc model. Last but not least it will be shown that the Gaussian curvature of the hyperbolic plane is constantly -1, by computing the Gaussian curvature in the Upper Half-plane model.
Two definitions of embedded submanifolds In connection with the course "Riemannian geometry" in the fall of 2008, I did a seminar on the topic of submanifolds. In the notes I prove the equivalence of two definitions of embedded submanifolds.
Bachelorprojekt My B.Sc. in mathematics was completed with this assignment on semigroups of contraction operators. I prove the classical theorem by Hille and Yoshida, and another classical theorem of Stones. The paper is written in Danish.
RSA encryption on TI-89 This note contains a torough description of how you can use your TI-89 CAS calculator to do very smallscale RSA encryption. The note is in Danish.

I denne note findes en grundig gennemgang af, hvordan man bruger sin TI-89 til RSA-kryptering. Det siger sig selv, at det ikke bliver en særlig stærk kryptering, men det illustrerer princippet. Noten skal ses som et supplement til denne note om kryptering.