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  3. PhD position in Solvable quantum knot invariants (1.0 FTE)

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PhD position in Solvable quantum knot invariants (1.0 FTE)

In some sense knots are the integers of topology. They provide a language to discuss space at a fundamental level. Part of the pleasure of knot theory is the many interactions with other fields such as (2,3 and 4)-dimensional topology, quantum field theory, representation theory,

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Arbeidsvoorwaarden

Standplaats:
Broerstraat, Groningen, Groningen
Dienstverband:
Tijdelijk contract / Tijdelijke opdracht
Uren per week:
38 - 38 uur
Salarisindicatie:
€ 3061 - € 3061 per maand
Opleidingsniveau:
WO

Functieomschrijving

In some sense knots are the integers of topology. They provide a language to discuss space at a fundamental level. Part of the pleasure of knot theory is the many interactions with other fields such as (2,3 and 4)-dimensional topology, quantum field theory, representation theory, Lie theory, number theory, (non-)commutative (algebraic) geometry and computer algebra.

Your job is to learn how knot theory can be approached from other fields of mathematics and how you can apply and strengthen the recently developed knot invariants of Bar-Natan and van der Veen in some of these contexts. See the full research proposal linked below for a more detailed account.

The subject is very much driven by intuition, both from cut-and paste topology and particle physics. However we will insist to build a firm mathematical and computational foundation for everything we do. In addition to the usual definitions, theorems and proofs this means we also use symbolic algebra on a computer to experiment and actually verify many of our statements precisely.

You will be part of my active research group with currently five other PhD students some of which are joint with other institutes such as NTU Singapore and the Groningen physics department as part of our fundamentals of the universe program www.fundamentalsoftheuniverse.com
There are also frequent interactions with my colleagues in the University of Toronto, Canada and SUSTech, Shenzhen China.

The objective of the temporary position is the production of a number of research articles in peer-reviewed scientific journals and conference proceedings, which together will form the basis of a thesis leading to a PhD degree (Dr) at the University of Groningen.

Also recommend browsing through the excellent and easy-going introductory book “The Knot Book” by Colin Adams.

Functie-eisen

The successful candidate should:

• have excellent writing and communication skills in English
• have a master’s degree in mathematics or mathematical physics
• have good command of commutative algebra and topology
• experience with programming and/or physics is a plus.

Conditions

We offer you, following the Collective Labour Agreement for Dutch Universities:

• a salary of € 2,395 gross per month in the first year, up to a maximum of € 3,061 gross per month in the fourth and final year for a full-time working week
• a holiday allowance of 8% gross annual income and an 8.3% year-end bonus
• a full-time position (1.0 FTE). The successful candidate will first be offered a temporary position of one year with the option of renewal for another three years. Prolongation of the contract is contingent on sufficient progress in the first year to indicate that a successful completion of the PhD thesis within the next three years is to be expected. A PhD training programme is part of the agreement and the successful candidate will be enrolled in the Graduate School of Science and Engineering.

The starting date is negotiable but is preferably December 2021.

Additional information

Roland van der Veen
r.i.van.der.veen@rug.nl

Roland van der Veen
The full research proposal