Post-doctoral position in Mathematics: Diophantine Problems with Restricted Sets of Variables, PAR 2019/1502

The Department of Mathematical Sciences at the University of Gothenburg is shared with Chalmers University of Technology. With about 200 employees we are the largest department of mathematics in Sweden. The department has three scientific divisions, Algebra and Geometry, Analysis and Probability Theory, and Applied Mathematics and Statistics.

We conduct successful research in a number of areas in pure and applied mathematics including mathematical statistics. The department is an important partner of other sciences and industrial projects. We make a significant contribution to the benefit of society by extensive education. We are a parent-friendly organization and we actively promote equal opportunities.

At the Division of Algebra and Geometry we conduct renown research in areas such as several complex variables, algebraic and complex geometry, number theory, algebra, and mathematical physics. The work environment is supportive, creative and international, with a steady flow of guests. More information about us is available on the website http://www.chalmers.se/math/

Specific subject description
We are looking for a person who will work on the project “Diophantine Problems with restricted sets of variables” together with associate senior lecturer Julia Brandes at the division of Algebra and Geometry.

The purpose of the project is to apply some of the recent advances on Vinogradov’s mean value theorem in order to give quantitative bounds for the number of solutions of Diophantine equations where the variables are restricted to lie in certain small sets.

One of the great breakthroughs at the interface of analytic number theory and harmonic analysis was the resolution of the main conjecture in Vinogradov’s mean value theorem, achieved more or less simultaneously by Wooley, and Bourgain, Demeter and Guth. The project aims at developing the ideas going into the proofs further, with a special focus on problems motivated in number theory. The project has a two-pronged approach and aims on the one hand at exploiting the structure of the existing methods in order to solve problems in additive number theory with special consideration given to additive problems over fractal sets, and on the other hand to generalise the methods and make them less dependent on certain homogeneity constraints on the size of the variables.

The project is financed by a grant from the Knut and Alice Wallenberg Foundation.

Outstanding applications from all research areas in mathematics will be considered. Precedence will however be given to those who have a research profile compatible with the subject description.

Job assignments
You will work on adapting the technology of efficient congruencing/efficient boxing or l^2-decoupling to additive problems restricted to certain small sets of variables. Of particular interest are sets with a fractal structure (including numbers with restrictions on which digits are permitted), as well as variables lying in small and disparate domains. You are expected to contribute by developing new ideas both independently and in collaborations. You should be highly motivated and independent. Your ability to collaborate and communicate will be taken into account in the assessment.

Teaching as well as supervision of students’, including Ph.D. students, independent work may be part of your duties up to an extent of 20 %. Our teaching languages are English and Swedish. As most of our teaching is in Swedish, the options will vary according to your language skills. University of Gothenburg offers courses in the Swedish language.

Eligibility
The eligibility for academic positions is given in the Swedish Higher Education Ordinance. To qualify for the position, you should have completed a Ph.D. degree in mathematics, or equivalent, by the deadline of the application. The degree should generally not be older than three years at the time of the application.

Assessment
Regulations for the evaluation of qualifications for academic positions are given in the Swedish Higher Education Ordinance. The assessment of your application will be based mainly on your scientific skills. You are expected to provide evidence of excellence in research.

Experience in the following areas is meritorious: The Hardy-Littlewood circle method, Efficient congruencing and/or l^2-decoupling.

Fluency in English is expected. The applications will be assessed by a local recruitment committee at Mathematical Sciences.

Employment
Type of employment: Fixed-term employment, 2 years
Extent: 100 %
Location: Department of Mathematical Sciences, University of Gothenburg
First day of employment: January 6, 2020 or as agreed

For further information:
Head of unit within the Division of algebra and geometry, Håkan Samuelsson Kalm, hasam@chalmers.se, +46 31 772 3568

Project leader, Julia Brandes, brjulia@chalmers.se, +46 31 772 5367

Closing date: 11 December, 2019


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2019-12-11


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