PhD scholarship in Algebraic Function Fields and Coding Theory – DTU Compute

We are looking for a bright and motivated PhD student for a 3-year fully funded PhD position starting 1 April 2025. The project is financed by Villum Fonden, and it is part of the Villum YIG “CREATE”, whose aim is to investigate algebraic function field techniques in coding theory.
We are looking for a bright and motivated PhD student for a 3-year fully funded PhD position starting 1 April 2025. The project is financed by Villum Fonden and it is part of the Villum Young Investigator project CREATE “algebraiC cuRvEs in informAtion ThEory: a treasure yet to discover”. It is an excellent opportunity to be involved in advanced research on algebra and coding theory, particularly algebraic function field theory and Algebraic-Geometry codes.

The project CREATE aims to investigate the full potential of algebraic curves and algebraic function field techniques in relation with two very important applications: network communication (rank-metric codes) and distributed cloud storage (locally recoverable codes). To investigate this potential, theoretical results about function fields with many rational places and automorphisms are necessary. The purpose of the PhD position is to construct and classify maximal function fields (particularly introducing the invariant a-number as a parameter to distinguish function fields) and function fields with many automorphisms.

Responsibilities
Upon joining this project, you will become a member of the algebra group within the Section for Mathematics. You will also join the DTU Compute PhD school and take part in its courses and activities. As part of your PhD training and research activities, you will have research stays at the academic collaborators’ universities.

The PhD position will involve:

• Conducting research in the area of algebraic function field and coding theory
• studying the literature on automorphism groups of algebraic curves and function fields
• Finding new bounds for the size of automorphism groups and their structure, as well as obtaining classification results for function fields with many automorphisms
• Exploring methods for computing a-numbers of function fields and its geometric characterization (i.e. in connection with the automorphism group or other invariants)
• Using the Computer Algebra System MAGMA to collect data through experiments
• Proposing methodologies for using the a-number to classify (up to isomorphism) function fields, and in particular maximal function fields.

Your duties will also include some teaching assistance work at DTU, and (possibly) the co-supervision of BSc and MSc student projects related to your research.

Qualifications
To be considered for the position, you need to have background in algebra (group theory, ring/field theory and preferably function field theory) and basic coding theory. You will need to document these skills by listing the relevant university courses you took, or the relevant experience you have.

You must have a two-year master's degree (120 ECTS points) or a similar degree with an academic level equivalent to a two-year master's degree. You can apply prior to obtaining the degree, providing the expected graduation date.

Approval and Enrolment
The scholarship for the PhD degree is subject to academic approval, and the candidate will be enrolled in one of the general degree programmes at DTU. For information about our enrolment requirements and the general planning of the PhD study programme, please see DTU's rules for the PhD education.

Assessment
The assessment of the applicants will be made by the main supervisor Associate Professor Maria Montanucci, co-supervisor Professor Peter Beelen and hiring manager (and head of the section for Mathematics) Professor Morten Brøns. The assessment of the applicants will take place in January/February 2025.

We offer
DTU is a leading technical university globally recognized for the excellence of its research, education, innovation and scientific advice. We offer a rewarding and challenging job in an international environment. We strive for academic excellence in an environment characterized by collegial respect and academic freedom tempered by responsibility.

Salary and appointment terms
The appointment will be based on the collective agreement with the Danish Confederation of Professional Associations. The allowance will be agreed upon with the relevant union.

The period of employment is 3 years. The position is a full-time position The expected starting date for the PhD position is 1 April 2025 (or the earliest available date after that, by mutual agreement).

You can read more about career paths at DTU here.

Further information
For further information please contact Maria Montanucci at [email protected].

You can read more about DTU Compute at www.compute.dtu.dk/english and about the Section for Mathematics at www.compute.dtu.dk/sections/math.

If you are applying from abroad, you may find useful information on working in Denmark and at DTU at DTU – Moving to Denmark. Furthermore, you have the option of joining our monthly free seminar “PhD relocation to Denmark and startup “Zoom” seminar” for all questions regarding the practical matters of moving to Denmark and working as a PhD at DTU.

Application procedure
Your complete online application must be submitted no later than 30 November 2024 (23:59 Danish Time). Applications must be submitted as one PDF file containing all materials to be given consideration. To apply, please open the link "Apply now", fill out the online application form, and attach all your materials in English in one PDF file. The file must include:

• A letter motivating the application (cover letter)
• Curriculum vitae
• Grade transcripts and BSc/MSc diploma (in English) including official description of grading scale
• 1-2 recommendation letters (optional)

You may apply prior to ob­tai­ning your master's degree but cannot begin before having received it.

Applications received after the deadline will not be considered.

All interested candidates irrespective of age, gender, race, disability, religion or ethnic background are encouraged to apply.

DTU Compute
DTU Compute is a unique and internationally recognized academic environment spanning the science disciplines mathematics, statistics, computer science, and engineering. We conduct research, teaching and innovation of high international standard - producing new knowledge and technology-based solutions to societal challenges. We have a long-term involvement in applied and interdisciplinary research, big data and data science, artificial intelligence (AI), internet of things (IoT), smart and secure societies, smart manufacturing, and life science.

Technology for people
DTU develops technology for people. With our international elite research and study programmes, we are helping to create a better world and to solve the global challenges formulated in the UN’s 17 Sustainable Development Goals. Hans Christian Ørsted founded DTU in 1829 with a clear mission to develop and create value using science and engineering to benefit society. That mission lives on today. DTU has 13,500 students and 6,000 employees. We work in an international atmosphere and have an inclusive, evolving, and informal working environment. DTU has campuses in all parts of Denmark and in Greenland, and we collaborate with the best universities around the world.

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