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Vacature - PhD position in algebraic geometry at Utrecht University (1.0 FTE) HRS4R

Specificaties - (uitleg)

FunctietypesResearch, Development, Innovation
Uren 36,0 - 40,0 uren per week
Salaris € 2222 - € 2840
Werk-/denkniveauUniversity Graduate
Vacaturenummer 953105
Vertalingen
About employer Utrecht University
Short link www.academictransfer.com/44700

Solliciteer binnen 55 dagen op deze vacature

Functiebeschrijving

The aim of this PhD project is to explore invariants of moduli spaces of sheaves on general type surfaces and their relation to modular forms and Donaldson-Thomas theory.

Moduli spaces of sheaves on complex algebraic surfaces appeared in relation to a certain quantum field theory called N  = 4 supersymmetric Yang-Mills. Strong-weak duality of this theory led Vafa-Witten (1994) to predict that generating functions of invariants of these moduli spaces are modular forms. Their prediction was mathematically verified for several classes of surfaces, such as rational and K3 surfaces. However, no mathematical verifications were known for general type surfaces.


Recent progress in algebraic geometry led to mathematical verifications of Vafa-Witten’s prediction for general type surfaces, refinements of their prediction, and links to Donaldson-Thomas theory.


This PhD position, financed by NWO TOP2.613.001.701, explores new avenues that have become available since these recent advances. The PhD student will be part of the Utrecht Geometry Centre of the Mathematical Institute at Utrecht University

Functie-eisen

We are looking for an enthusiastic, motivated and skilled applicant who is expected to have finished an MSc in mathematics with top grades. It is a great advantage when the applicant has taken some basic algebraic geometry courses or has done an MSc thesis in algebraic geometry. The applicant is expected to have strong analytic skills. A decent level of English is required.

Arbeidsvoorwaarden

You will be offered a full-time position for four years. The gross monthly salary will amount to €2,222 in the first year to €2,840 in the fourth year (P-scale of the Collective Labour Agreement Dutch Universities). It is supplemented with a holiday bonus of 8% and an end-of-year bonus of 8.3% per year.

In addition Utrecht University offers a pension scheme and a partially paid parental leave and flexible employment conditions. Conditions are based on the Collective Labour Agreement Dutch Universities. The research group will provide the candidate with necessary support on all aspects of the project. You’ll find more information about working at Utrecht University here.

Starting date: 1 September 2018.

Werkgever

A better future for everyone. This ambition motivates our scientists in executing their leading research and inspiring teaching. At Utrecht University, colleagues from various disciplines collaborate intensively towards major societal themes. Our focus is on Dynamics of Youth, Institutions for Open Societies, Life Sciences and Sustainability.

The city of Utrecht is one of the oldest cities in the Netherlands, with a charming old center and an internationally oriented culture that is strongly influenced by its century-old university. Utrecht city has been consistently ranked as one of the most livable cities in the Netherlands.

The Faculty of Science consists of six departments: Biology, Pharmaceutical Sciences, Information and Computing Sciences, Physics and Astronomy, Chemistry and Mathematics. The Faculty is home to 5600 students and nearly 1500 staff and is internationally renowned for the quality of its research. The Faculty's academic programmes reflect developments in today's society. Read the overall impression 2016 of the Faculty of Science.

The Mathematical Institute of the Department of Mathematics organizes and teaches the BSc curricula in Mathematics as well as the (English-taught) MSc programme in Mathematics. The Institute currently comprises about 10 full professors, 17 further faculty members, 20 PhD students, 10 post-docs, and teaches 500 students. The Institute is internationally recognized for its excellent research in both pure and applied mathematics. It has a long-standing tradition of transdisciplinary collaboration with other scientific fields. Interdisciplinary activities include, but are not limited to, theoretical physics, theoretical biology, and life sciences.

Additionele informatie

Additional information about the vacancy can be obtained from Dr. M. Kool, e-mail: M.Kool1@uu.nl.

bewaar

Specificaties - (uitleg)

FunctietypesResearch, Development, Innovation
Uren 36,0 - 40,0 uren per week
Salaris € 2222 - € 2840
Werk-/denkniveauUniversity Graduate
Vacaturenummer 953105
Vertalingen
About employer Utrecht University
Short link www.academictransfer.com/44700

Solliciteer binnen 55 dagen op deze vacature

Functiebeschrijving

The aim of this PhD project is to explore invariants of moduli spaces of sheaves on general type surfaces and their relation to modular forms and Donaldson-Thomas theory.

Moduli spaces of sheaves on complex algebraic surfaces appeared in relation to a certain quantum field theory called N  = 4 supersymmetric Yang-Mills. Strong-weak duality of this theory led Vafa-Witten (1994) to predict that generating functions of invariants of these moduli spaces are modular forms. Their prediction was mathematically verified for several classes of surfaces, such as rational and K3 surfaces. However, no mathematical verifications were known for general type surfaces.


Recent progress in algebraic geometry led to mathematical verifications of Vafa-Witten’s prediction for general type surfaces, refinements of their prediction, and links to Donaldson-Thomas theory.


This PhD position, financed by NWO TOP2.613.001.701, explores new avenues that have become available since these recent advances. The PhD student will be part of the Utrecht Geometry Centre of the Mathematical Institute at Utrecht University

Functie-eisen

We are looking for an enthusiastic, motivated and skilled applicant who is expected to have finished an MSc in mathematics with top grades. It is a great advantage when the applicant has taken some basic algebraic geometry courses or has done an MSc thesis in algebraic geometry. The applicant is expected to have strong analytic skills. A decent level of English is required.

Arbeidsvoorwaarden

You will be offered a full-time position for four years. The gross monthly salary will amount to €2,222 in the first year to €2,840 in the fourth year (P-scale of the Collective Labour Agreement Dutch Universities). It is supplemented with a holiday bonus of 8% and an end-of-year bonus of 8.3% per year.

In addition Utrecht University offers a pension scheme and a partially paid parental leave and flexible employment conditions. Conditions are based on the Collective Labour Agreement Dutch Universities. The research group will provide the candidate with necessary support on all aspects of the project. You’ll find more information about working at Utrecht University here.

Starting date: 1 September 2018.

Werkgever

A better future for everyone. This ambition motivates our scientists in executing their leading research and inspiring teaching. At Utrecht University, colleagues from various disciplines collaborate intensively towards major societal themes. Our focus is on Dynamics of Youth, Institutions for Open Societies, Life Sciences and Sustainability.

The city of Utrecht is one of the oldest cities in the Netherlands, with a charming old center and an internationally oriented culture that is strongly influenced by its century-old university. Utrecht city has been consistently ranked as one of the most livable cities in the Netherlands.

The Faculty of Science consists of six departments: Biology, Pharmaceutical Sciences, Information and Computing Sciences, Physics and Astronomy, Chemistry and Mathematics. The Faculty is home to 5600 students and nearly 1500 staff and is internationally renowned for the quality of its research. The Faculty's academic programmes reflect developments in today's society. Read the overall impression 2016 of the Faculty of Science.

The Mathematical Institute of the Department of Mathematics organizes and teaches the BSc curricula in Mathematics as well as the (English-taught) MSc programme in Mathematics. The Institute currently comprises about 10 full professors, 17 further faculty members, 20 PhD students, 10 post-docs, and teaches 500 students. The Institute is internationally recognized for its excellent research in both pure and applied mathematics. It has a long-standing tradition of transdisciplinary collaboration with other scientific fields. Interdisciplinary activities include, but are not limited to, theoretical physics, theoretical biology, and life sciences.

Additionele informatie

Additional information about the vacancy can be obtained from Dr. M. Kool, e-mail: M.Kool1@uu.nl.

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