PhD studies

The PhD education is a four year program intended to teach the methods of mathematical research. An important part of the education is the writing of a thesis which is presented at a PhD defence.

On these pages you will find information about PhD studies, intended for PhD students, their supervisors and for those considering to apply.


Admission to PhD studies

PhD student positions in mathematics, mathematical statistics and computational mathematics are usually announced in April each year.

Vacant positions at the Department of Mathematics

General eligibility

A general eligibility of 240 credits is required, corresponding to 4 years full time university studies, or a university degree at an advanced (master) level or the equivalent competence.

Special eligibility

To be qualified you must have a university degree containing at least the following courses in mathematics:

  • Algebra: groups, rings, euclidean and principal ideal rings, fields, extension fields.
  • Foundation of analysis: real numbers, Bolzano-Weierstrass, derivation and integration in Rn, series of functions, implicit functions.
  • Analytic functions: integral and series expansion, residue calculus, conformal mappings, harmonic functions.

The textbooks we use are

Rudin: Principles of mathematical analysis,
Beachy and Blair: Abstract algebra, and
Saff and Snider: Fundamentals of complex analysis.

Selection and admission

The selection of candidates is made from certificate of courses, quality of thesis, references, and interviews. Information about admission will be given latest in June.

Those who are accepted are normally financed with study grants. If you intend to finance your education in some other way, you must inform us about that.

General eligibility

A general eligibility of 240 credits is required, corresponding to 4 years full time university studies, or a university degree at an advanced (master) level or the equivalent competence.

Special eligibility

To be qualified you should have taken courses including most of the
following material:

  • Probability Theory: Simultaneous and conditional distributions; conditional expectation and variance, multidimensional normal distribution, limit/convergence theorems (Law of Large Numbers; Central Limit Theorem), convergence of random variables (in distribution, probability, mean or almost surely); transforms (probability generating, moment generating, characteristic); martingales.
  • Stochastic Processes: Finite state Markov processes in discrete and continuous time, in particular Poisson and birth-death processes; queueing theory; renewal processes; Brownian motion; stationary stochastic processes; methods of stochastic simulation.
  • Statistical inference: Exponential families; likelihood; sufficiency; information bounds; consistency; efficiency; maximum likelihood theory; likelihood ratio tests; uniformly most powerful tests.

The books we use in courses that are prerequisites are:

Gut: An intermediate course in probability,
Ross: Introduction to probability models, and
Lindgren, B. W.: Statistical Theory.

Selection and admission

The selection of candidates is made from certificate of courses, quality of thesis, references, and interviews. Information about admission will be given latest in June.

Those who are accepted are normally financed with study grants. If you intend to finance your education in some other way, you must inform us about that.

General eligibility

In order to meet the general eligibility requirements, the applicant must have completed courses equivalent to at least 240 higher education credits (4 years full time study), of which 60 credits must be in the second cycle, or have otherwise acquired equivalent knowledge in Sweden or elsewhere.

Special eligibility

In order to meet the special eligibility requirements, the applicant must have completed courses equivalent to at least 60 credits in mathematical subjects and at least 30 credits in either numerical analysis or computer science.

Selection and admission

The selection of candidates is made from certificate of courses, quality of thesis, references, and interviews. Information about admission will be given latest in June.

Those who are accepted are normally financed with study grants. If you intend to finance your education in some other way, you must inform us about that.

Possible PhD thesis projects

This section contains information about available PhD supervisors and suggestions for PhD thesis projects. Please note that there are three separate announcements of PhD student positions, one for each of the three subjects mathematics, mathematical statistics and computational mathematics, respectively.

For further information about ongoing research at the department, please see the webpages of the research groups and the personal homepages of our researchers.

This section contains information about available PhD supervisors and suggestions for PhD thesis projects in mathematics.

Available PhD supervisors

Algebra, Geometry and Combinatorics: Gregory Arone, Alexander Berglund, Jonas Bergström, Rikard Bøgvad, Wushi Goldring, Samuel Lundqvist, Dan Petersen, Sven Raum, Boris Shapiro.

Analysis: Pavel Kurasov, Annemarie Luger, Salvador Rodríguez-López, Sven Raum, Jonathan Rohleder, Alan Sola.

Logic: Peter LeFanu Lumsdaine.

Suggestions for PhD thesis projects

In the 2021 call with deadline April 23, we especially seek to recruit PhD students for the following three projects:

Mathematics - Goldring, Generation by groups (pdf) (178 Kb)

Mathematics - Kurasov, Quasicrystals and networks (pdf) (5602 Kb)

Mathematics - Lumsdaine, Homotopy type theory as a foundation for mathematics (pdf) (74 Kb)

Further project suggestions are listed below

Mathematics - Berglund, Topics in algebraic topology (pdf) (12 Kb)

Mathematics - Bergström, Moduli spaces, varieties over finite fields, Galois representations (pdf) (63 Kb)

Mathematics - Lundqvist, Topics in (computational) commutative algebra (pdf) (161 Kb)

Mathematics - Raum, Operator algebras and group theory (pdf) (12 Kb)

Mathematics - Rohleder, Spectral properties of differential operators on domains and graphs (pdf) (27 Kb)

When you apply for a PhD student position in mathematical statistics, you must choose one of the projects suggested in the announcement.

Mathematical statistics - Lindensjö, Stochastic control - with applications to finance (pdf) (347 Kb)

Mathematical statistics - Lindskog, Valuation and decision making in insurance (pdf) (66 Kb)

When you apply for a PhD student position in mathematical statistics, you must choose one of the projects suggested in the announcement.

Computational Mathematics - Arvestad and Li, project descriptions (pdf) (38 Kb)

Study plans

The study plan describes the content of the PhD program and contains information about admission and eligibility. The individual study plan, which is created at the start of the program, contains specifications such as the choice of courses and the research plan.

Information for PhD students from the Faculty of Science
Handbook for postgraduate students from the Swedish National Agency for Higher Education

If you have any questions please contact the Directors of PhD Studies. You can find their contact details at the bottom of the page.

PhD students' council

The PhD students at the Department of Mathematics have a council (doktorandrådet) which looks after their interests and has a representative on the department board.

The council is headed by the following PhD students:

Chairman: Måns Karlsson
Secretary: Erik Thorsén
Treasurer: Hadrien Espic


Preparing for thesis defence (PhD and Licentiate)

Before the defence of the doctoral dissertation some formal procedures have to be dealt with.

Stockholm University information about PhD defence
Guidelines from the Faculty of Science

These documents contain practical information specifically for the Department of Mathematics.

Checklist for PhD thesis defense (pdf) (36 Kb)
Checklist for licentiate thesis presentation (pdf) (112 Kb)

See also the following guidelines for information on how the PhD defence is conducted in Sweden.

Guidelines for opponents (pdf) (16 Kb)


PhD courses

The planned PhD-Courses in mathematics, mathematical statistics and computational mathematics, during the academic year 2020/2021, can be seen here.

Mathematics Autumn 2020 Mathematics Spring 2021
Modular forms, Lilian Matthiesen, KTH Combinatorial and Algebraic Statistics, Liam Solus, KTH
Geometric function theory, Alan Sola, SU, and Fredrik Viklund, KTH Geometric group theory, Sven Raum, SU
Random Matrices, Kurt Johansson, KTH Indefiniteness, Annemarie Luger, SU
Tropical Combinatorics and Geometry (reading course), Johannes Hofscheier, Nottingham, and Katharina Jochemko, KTH  
Mixed Shimura varieties and other advanced topics about families of mixed Hodge structures (reading course), Wushi Goldring, SU  

 

Mathematical statistics Autumn 2020 Mathematical statistics Spring 2021
Networks and epidemics, Tom Britton, Mia Deijfen, Pieter Trapman, SU Soft skills for mathematicians, Tom Britton, SU
Probability theory, Guo Jhen Wu, KTH  

 

Computational Mathematics Autumn 2020 Computational Mathematics Spring 2021
TBA TBA

Academic Year 2019/20

Academic Year 2018/19

Academic Year 2017/18

  • Algebraic Groups, Wushi Goldring, SU Autumn
  • Introduction to Sectorial Operators, Jonathan Rohleder, SU Autumn
  • Topics in Analysis, Danijela Damianovic and Henrik Shahgholian, KTH Autumn
  • Constructive and Computational Mathematics, Peter LeFanu Lumsdaine, SU Spring
  • Geometric Function Theory, Alan Sola (SU) and Fredrik Viklund (KTH), Spring
  • Polynomial Functors in Algebra and Topology, Greg Arone, SU Spring
  • Riemann-Hilbert Methods in Asymptotic Analysis, Maurice Duits, KTH Spring

Academic Year 2016/17

Academic Year 2015/16

Academic Year 2014/15

Academic Year 2013/14

Spring 2000 to spring 2013

Courses given between the spring 2000 and the spring 2013 can be found on the Swedish version of this page.

Academic Year 2019/20

  • Data-driven statistical modelling with optimisation, Tobias Rydén, SU, Autumn 2019
  • Mathematics education at university level, Torbjörn Tambour, SU, Autumn 2019
  • Stochastic finance in discrete time, Filip Lindskog, SU, Autumn 2019
  • Advanced probability, Henrik Hult, KTH, Autumn 2019
  • Unsupervised learning, Chun-Biu Li, SU, Spring 2020

Academic Year 2018/19

  • Optimal Stochastic Control, Kristoffer Lindensjö, SU Autumn 2018
  • Probability Theory, Jimmy Olsson, KTH Autumn 2018
  • Topics in Discrete Probability, Timo Hirscher, SU Spring 2019
  • Computational Methods for Stochastic Differential Equations, Mattias Sandberg och Anders Szepesy, KTH Spring 2019
  • Computational Methods for Stochastic Differential Equations, Mattias Sandberg och Anders Szepesy, KTH Spring 2019
  • Soft Skills for Mathematicians, Tom Britton, SU
  • Causal Inference, Timo Koski, KTH

Academic Year 2011/12

  • Statistical Constultancy Methodology, Rolf Sundberg, Autumn
  • Computer-intensive Statistical Methods, Tom Britton, Alexander Ploner and Niclas Noren, Spring
  • Probability Theory IV, Dmitrii Silvestrov, Spring
  • Statistical Models, Rolf Sundberg, Spring

Academic Year 2010/11

  • Statistical Constultancy Methodology, Rolf Sundberg, Autumn
  • Standastic Processes III, Pieter Trapman, Autumn
  • Writing and Presenting Mathematical Papers, Tom Britton, Autumn
  • Statistical Models, Rolf Sundberg, Spring
  • Standastic Processes IV, Dmitrii Silvestrov, Spring

Academic Year 2009/10

  • Computer Intensive Statistical Methods, Britton et al, Autumn
  • Probability Theory IV, Dmitrii Silvestrov, Spring
  • Statistical Models, Rolf Sundberg, Spring

Academic Year 2008/09

  • Study Group in Random Networks, Britton, Autumn
  • Standastic Processes III, Hössjer, Autumn
  • Probability Theory, Gut, Uppsala University
  • Study Group in Phylogenetics and Comparative Genomics: Bio, Maths, Stats and Algorithms, Britton

Academic Year 2007/08

  • Probability Theory, Hössjer, Autumn
  • Statistical Methods of Population Genetics and Gene Mapping, Palmgren and Hössjer, Spring
  • Writing and Presenting Mathematics/Statistics, Britton, Spring

Academic Year 2006/07

  • Large Deviations, Martin-Löf, Autumn
  • Inference for Standastic Processes, Svensson, Spring
  • Likelihood Based Inference, Pawitan, KI
  • Random Graphs (Study Circle), Britton

Academic Year 2005/06

  • Standastic Methods of Population Genetics, Hössjer, Autumn

Academic Year 2004/05

  • Statistical Theory for Exponential Families, Sundberg
  • Statistical Genetics and Bioinformatics (Seminar Series), Palmgren
  • Markov Population Models, Martin-Löf
  • Statistical Consulting Methodology, Sundberg
  • Probabilistic Properties of DeSemesteristic Systems, Tyrcha
  • Statistics for Microarrays, Sundberg

Academic Year 2003/04

  • Standastic Epidemic Models and Their Statistical Analysis, Britton
  • Probability Theory, Gut, Uppsala University
  • Statistical Modeling and Inference using Likelihood, Pawitan, KI

Academic Year 2002/03

  • Statistical Genomics, Greenwood
  • Statistical Methods in Molecular Medicine and Genetic Epidemiology, Palmgren

Academic Year 2001/02

  • Att skriva matematisk statistik, Svensson
  • Statistisk inferensteori

Academic Year 2019/20

Contact

Director of studies for the PhD programme in mathematics
Director of studies for the PhD programme in mathematical statistics
Director of studies for the PhD programme in computational mathematics

Search among our courses and programmes