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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 and Geometry: Per Alexandersson, Gregory Arone, Alexander Berglund, Jonas Bergström, Rikard Bøgvad, Wushi Goldring, Samuel Lundqvist, Dan Petersen, Boris Shapiro, Sofia Tirabassi.

Analysis: Pavel Kurasov, Annemarie Luger, Salvador Rodríguez-López, Oliver Lindblad Petersen, Jonathan Rohleder, Olof Sisask, Alan Sola.

Logic: Peter LeFanu Lumsdaine (see also PhD thesis projects in computational mathematics for supervisors in logic).

Suggestions for PhD thesis projects

In the 2025 call we would welcome applications for the following seven projects in particular:

Mathematics - Berglund, Topics in algebraic topology (pdf) pdf, 188.8 kB. (188 Kb)

Mathematics - Bergström, Arithmetic geometry (pdf) pdf, 36.8 kB. (36 Kb)

Mathematics - de Courcy-Ireland, Topics in Diophantine Analysis (pdf) pdf, 57.1 kB. (57 Kb)

Mathematics - Goldring, Group theory, arithmetic geometry and representation theory (pdf) pdf, 34.6 kB. (34 Kb)

Mathematics - Kurasov, Analysis and geometry: crystalline structures (pdf) pdf, 248 kB. (247 Kb)

Mathematics - Dan Petersen, Topology of moduli spaces (pdf) pdf, 77.5 kB. (77 Kb)

Mathematics - Oliver Petersen, Geometric analysis with applications to general relativity (pdf) pdf, 92.7 kB. (92 Kb)

Some other suggestions for projects are:

Mathematics - Alexandersson, Enumeratics combinatorics and symmetric functions (pdf) pdf, 272.7 kB. (272 Kb)

Mathematics - Rohleder, Spectral theory of partial differential equations (pdf) pdf, 47.6 kB. (47 Kb)

Mathematics - Sola, Topics in complex analysis, harmonic analysis, and complex geometry (pdf) pdf, 240.2 kB. (240 Kb)

This section contains information about available PhD supervisors and PhD thesis projects in mathematical statistics in the 2025 call.

PhD supervisors

Daniel Ahlberg, Johannes Heiny, Mathias Lindholm.

PhD projects

Mathematical statistics - Ahlberg, Discrete probability theory (pdf) pdf, 323 kB. (322 Kb)

Mathematical statistics - Heiny, Random matrices, high-dimensional statistics and beyond (pdf) pdf, 167.7 kB. (167 Kb)

Mathematical statistics - Lindholm, Insurance mathematics - AI tools in health insurance (pdf) pdf, 59.4 kB. (59 Kb)

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

Computational Mathematics - project descriptions spring 2025 (pdf) pdf, 58.8 kB. (58 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:

Chair: Taariq Nazar
Vice chair: Benedetta Andina
Secretary: Alice Brolin

You can reach the PhD council at phdcouncil@math.su.se

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, 155.6 kB.
Checklist for licentiate thesis presentation (pdf) pdf, 80.7 kB.
Routines for half-time check for PhD students (pdf)

In this calendar you can see upcoming PhD and licentiate defences at SU and KTH.

SU/KTH calendar for PhD and licentiate thesis defences

See also the department's informal guidelines below, for information on how the PhD defence is conducted.

Guidelines for opponents (pdf) pdf, 56.6 kB. (56 Kb)

PhD courses

The planned PhD-Courses in mathematics, mathematical statistics and computational mathematics, during the academic year 2023/2024, can be seen here. Further down you can find courses from previous years.

Mathematics Autumn 2025Mathematics Spring 2026

Additive combinatorics, Olof Sisask (SU)
Analysis/Algebra 

Access the course website

Algebraic groups, Marion Jeannin (SU)
Algebra/Geometry

Classical analysis, Danijela Damjanovic (KTH) & Henrik Shahgholian (KTH)
Analysis
 

Derived categories, David Rydh (KTH) & Sofia Tirabassi (SU)
Algebra/Geometry

Homotopy theory, Alexander Berglund (SU) &  Dan Petersen (SU)
Algebra/Geometry

Access the course website

Evolution equations, Jonathan Rohleder (SU)
Analysis

  
Mathematical statistics Autumn 2025Mathematical statistics Spring 2026

Probability theory

Charlie Guera (KTH)

Theoretical statistics

Ola Hössjer (SU)

Malliavin calculus

Nacira Agram (KTH)

Deep Diffusion Models

Chun-Biu Li (SU)

Computational Mathematics Autumn 2025Computational Mathematics Spring 2026

TBA

TBA
  

Academic Year 2024/2025

Academic Year 2023/2024

Academic Year 2022/2023

Academic Year 2021/22

Academic Year 2020/21

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 2024/2025

  • Soft Skills (Tom Britton), Autumn 2024
  • Topics in network science and graph theory (Mia Deijfen, Marc hellmuth), Spring 2025

Academic Year 2023/2024

  • Stochastic theormodynamics, Chun-Biu Li, SU, Autumn 2023
  • Probability theory, Boualem Djehiche, KTH, Autumn 2023
  • Topics in probability and statistics, Mathias Lindholm/Johannes Heiny/Daniel Ahlberg, SU, Spring 2024
  • Markov chains and processes, Boualem Djehiche, KTH, Spring 2024

Academic Year 2022/2023

  • Topics in stochastic control and stopping, Kristoffer Lindensjö, SU, Autumn 2022
  • Networks and epidemics, Mia Deijfen/Tom Britton, SU, Autumn 2022
  • Brownian motion and stochastic differential equations, Kristoffer Lindensjö, SU, Autumn 2022
  • Advanced causal inference, Arvid Sjölander, KI, Autumn 2022
  • Epidemiological theory from a statistical perspective, KI, Autumn 2022
  • Computational methods for stochstic differential equations, Mathias Sandberg/Anders Szepessy, KTH, Spring 2023

Academic Year 2021/22

  • Markov processes, Daniel Ahlberg, Autumn 2021
  • Deep learning, Chun-Biu Li, all year
  • Statistical inference, KTH, Spring 2022
  • Causal inference, Arvid Sjölander, KI, Autumn 2021

Academic Year 2020/21

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

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 2022/2023

  • Computer Science, Lars Arvestad, SU, Autumn 2022
  • Computational Biology, Marc Hellmuth, SU, Spring 2023
  • Categorical Logic, Ivan Di Liberti, SU, Spring 2023

Academic Year 2021/2022

  • Deep Understanding of the Information Processing in Depp Learning, Chun-Biu Li, SU, Autumn 2021 and Spring 2022
  • Computational Biology, Lars Arvestad and Marc Hellmuth, SU, Spring 2022

Academic Year 2019/20

Reading courses

In addition to the PhD courses that are planned on a yearly basis in coordination wih KTH, spontaneously organized activities such as reading courses can sometimes also yield course credits. In order for a reading course to yield course credits, here are necessary conditions:

  • There has to be a responsible teacher/examiner for the course.
  • A course plan (including a brief description, a rough timetable, examination form, and number of credits) should be approved by the director of PhD studies before the reading course starts.
  • The reading course should be announced (e.g. through the SMC calendar) before it starts, so that other interested PhD students at SU or KTH can join.

Last updated: 2025-11-26

Source: Department of Mathematics