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
Eligibility and selection for PhD studies in 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, BolzanoWeierstrass, 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.
Eligibility and selection for PhD studies in mathematical statistics
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 birthdeath 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.
Eligibility and selection for PhD studies in computational mathematics
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.
PhD thesis projects in mathematics
This section contains information about available PhD supervisors and suggestions for PhD thesis projects in mathematics.
Available PhD supervisors
Algebra and Geometry: Gregory Arone, Alexander Berglund, Jonas Bergström, Rikard Bøgvad, Wushi Goldring, Samuel Lundqvist, Dan Petersen, Boris Shapiro, Sofia Tirabassi.
Analysis: Pavel Kurasov, Annemarie Luger, Salvador RodríguezLópez, Jonathan Rohleder, Alan Sola.
Logic: Peter LeFanu Lumsdaine.
Suggestions for PhD thesis projects
In the 2023 call we would welcome applications for the following two projects in particular:
Mathematics  Kurasov, Spectral geometry and zetafunctions: analysis on graphs and fractals (pdf) (89 Kb)
Mathematics  Rohleder, Critical points of eigenfunctions for elliptic differential operators (pdf) (44 Kb)
Some other suggestions for projects are:
Mathematics  Arone, Algebraic topology and related fields (pdf) (115 Kb)
Mathematics  Berglund, Topics in algebraic topology (pdf) (81 Kb)
Mathematics  Goldring, Group theory, arithmetic geometry and representation theory (pdf) (73 Kb)
Mathematics  Luger, Measures for analytic functions in several variables (pdf) (168 Kb)
Mathematics  Tirabassi, Topics in Algebraic Geometry (pdf) (38 Kb)
Mathematical statistics  Ahlberg, Random spatial processes (pdf) (489 Kb)
Participants interested in this last project are encouraged to apply for it via both the PhD program in mathematics and the PhD program in mathematical statistics.
PhD thesis projects in mathematical statistics
When you apply for a PhD student position in mathematical statistics, you must choose one of the projects suggested in the announcement.
Mathematical statistics  Ahlberg, Random spatial processes (pdf) (489 Kb)
Participants interested in this project are encouraged to apply for it via both the PhD program in mathematics and the PhD program in mathematical statistics.
PhD thesis projects in computational mathematics
When you apply for a PhD student position in computational mathematics, you must choose one of the projects suggested in the announcement.
Computational Mathematics  Hellmuth, Computational and mathematical studies of ancient DNA (pdf) (29 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.
Study plans  files
Individual study plan
Individual Study Plan (odt) (279 Kb)
ISP appendix (docx) (77 Kb)
ISP attachment regarding the effects of the Covid19 pandemic on the PhD education (docx) (14 Kb)
General study plans, current
Study plan for PhD studies in mathematics, starting after 20170701, Swedish (pdf) (247 Kb)
Study plan for PhD studies in mathematical statistics, starting after 20230406 (pdf) (267 Kb)
Study plan for PhD studies in computational mathematics (pdf) (165 Kb)
General study plans, older versions
Study plan for PhD studies in mathematics, starting before 20170701 (pdf) (212 Kb)
Study plan for PhD studies in mathematical statistics, starting before 20230406 (pdf) (414 Kb)
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: Josefien Kuijper
Secretary and treasurer: Vilhelm Niklasson
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) (136 Kb)
Checklist for licentiate thesis presentation (pdf) (119 Kb)
See also the following guidelines for information on how the PhD defence is conducted in Sweden.
Guidelines for opponents (pdf) (56 Kb)
PhD courses
The planned PhDCourses 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 2023 
Mathematics Spring 2024 

Gaussian fields and random surfaces 

Differential geometry, Klaus Kröncke (KTH) 
Stacks, David Rydh (KTH) 
Quasiconformal maps in the plane, Alan Sola (SU) and Fredrik Viklund (KTH) Analysis Course homepage 
Differential topology, Greg Arone (SU) Geometry 
DModules and holonomic functions, AnnaLaura Sattelberger (KTH) Algebra Course homepage 
Mathematical methods of quantum mechanics, Pavel Kurasov (SU) Analysis 
Mathematical statistics Autumn 2023  Mathematical statistics Spring 2024 

TBA  TBA 
Computational Mathematics Autumn 2023  Computational Mathematics Spring 2024 

TBA 
TBA 
Previous years' PhD courses in mathematics
Academic Year 2022/2023
 Constructions in dynamical systems, Bjerklöv and Saprykina, KTH, Autumn 2022
 Expander graphs, Raum, SU, Autumn 2022
 Homotopy theory, Berglund and Petersen, SU, Autumn 2022
 Synthetic Spectra (reading course), Autumn 2022
 Abelian varieties, Tirabassi, SU, and Skjelnes, KTH, Spring 2023
 Classical analysis and its applications, Shahgholian and Damjanovic, KTH, Spring 2023
 Function spaces in complex analysis, Luger and RodriguezLopez, SU, Spring 2023
 Probabilistic number theory, Matthiesen, KTH, Spring 2023
Academic Year 2021/22
 Characteristic classes, Arone, SU, and Bauer, KTH, Autumn 2021
 Homotopical models for type theories, Lumsdaine and Mörtberg, SU, Autumn 2021
 Reading course: Complex Dynamics, Sola, SU, Autumn 2021
 Introduction to the Langlands program over number fields, Goldring, SU, Spring 2022
 Spectral theory of partial differential equations, Rohleder, SU, Spring 2022
 The AtiyahSinger index theorem, Dahl, KTH, Spring 2022
 Polytope Theory (7,5 credits), Svante Linusson, KTH, Spring 2022
Academic Year 2020/21
 Modular forms, Lilian Matthiesen, KTH, Autumn 2020
 Geometric function theory, Alan Sola, SU, and Fredrik Viklund, KTH, Autumn 2020
 Random Matrices, Kurt Johansson, KTH, Autumn 2020
 Tropical Combinatorics and Geometry (reading course), Johannes Hofscheier, Nottingham, and Katharina Jochemko, KTH, Autumn 2020
 Mixed Shimura varieties and other advanced topics about families of mixed Hodge structures (reading course), Wushi Goldring, SU, Autumn 2020
 Combinatorial and Algebraic Statistics, Liam Solus, KTH, Spring 2021
 Geometric group theory, Sven Raum, SU, Spring 2021
 Indefiniteness, Annemarie Luger, SU, Spring 2021
Academic Year 2019/20
 Spectral theory of quantum graphs and inverse problems, Pavel Kurasov, SU, Autumn 2019
 Infinity categories, Peter LeFanu Lumsdaine, SU, Autumn 2019
 Mathematics education at university level, Torbjörn Tambour, SU, Autumn 2019
 Reading seminar on the Kervaire invariant one problem (Reading course), Gregory Arone, SU, Autumn 2019
 Introduction to operator algebras, Sven Raum, SU, Spring 2020
 Geometric measure theory, John Andersson, KTH, Spring 2020
 Complex algebraic geometry, David Rydh, KTH, Spring 2020
Academic Year 2018/19
 Theory of distributions, Pavel Kurasov, SU Autumn 2018.
 SemiRiemannian geometry (reading course), Mattias Dahl, KTH Autumn 2018
 Partial Differential Equations, John Andersson, KTH Autumn 2018
 Fourier analysis methods for PDEs, Salvador RodriguezLopez och Odysseas Bakas, SU Spring 2019
 Characteristic classes, Tilman Bauer, KTH Spring 2019
 Tannakian categories, Wushi Goldring och Andreas Holmström, SU Spring 2019
 Advanced Topics in Proof Theory and the Foundations of Mathematics, Erik Palmgren, SU from Autumn 2018 to Spring 2019
 CohenMacaulay Complexes (minicourse), Afshin Goodarzi, KTH, Spring 2019
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
 RiemannHilbert Methods in Asymptotic Analysis, Maurice Duits, KTH Spring
Academic Year 2016/17
 Computational Clgebraic Geometry (Reading course), Mats Boij, (KTH) and Samuel Lundqvist (SU), Autumn
 Constructions in Dynamical Systems (Reading course), Kristian Bjerklöv and Maria Saprykina, KTH Autumn
 Differential Geometry, Mattias Dahl and Hans Ringström, KTH Autumn
 Mathematical Analysis For All!, John Andersson, KTH Autumn
 Real and Complex Analysis (Reading course), 15hp, Fredrik Viklund, KTH Full year
 Algebraic Topology, Gregory Arone (SU), Tilman Bauer and Wojciech Chacholski (KTH), Spring
 Classical Combinatorics, Linusson and Brändén, KTH Spring
 An Introduction to Pseudodifferential Operators, RodriguezLopez, SU Spring
 Matematical Didactics, Tambour, SU Spring
 Mathematical Physics. (Topics in Mathematics IV), Lundholm, KTH Spring
 Realizability: Computational Interpretations of Logic, Erik Palmgren, SU Spring
 Topics in Applied Algebraic Geometry, Dickenstein and Di Rocco, KTH Spring
Academic Year 2015/16
 Commutative Algebra, Roy Skjelnes, Autumn
 Cluster Algebras, Michael Shapiro, Autumn
 Elliptic Partial Differential Equations and Harmonic Function Theory (Reading course), Jonatan Lenells and Henrik Shahgolian, Autumn
 Random Matrices, Maurice Duits and Kurt Johansson, Autumn
 Model Theory, Erik Palmgren, Autumn
 Algebraic and Enumerative Combinatorics, Petter Bränden, Spring
 Clifford Algebras, Douglas Lundholm and Lars Svensson, Spring
 Étale Cohomology, Jonas Bergström and David Rydh, Spring
 Spectral Theory for Quantum Graphs, Pavel Kurasov, Spring
 Several Complex Variables (Reading course), Håkan Hedenmalm, Spring
 Operads in Algebraic Topology, Alexander Berglund and Stephanie Ziegenhagen, Spring
Academic Year 2014/15
 Infinitycategories and Homotopy Type Theory, Ph. Hackney and P. Lumsdaine, Autumn
 Riemann Surface, Analytic and Algebraic Aspects, J. E. Björk and B. Shapiro, Autumn
 Gröbner Bases, J. Backelin, Spring
 Spectra of (nonselfadjoint) Matrices and Operators, A. Luger and Christiane Tretter (Bern), Spring
Academic Year 2013/14
 Commutative Algebra II, Christian Gottlieb, SU Autumn
 Type Theory, Erik Palmgren, SU Autumn
 Fourieranalys, KTH Autumn
 Analysis on Manifolds, Olga Rossi, Spring
 Spectral Theory for Quantum Graphs, Pavel Kurasov, Spring
 Cathegory theory, Spring
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.
Previous years' PhD courses in mathematical statistics
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, ChunBiu 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
 Datadriven 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, ChunBiu 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
 Computerintensive 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, MartinLöf, 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, MartinLöf
 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
Previous years' PhD courses in computational mathematics
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, ChunBiu Li, SU, Autumn 2021 and Spring 2022
 Computational Biology, Lars Arvestad and Marc Hellmuth, SU, Spring 2022
Academic Year 2019/20
 Datadriven statistical modelling with optimisation, Tobias Rydén, SU, Autumn 2019
 Mathematics education at university level, Torbjörn Tambour, SU, Autumn 2019
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.
Contact
Last updated: September 6, 2023
Source: Department of Mathematics