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.

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 Rodríguez-López, Jonathan Rohleder, Olof Sisask, Alan Sola.

Logic: Peter LeFanu Lumsdaine.

Suggestions for PhD thesis projects

In the 2024 call we would welcome applications for the following four projects in particular:

Mathematics - Lundqvist, Powers of general linear forms (pdf) (196 Kb)

Mathematics - Petersen, Moduli, topology, and arithmetic (pdf) (56 Kb)

Mathematics - Sisask, Combinatorics of addition, number theory, harmonic analysis, probability (pdf) (172 Kb)

Mathematics - Tirabassi, Geometry of the Albanese Map (pdf) (113 Kb)

Some other suggestions for projects are:

Mathematics - Berglund, Topics in algebraic topology (pdf) (81 Kb)

Mathematics - Bergström, Arithmetic geometry: Moduli spaces and Galois representations (pdf) (34 Kb)

Mathematics - Goldring, Group theory, arithmetic geometry and representation theory (pdf) (81 Kb)

Mathematics - Luger, Measures for analytic functions in several variables (pdf) (168 Kb)

Mathematics - Rohleder, Spectral theory of differential operators in mathematical physics (pdf) (61 Kb)

Mathematics - Sola, Topics in complex analysis, harmonic analysis, and complex geometry (pdf) (212 Kb)

This section contains information about available PhD supervisors and PhD thesis projects in mathematical statistics in the 2024 call.

PhD supervisors

Daniel Ahlberg, Tom Britton, Johannes Heiny, Kristofer Lindensjö, Mathias Lindholm.

PhD projects

Ahlberg: Random processes with reinforcement (332 Kb)

Britton: Data intensive statistical modelling of infectious disease outbreaks (79 Kb)

Heiny: Random matrix structures and high-dimensional extremes (174 Kb)

Heiny: Deep learning and high-dimensional statistics (147 Kb)

Heiny: Statistical learning from the perspectives of random matrix theory (42 Kb)

Lindensjö: Stochastic control and optimal stopping for game theory (343 Kb)

Lindholm: Insurance mathematics (16 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 - Hellmuth, Computational and mathematical studies of ancient DNA (pdf) (29 Kb)

Individual study plan

Individual Study Plan (odt) (279 Kb)
ISP appendix (docx) (77 Kb)
ISP attachment regarding the effects of the Covid-19 pandemic on the PhD education (docx) (14 Kb)

General study plans, current

Study plan for PhD studies in mathematics, starting after 2017-07-01, Swedish (pdf) (247 Kb)
Study plan for PhD studies in mathematical statistics, starting after 2023-04-06 (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 2017-07-01 (pdf) (212 Kb)
Study plan for PhD studies in mathematical statistics, starting before 2023-04-06 (pdf) (414 Kb)

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 Rodriguez-Lopez, 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 Atiyah-Singer 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.
• Semi-Riemannian geometry (reading course), Mattias Dahl, KTH Autumn 2018
• Partial Differential Equations, John Andersson, KTH Autumn 2018
• Fourier analysis methods for PDEs, Salvador Rodriguez-Lopez 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
• Cohen-Macaulay Complexes (mini-course), 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
• Riemann-Hilbert 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, Rodriguez-Lopez, 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

• Infinity-categories 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 (non-selfadjoint) 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.

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

• Data-driven statistical modelling with optimisation, Tobias Rydén, SU, Autumn 2019
• Mathematics education at university level, Torbjörn Tambour, SU, Autumn 2019