Summer School in Mathematics

Institute of Mathematics, Eötvös Loránd University, Budapest, Hungary
July 10 – July 14, 2023


Important Dates

Application for
financial support:

May 21, 2023
Deadline for paying
the reduced fee:

June 15, 2023
Registration deadline:
July 2, 2023
Summer school:
July 10 – July 14, 2023
Summer School 2023

The Institute of Mathematics at Eötvös Loránd University is pleased to announce its regular one week long summer school in mathematics titled

Paradoxical decompositions, fractals and dynamics

The ancient problem of squaring the circle came to a conlusion by the work of Lindemann at the end of the 19th century when he proved that π is transcendental: this result implied that it is impossible — by using compass and straightedge only — to construct a square with the same area as a circle with a radius of unit length. However, a few decades later the emergence of paradoxical decompositions — the most famous example of which is the Banach–Tarski paradox cutting a ball into a finite number of pieces and rearranging the pieces so that they form two balls isometric to the original one — the problem of squaring the circle was reopened: in 1925 Alfred Tarski posed the question whether the circle could be decomposed into a finite number of pieces and then the pieces rearranged so that they form a square. Although the question in the classical sense — i.e. cutting the circle by scissors — was again proved to be impossible, a surprising result by Miklós Laczkovich in 1990 showed that by allowing more general shapes as pieces the answer is “yes”. In recent years a lot of work was done to find decompositions with nicer and fewer number of pieces (the original, non-constructive proof of Laczkovich dealt with an astounding number of 1050 non-measurable pieces). Such nicer deocompositions were presented for example by András Máthé, Jonathan A. Noel and Oleg Pikhurko. (A visualization of such a decomposition can be seen above.)

The summer school will offer a first hand introduction into this exciting field but also to many other wonders of analysis, like theory of fractals, measure theory, ergodic theory and dynamical systems. Lecture series will be supplemented by tutorials and problem solving sessions.

The minicourses will be aimed at advanced undergraduate/starting graduate students but interested PhD students are also welcome. We expect that participants would have a solid background in basic undergarduate mathematics but we do not assume preliminary acquaintance with the special topics of the school. We also plan to give exercises/problems which can be discussed in the afternoon sessions.

The lecturers are professors at Eötvös Loránd University (ELTE) in Budapest, of Alfréd Rényi Institute of Mathematics in Budapest or of University of Warwick (UK). The lectures will take place at the Lágymányos Campus of Eötvös Loránd University (1117 Budapest, Pázmány Péter sétány 1/c, Hungary).

The lecturers are:

  • Zoltán Buczolich (ELTE)
  • Márton Elekes (Rényi / ELTE)
  • Tamás Keleti (ELTE)
  • Miklós Laczkovich (ELTE)
  • András Máthé (Warwick)
  • Zoltán Vidnyánszky (ELTE)

We encourage participation of advanced BSc students of mathematics as well as MSc and PhD students, interested in this dynamic and highly appreciated area of mathematics.

Also, if you are interested in a true European metropolitan city with a vivid cultural life, then Budapest is an obvious choice.

Cost and Deadlines

The fee for participation in the Summer School is 120 euros (135 USD) if paid by June 15, and 170 euros (190 USD) afterwards. The fee covers printed course material and refreshments.

Please note that the university is not able to refund the registration fee in case of cancellation.

Deadline of application for financial support: May 21, 2023

Registration (and payment of the fee) begins on April 14, 2023 and will be closed on July 2, 2023 (with the possibility of paying the higher fee during the event). See the payment information.

First day of classes: July 10, 2023 (9 AM)

Last day of classes: July 14, 2023 (early afternoon)

Cancellation policy

  • Please, note that due to university restrictions we are unable to send back the transferred registration fee even if you have to cancel your participation for medical reasons or for travel restrictions affecting your entrance to Hungary. However in this case you may use your fee to cover the registration cost of another (registered or unregistered) participant. Please, let us know if you would like to ask for such an arrangement.
  • The organizers would like to reserve the right to cancel the event if the external circumstances would warrant such measures. In this exceptional case we will try to refund the participants by sending back the registration fee (within a month). However we will ask each participant to apply for such remibursement individually and let us know the account number to which the money should be sent back. — If cancellation seems to be unavoidable, we would inform participants about this by June 10, 2023.

Financial support

Financial support — made possible by the donation of the Alfréd Rényi Institute of Mathematics — will be available for the participants in the form of reduction or complete waiver of the registration fee. Please, send a letter before May 21, 2023 to the organizers. The letter should contain:

  • a short CV, containing among others your study data
  • a recommendation letter

Please, send the letter before May 21, 2023. A decision based on academic excellence and financial circumstances will be made by the organizers before May 28, 2023. Due to the limited amount of available resources we encourage everyone to apply for external funding, too.




Address of the university: 1117 Budapest, Pázmány Péter sétány 1/C
Lectures will be held in room 3-219, in the Southern Building of ELTE.