Summer School in Mathematics

Institute of Mathematics, Eötvös Loránd University, Budapest, Hungary

June 27 - July 1 2022



Important Dates

Application for
financial support:

May 22, 2022.

Registration deadline:
June 15

Summer school:
June 27 - July 1

Summer School 2022

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

"Topics in number theory:
ancient problems, recent results"

Number theory is one of the most ancient, yet in modern times also very active areas of mathematics (with over 2000 submissions per year to arxiv!). German mathematician Carl Friedrich Gauss said "Mathematics is the queen of the sciences – and number theory is the queen of mathematics." One of the beauties of number theory is that there are many problems which can be stated in an elementary way but the solution is very deep or even still open. As a consequence the methods used to tackle such problems are diverse making number theory related to almost all areas of mathematics. In this summer school we intend to introduce the participants to many of these various techniques.

The five minicourses will be aimed at advanced undergraduate/starting graduate students. A first course in complex analysis and abstract algebra would certainly be useful 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) and the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences. The lectures will take place at the Lágymányos Campus of Eötvös Loránd University (1117 Budapest, Pázmány Péter sétány 1/c, Hungary).

The titles of the minicourses (change in the program!):

Róbert Freud (ELTE): A problem of Erdős and two proofs from "The Book" (NEW LECTURE!)
Gyula Károlyi (ELTE / Rényi): The polynomial method in combinatorial arithmetic CANCELLED!
Péter Maga (Rényi): Distribution of primes in arithmetic progressions
János Pintz (Rényi): Small and bounded gaps between primes
Árpád Tóth (ELTE): Introduction to ellpitic curves
Gergely Zábrádi (ELTE): p-adic methods in arithmetic

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 until June 15, and 170 EUR (190 USD) if payed later than June 15. 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 22

Registration (and payment of the fee) begins: March 1 and will be closed: June 26 See the payment information.

First day of classes: June 27

Last day of classes: July 1

Cancellation policy
1. As mentioned earlier, 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 participant. Please, let us know if you would like to ask for such an arrangement.
2. The organizers would like to reserve the right to cancel the event if the pandemic situation would warrant such measures. In this case we will try to refund the participants by sending back the registration fee (within a month). However we will kindly 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 May 31.
3. Please, follow closely the announcements about travel restrictions both in your country and in Hungary.

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 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 22, 2022. A decisison based on academic excellence and financial circumstances will be made by the organizers before May 29, 2022. Due to the limited amount of available resources we encourage everyone to apply for external funding, too.


Here is the tentative program of the summerschool (please, note the change in the program):
Schedule 2022



List of minicourses

Róbert Freud (ELTE): A problem of Erdős and two proofs from "The Book" (NEW LECTURE)

Gyula Károlyi (ELTE): The polynomial method in combinatorial arithmetic (CANCELLED)

Péter Maga (Rényi): Distribution of primes in arithmetic progressions

János Pintz (Rényi): Small and bounded gaps between primes

Árpád Tóth (ELTE): Introduction to elliptic curves

Gergely Zábrádi (ELTE): p-adic methods in arithmetic


Address of the university: 1117 Budapest, Pázmány Péter sétány 1/C
Lectures will be held in room 3-218, in the Southern Building of ELTE.

For more local information see the Latest circular letter in the menu.

Lecture notes

The volume containing list of participants and lecture notes is now available.