APEXMaths
APEX Maths 2025
APEX Maths 2025 takes place in Reșița, Romania, between July 27th and August 16th
We are no longer accepting applications for this camp.
- July 27, 2025 - August 16, 2025
- Reșița, România
APEX-Maths is an intensive and immersive 3-weeks-long summer residential program offering a unique opportunity to get a taste of mathematical research and scientific discovery. The participants – a maximum number of 40 – will be able to experience the world of research from within, as they will explore new mathematical concepts under the guidance of top internationally recognized university professors (Olivier Schiffmann, Alexis Bouthier and Siarhei Finski) and PhD students. A high-level training in rigorous thought and abstract reasoning is an increasingly vital asset to thrive in today’s world, regardless of the type of career you aim for. APEX’s goal is to provide such training as well as to create a community of young scientists highly passionate for mathematics. We cultivate and encourage excellence.
The language of communication is English.
APEX Maths 2025 invited lecturers
- Olivier Schiffmann, CNRS, Université Paris-Saclay and IMAR.
- Alexis Bouthier, Paris-Sorbonne University;
- Siarhei Finski, Ecole Polytechnique.
Algebra(ic) Geometry
The program invites the participants to explore the geometry of curves, surfaces, etc. defined by polynomial equations and to discover how their properties may be studied and understood using algebra. A typical question which we’ll try to answer: how many times should two curves in the plane intersect (depending on the degrees of the polynomials defining these equations)? And how many times should three surfaces in 3-space intersect?
Amazingly, one can reverse the point of view and study algebraic properties of rings and algebras…using geometry!
More precisely, the following topics will be discussed:
- Polynomials in two variables and curves in the plane
- Polynomial rings
- Ideals (radical, prime, maximal,…) and algebraic varieties
- Systems of polynomial equations
- Projective spaces (or how to add just the right amount of points at infinity)
- Bezout’s theorem on plane curves
The program is designed for advanced participants; prerequisites include: complex numbers, rings and algebras, polynomials; some familiarity with linear algebra.
Please download the problems file below and send us your solutions before June 22nd, 2025.
The city of Reşiţa is in the Western part of Romania, about 80 km away from Timişoara (European capital of culture in 2023 – details here).
Accommodation is provided in the facilities of the University Centre of Babeș-Bolyai University in Reșița. The dormitory has rooms with two beds, specific furniture (bathroom in the room), spaces for preparing and serving meals and laundry.
It is not our goal to do so. Of course, participation in APEX-maths will give you advantages if you decide to participate in maths competitions, but our goal is to provide you with an immersive experience in the real life of high-level mathematicians, that goes well beyond increasing your capacity to solve Olympiads-type problems. Participation at APEX-maths will surely be an advantage if you apply to top universities.
Indicative price at your charge is 1500 euros for the entire APEX-Maths camp. This may slightly vary until final booking day. This is made possible by very generous sponsoring from the City of Reşiţa, Foundation Dacia for Romania, Banca Aqua Carpatica, Banca Transilvania; the real cost of the event being in fact much higher, is generously covered by our sponsors. IMAR is responsible for the scientific aspects of the program, while InformART is responsible for all the logistics, including payment details.
If you are selected the price includes: the Maths courses and seminars, accommodation for the entire period of APEX-Maths camp (newly refurbished rooms of 2 at the Reşiţa campus of the Babeş-Bolyai University), three meals a day, free bottled water, free internet access on the campus, some free time activities.
Things not included in the price: travel costs to and from your home location to Timişoara, accompanying person costs (travel, accommodation, subsistence, field trips etc. for accompanying person) and minor traveller costs, travel insurance, laundry costs, extra spendings.
Can the students be accompanied by the parents?
Yes. However, the students must be housed together with the entire group, since one of the goals of the APEX-Maths camp is to create a community of young mathematicians. The parents should make their own arrangements (we can suggest Travel Agencies which can assist you).
Can I contact my child at any time?
Yes. Mobile phones will be available anytime, except for the two hours of daily lectures. There will be an emergency number as well. At all times there will be at least two experienced staff with the group. Medical assistance is also available on the site, should there be an emergency.
Once the participation is confirmed, the participant/legal representative of the participant will receive a set of documents including the contracts, payment details, camp regulations, full detailed programme, participant personal file, GDPR agreement as well as suggestions for travel insurance etc. The camp will follow all the strict requirements of safety imposed by Romanian legislation. Transportation and tourist activities will be organised according to highest safety standards provided by Romanian legislation only by authorised entities.