Thursday at 15:00, in Room 102
Prof. László BABAI , (University of Chicago): Groups, graphs, matrices, avalanches: The Abelian Sandpile Model
Abstract: Originating in statistical physics and nearly simultaneously and independently introduced in algebraic graph theory and in theoretical computer science in the 1990s, the Abelian Sandpile Model associates a variety of structures with a diffusion process on finite graphs. The model gives rise to a remarkably rich theory which connects the fields of graph theory, stochastic processes, commutative semigroups and groups, matrices and determinants, lattices in n-dimensional space, algorithms, number theory, discrete dynamical syetems, and more.
After a general introduction based on joint work with my former graduate student Evelin Toumpakari, I will outline work I have done with then undergraduate Igor Gorodezky; the collaboration started at a summer REU.
Laci Babai is a professor of mathematics and computer science at the University of Chicago, co-founder and Board member of BSM. He is also an excellent lecturer, do not miss his lecture.
December 6 and 9
Friday and Thursday 15:00, at the Central European University (Zrinyi utca 14. 3. floor, room 310/A , Budapest, Hungary)
Peter Maga and Daniel Glasscock , CEU: Tao's Proof of Szemerédi's Theorem
Abstract: Theorem (Szemerédi 1975) Let k >= 1 be an integer and 0 < \delta <= 1. There exists an integer N(k,\delta) >= 1 such that if N >= N(k,\delta) and A \subset N has density at least \delta (i.e. |A|/|N| >= \delta), then A contains an arithmetic progression of length k.
Wednesday at 14:00, in the Ceremonial Hall of the Hungariana Academz of Sciences
Presentation of the 2010 János Bolyai International Mathematical Prize , followed by lectures of Yuri I. Manin, Bolyai Prize 2010 recepient and Stanislav Smirnov, Fileds Medal recepient (2010)
Abstract: For details, see the official invitation
Thursday at 16:30, at the Central European University (Zrinyi utca 14. 3. floor, room 310/A , Budapest, Hungary)
Prof. András Némethi, Central European University / Rényi Institute : Algebraic Plane Curves
Abstract: The study of algebraic curves is the oldest theory of mathematics, and maybe the most beautiful. Lines, circles, conics were already studied by the Greek mathematicians, later famous mathematicians (e.g. Pascal, Newton) developed the classical theory. The modern approach started with the Italian and German geometry (Hilbert). We will discuss some classical subjects too, and also some connections with knot theory (low dimensional topology) and algebra. We try to follow the historical developments by many-many pictures.
Thursday at 16:45, at Eotvos University, (Pazmany Peter setany
1/A - north building, "Északi tömb" - Marx Gyorgy Lecture Hall (room 0-87); see remark below)
Prof. József Pelikán, Eötvös University: The Thue-Morse sequence and its relatives
Abstract: The Thue-Morse sequence is one of the most famous binary sequences, with many remarkable properties. It pops up unexpectedly in many parts of mathematics. Other naturally defined sequences also show curious behaviour on the borderline of order and disorder. Besides the known results, several open problems will also be mentioned.
The time is 4:45pm, allowing all of you to reach the place.
You will have a chance to meet some of the faculty and math students of the Institute of Mathematics over there.
Friday at 16:45 (apprx.), at Bolyai Institute (Aradi vertanuk tere 1, Szeged, Hungary)
Prof. Miklós Maróti, Bolyai Institute, University of Szeged: The identities of the natural numbers
Abstract: We learn eleven identities of the positive integers in high school that involve addition, multiplication, exponentiation and the constant 1. Can the teacher find an identity that holds for all positive integers, but the students cannot prove it using these eleven identities? Can the teacher check if an identity given by the students is actually valid for all positive integers? We will answer these and related questions in this talk.
Thursday at 16:15, in Room 102
Having any problems in organizing your life in Budapest? We all come together on Thursday to help each other.
This is the perfect opportunity to discuss your first impression about the courses, instructors, and the BSM program. Your opinion can be valuable to us, as well as to others in making the big decision.
Also, this late afternoon is the deadline for registration. If you are uncertain what to keep and what to drop, the 'Feedback' will help to solve this clue. In any case, we finally have to form the classes, decide the fate of ones with low/high audience.
September 16Thursday 16.30 pm: "N is a number", a movie about Paul Erdős. Please note that the movie will be shown in the Main Lecture Hall of the Renyi Institute, which you can find according to this map.