## December 16

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.

*Remark1:*Second year MS Student Daniel Glasscock and PhD Candidate Péter Maga will deliver a two part lecture on Tao's proof of Szemerédi's theorem ("A quantitative ergodic theory proof of Szemerédi's theorem"). The lectures will focus on the specific tools needed in Tao's proof and will assume no previous knowledge of ergodic theory or Tao's work, however the second lecture will build on the first.

*REMARK2:*The venue of the lecture is the headquarters of the Department of Mathematics and it's Application at Zrinyi utca, downtown Budapest. You are assumed to find the location by yourself, with the following help: general directions general directions and map of the neighborhood.

## December 1

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

## October 28

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.

*REMARK:*This will be the first lecture in the sequence introducing fine Hungarian higher education mathematics centers. CEU is an international graduate level university in the truest sense: Its students come from more than 80 countries; its faculty, from more than 30 countries--with the mix of nationalities increasing every year. The language of instruction and communication is English. It has it's own mathematics department and MSc and PhD math programs, which will also be shortly introduced. The venue of the lecture is the headquarters of the Department of Mathematics and it's Application at Zrinyi utca, downtown Budapest. You are assumed to find the location by yourself, with the following help: general directions general directions and map of the neighborhood.

## October 21

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.

*REMARK:*Another exceptional, out of the building colloquium lecture. The venue will be at the Eötvös University, Faculty of Sciences campus, north building (Északi tömb, 1/A on this map). A more detailed map, and the sketch of the interior of the building . The exact location of the lecture room is the darkened region on this copy of the map.

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.

## October 8

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.

*REMARK:*This will be an exceptional, out of town colloquium lecture at an exceptional time, Friday afternoon. This Friday the last classes (from noon) will be canceled (and made up later) and the group will leave from Nyugati railway station at 13:53 with TÖMÖRKÉNY intercity train. You will be met at the Szeged railway station at the arrival time, at quarter past 4 and be ushered to the site of the lecture. Anna takes care of the train ticket (to Szeged) and the dormitory type accommodation, see her in case you intend to attend the lecture and visit Szeged.

## September 23

Feedback Session

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 16

Thursday 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.

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