## May 19

Thursday at *17:00*, at the AIT campus (1031 Budapest Záhony u. 7. Graphisoft Park - Conference Building)

*Albert-László Barabási*, Northeastern University **Network Science: From the structure of complex systems to controlling networks**

*Abstract: * Systems as diverse as the world wide web, Internet or the cell are described by highly interconnected networks with amazingly complex topology. Recent studies indicate that these networks are the result of self-organizing processes governed by simple but generic laws, resulting in architectural features that makes them much more similar to each other than one would have expected by chance. I will discuss the amazing order characterizing our interconnected world and its implications to network robustness, social networks and mobile telephony, and may cover some recent results on controlling networks.

*REMARK:*Prof. Albert-László Barabási is a Distinguished University Professor at Northeastern University, where he directs the Center for Complex Network Research, and holds appointments in the Departments of Physics, Computer Science and Biology, as well as in the Department of Medicine, Harvard Medical School and Brigham and Women Hospital, and is a member of the Center for Cancer Systems Biology at Dana Farber Cancer Institute. He is, among many other duties - a member of the Scientific Board of AIT, Aquincum Institute of Technology and will give his lecture on this joint event of BSM and AIT on the AIT campus (for directions see here).

## April 28

Thursday at *16:15*, in Room 102

*Prof. József Pelikán*, Eötvös University: **Some manifestations of high-degree symmetry **

*Abstract: * In this lecture I will speak about Steiner systems, multiply
transitive permutation groups, sporadic simple groups,
error-correcting codes, the Leech lattice, sphere packings in high
(and low) dimensions, quadratic forms - and their many interrelations.

It will emerge, that high-degree symmetry is very rare in nature, but
when it occurs, it has truly remarkable consequences.

All the concepts mentioned in the first sentence will be defined and
explained - no previous knowledge of them is required.

*REMARK:*Another colloquium lecture to present the fine math centers and possible institutions to continue your (graduate) studies in Hungary. The venue will be this time the Bethlen ter headquarters of BSM, but the lecturer will come from the Eötvös University. Prof. Pelikán is, by the way, an experienced BSM professor as well, a brilliant lecturer who is, unfortunately, on his "sabbatical" from BSM during this academic year.

## April 14

Thursday at *16:15*, in Room 102

*Kenneth Mulder*, Green Mountain College **Fossil Free Agriculture or How a BSM grad started farming with oxen.**

*Abstract: * Easy access to fossil fuels has had a dramatic effect on American agricultural productivity as well as energy intensity, to a point where some commentators have describe Americans as "easting oil". In this talk I will look at the role of fossil fuels in the American food system and discuss what we know about the feasibility of kicking the American food system's addiction to oil. The talk will be from an economic, ecological and agricultural perspective.

*REMARK:*Kenneth Mulder is a BSM alumnus from 1989. This, exceptionally not strictly mathematical - colloquium lecture will give a chance to meet a BSMer from the old ("communist") age, talk to him about the life in Budapest that time and see a "BSM grad carrier" line.

## April 7

Thursday at *16:15*, in Room 102

*Prof. Tamás SZAMUELY*, Rényi Institute:
**Galois Theory: Past and Present**

*Abstract: * In 2011 we celebrate the 200th anniversary of the
birth of Evariste Galois.
On this occasion I shall explain what Galois himself discovered in the
theory of algebraic equations and outline some of the main directions in
present-day research in the field.

## March 25

Friday at *16:45 (apprx.)*, at Bolyai Institute (Aradi vertanuk tere 1, Szeged, Hungary)

*Prof. Ferenc FODOR *, Bolyai Institute, University of Szeged:
**Behaviour of volume in high dimensions**

*Abstract: * In this talk we will investigate some surprising properties of volume
in high dimensions. In particular, we will discover how the volume of
the d-dimensional unit ball behaves when d tends to infinity, and where
this volume is concentrated.

*REMARK:*This will be another exceptional, this time out of the 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.

## March 16

Wedneday *16:45*, in Room 102

*Prof. László BABAI *, (University of Chicago):
**Asymptotic cubology and card shuffling:
diameter and mixing rate of finite groups**

*Abstract: * After decades of Rubik's-cube enthusiasm, it is now said
that we know the number of moves it takes to solve
Rubik's cube. What about a 4 X 4 cube?

How many times do we need to shuffle a deck of cards to
have them thoroughly mixed?

A generalization of these questions takes a finite group G and
a set S of generators, and asks the smallest value d=d(G,S)
such that every element of G can be written as a word of length at
most d over S. This is the "diameter" of G with respect to S.
A random walk on the group in steps defined by the generators and
their inverses produces the "mixing rate" parameter.

We shall discuss long standing open problems and recent major
progress on these two related quantities. No prior knowledge
of group theory or probability theory will be required.

*Remark: *
This is exceptionally scheduled talk, but the lecturer is available only this time (visiting Budapest from Chicago).
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.

## March 3

Thursday at *16:45*, at the Central European University (Zrinyi utca 14. 3. floor, room 310/A , Budapest, Hungary)

*Prof. Pál Hegedűs*, Central European University :
**Algorithmic thinking in algebra**

*Abstract:* We will be reviewing a few important algorithms from algebra. The
focus will be on groups and polynomials. These approaches are
interesting in that they reveal theoretically important results. This
is one aspect among many that indicates why "pure" vs "applied"
categorization of mathematical thinking is improper.

*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.

## February 24

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.

## February 17

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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