## April 6

Thursday at *16:15*, in Room *102*

*Prof. János Pintz *, Rényi Institute: Famous problems on primes.

## March 16

Thursday at *16:15*, in Room *102*

*Prof. Laszlo Babai *, University of Chicago: Asymptotic cubology and card shuffling:
diameter and mixing rate of finite groups.

*Abstract:*After decades of Rubik's-cube enthusiasm, the question of
the number of moves required to solve Rubik's cube is
still not known, even approximately.

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 conjectures and recent results
on these two related quantities. No prior knowledge of group
theory or probability theory will be required.

## March 2

Thursday at *16:15*, in Room *102*

*Prof. Wlodzimierz Kuperberg*, Auburn University (Auburn, Alabama)
: A few touching problems on spheres and cylinders.

*Abstract:* Many problems in discrete geometry have an intuitive appeal, as they deal with shapes and configurations that can be visualized. The elementary nature of such problems makes it easy to understand their statements without much mathematical training. This is not to say that they are always easy to solve; to the contrary, they can be devilishly hard! Some have been solved by ingenuity, using ideas from various areas of mathematics that seemingly have nothing to do with the problem; some, unsolved for centuries, have been recently attacked with the aid of computers. Yet many remain unsolved--even though in some cases the "obvious" solution presents itself readily. A few examples will be presented in this talk, all concerning configurations of spheres, cylinders, or their combinations, in which touching (tangency) plays a crucial role.

## February 23

Feedback Session at *16:15*, in Room *102*

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. Next day, Friday, is the deadline for registration, if you are uncertain what to
keep and what to drop, the 'Feedback' will help to solve your clue. We finally have to form the classes. Having any
problems in organizing your life in Budapest? We all come together on Thursday to help each other.

## February 17

*Prof. Bollobás will offer a party after the lecture at his Budapest residence for the interested students.*

## February 16

Thursday 16.30 pm:*a movie about Paul Erdős.*Please note that the movie will be shown at the Renyi Institute, which you can find according to this map.

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