## December 7

Saturday *from 4pm to 7pm and 9pm to midnight*, In room 102, Bethlen ter

*Putnam Mathematical Competition*

as has been announced several times, the Putnam exam will be offered
at Budapest for the registered BSM students.

Venue: BSM headquarters, Bethlen ter 2, room 102

Time: Saturday, December 7th, 4pm to 7pm ("morning session") and 9pm
to midnight ("afternoon session")

If you plan to participate, be there 10 minutes prior the beginning of each session.

You are not permitted to bring in any paper, books, slide rulers,
rulers, calculators, computers, etc., in the exam room. CELL PHONES
SHOULD BE TURNED OFF COMPLETELY. Participants should bring sharpened
pencils (or pens) and erasers.

## November 23

Sarturday * from 10:00 am to 15:00 pm*, room TBA, Bethlen ter

**BSM local mathematics competition **

The local math competition * comes with cash prizes * as well as serves as a selection for the team representing BSM at the
International Mathematics Competition for University Students 2013.
Anyone is very welcome to compete and the participation of good problem solvers is highly
encouraged!

## November21

Thursday at *16:30*, at the Central European University (Zrinyi utca 14. 3. floor, room 310/A , Budapest, Hungary)

*Prof. Károly Böröczky*, Central European University and Rényi Institute:
**The isoperimetric inequality and its reverse**

*Abstract:* The classical isoperimetric inequality says that given the volume of a convex body in a Euclidean space, the surface area is minimized by the ball. A symmetrization process is presented that transforms a convex body into a ball while maintaining the volume, and decreasing the surface area. We also discuss what the converse of the isoperimetric inequality might be where we use some probabilistic inequalities. Classical and recent results are combined with open problems.

*REMARK:*This will be the second 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.

## November 15

Friday at *16:45 (apprx.)*, at Bolyai Institute (Mars ter 20, 2nd floor, room M7, Szeged, Hungary)

*Prof. Tamás WALDHAUSER: *, Bolyai Institute, University of Szeged:
**Analysis on the two-element set**

*Abstract: * We start with a light introduction to general algebra, which shall convince everyone that the 3-element set is so big that it is probably a hopelessly difficult task to fully understand it. Therefore, in the second part of the talk we focus on the two-element set, and we try to play multivariable calculus there. More precisely, we define order-theoretic analogues of partial derivatives of functions of several variables on {0,1} and investigate commutation properties of the resulting "differential operators".

*REMARK:*This will be an exceptional, out of the town colloquium lecture at an exceptional time, Friday afternoon. This Friday the last classes (from 1pm) might 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.

## November 7

Thursday at *16:15*, In room 102, Bethlen ter

*Dezső Miklós*, BSM and Rényi Institue: **Positive and zero subsums of a (positive) sum**

*NOTE:* the lecture will be preceded by the **presentation of Emily (Searle-White) and Daniel (Baron) about their finding** in the EUR project.

*Abstract:*
We will investigate (present, sometimes prove?) questions and results related to the topic in the address. We will also present relation of these questions and
finding subsets of the vertices of the n-dimensional hypercube (GF(2)^n, or simply 0,1 sentences of length n, as you like) with certain extremal properties, e.g.,
how many vertices (of certain properties, maybe) one can choose without the vertex (1,1,1,1...,1) being in the subspace (or cone) spanned by them.
To understand and enjoy more the topic and the lecture everybody is welcome, even encouraged to think before the lecture about the questions
found here and suggest best - or at least very good - solutions during the lecture.

## October 24

Thursday at *16:15*, at BSM, in Room 102, Bethlen tér

*Prof. Tibor Jordán *, Eötvös Lóránd University and BSM:
**Rigid frameworks and their applications : from scaffoldings to the
flexibility of molecules**

*Abstract:* The first structural result on rigidity properties of bar-and-joint
frameworks (sometimes
called geometric graphs) is due to Maxwell, who observed a necessary
condition concerning
the number of bars of a rigid framework in three-space. Since this result,
which is from
1864, several extensions and related results have been obtained.
This area has become extremely active in the last few years, due to a
number of breakthrough results and various new applications, ranging from
molecular flexibility to sensor network
localization. In this lecture I shall give an overview of these
developments focusing on the
combinatorial and algorithmic aspects.

*REMARK:*This will be the second lecture in the sequence introducing fine Hungarian higher education mathematics centers. Eötvös University has the oldest and most prestigious school of mathematics in Hungary and offers a master graduate program as well.

## October 17

Thursday at *16:15*, at BSM, in Room 102, Bethlen tér

*Prof. Bálint Virág *, University of Toronto and Rényi Institute:
**What is percolation?**

*Abstract:* Consider the n x n+1 square grid. Now erase every edge with probability 1/2. A simple problem is to show that the chance that the two short sides of the grid are still connected is 1/2.

Percolation theory studies what remains of the grid. It has made enormous advances in the past 10 years, yet many of the original problems are still open. This talk will be a light introduction.

## September 26

Friday at*16:15*, in Room

*102*

*Feedback Session*

*ATTENTION: MOVED TO THURSDAY AFTERNOON*

Having any problems in organizing your life in Budapest? We all come together on Friday 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, the morning of this day 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 26

*CANCELED*

Thursday at *16:15*, In room 102, Bethlen ter

** BSM EUR research plans presentation **

The Elective Undergraduate Research Groups will present their research plan. All BSMers are welcome to see the work of your peers.

## September 19

Thursday*16:30*:

*"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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