## May 13

Thursday at *16:15*, in Room 102

*Prof. Sándor KOVÁCS*, University of Washington: A glimpse into the sixth dimension

*Abstract: * Higher dimensional geometry is used in more places than most people realize. Anyone who uses a mobile phone (is there anyone who does not?) takes advantage of higher dimensional geometry during every call. Higher dimensional geometry is used in robotics and cryptography. If you ever bought something on the internet, you were able to do that safely because of higher dimensional geometry.

The main purpose of this talk is to discuss higher dimensions. This is usually an intriguing topic if for nothing else but because it is so out-of-this-world. My hope is that at the end of this discussion higher dimensions will seem perhaps less romantic and exotic, but more practical and useful and definitely at least as intriguing as it had been before.

As the main example of the usefulness of higher dimensions I will explain how the geometry of a six dimensional space can tell us about interesting questions about plane curves. (The cell phone, robotics, and cryptography applications would require a semester long course at least, but I will say a few words about those as well).

## April 16

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

*Prof. Ferenc Fodor*, Bolyai Institute, University of Szeged: Sphere packings

*Abstract: * We will investigate the problem of filling the Euclidean space with unit balls in an efficient way such that - roughly speaking - the ratio of space covered by the union of the balls is maximal. We will discuss Kepler's problem and its recent solution, and explore the connection of dense sphere packings with other branches of geometry.

*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 round trip train ticket (to Szeged) and the dormitory type accommodation, see her in case you intend to attend the lecture and visit Szeged.

## April 8

Thursday at *17:00*, at Eotvos University, (Pazmany Peter setany
1/C - south building - Bolyai Lecture Hall (room 0-821); see
remark below)

*Prof. Zoltán Buczolich*, Eötvös University: A Dynamical Introduction to Fractals

*Abstract:*
Motivated by dynamical systems we introduce
sets of fractional dimension.
We discuss the possible definitions of
fractional dimension, and survey some examples.

*REMARK:*Another exceptional, out of the building colloquium lecture. The venue will be at the Eötvös University, Faculty of Sciences campus, south building (Deli tomb, 1/C on this map). A more detailed map, and the sketch of the interior of the building .

The time is 5pm, 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.

## Marc 11

Thursday at *16:15*, in Room 102

*Prof. Paul Humke*, St. Olaf College / BSM : A Voyager from the Fourth Dimension

*Abstract: * When speaking about The Fourth Dimension I'm invariably asked

"How do you know this is what the 4th dimension really looks like?"

My answer is

"I know because we used a bit of mathematics to create a four
dimensional world and
then used the computer monitor as a window to view it."

Indeed, there is nothing magical or new in what I'll show you (it is
only elementary linear algebra), but there is a bit of magic in what you'll see.

## March 4

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

*Prof. Gergely Harcos*, Central European University / Rényi Institute
: Ellipsoids and the Riemann hypothesis

*Abstract:* Given an ellipsoid in Euclidean three-space one can ask how many lattice points it contains and how evenly the points are distributed. This question turns out to be surprisingly deep with multiple connections to the generalized Riemann hypothesis. I will tell you about the main results and issues in this theory with a certain amount of historical perspective.

*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 25

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 18

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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