Thursday at 16:15, In room 102, Bethlen ter
BSM EUR Conference
The Elective Undergraduate Research Groups will present their findings
Saturday from 10:00 am to 15:00 pm, In room 105, 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!
Thursday at 16:15, at BSM, in Room 102, Bethlen tér
Prof. Kimberly ROTH, Juniata College: Variations on a fractal theme: The Mandelbrot Set and Multibrot Sets We will look at three types of fractals: the Mandelbrot set discovered by Benoit Mandelbrot in 1975, the Multibrot sets that are a generalization of the Mandelbrot set, and the Julia sets related to them. We will learn about how the sets are mathematically generated, relationships between them, and some known and conjectured properties. No prior knowledge of fractals or complex analysis is needed.
Abstract: We will look at three types of fractals: the Mandelbrot set discovered by Benoit Mandelbrot in 1975, the Multibrot sets that are a generalization of the Mandelbrot set, and the Julia sets related to them. We will learn about how the sets are mathematically generated, relationships between them, and some known and conjectured properties. No prior knowledge of fractals or complex analysis is needed.
Friday at 16:45 (apprx.), at Szeged University (room M8 = 201, Mars ter 20, Szeged, Hungary)
Prof. Gábor CZÉDLI: , Bolyai Institute, University of Szeged: On the mathematics of simple juggling patterns
Abstract: Simple juggling patterns are described by certain finite sequences of nonnegative integers, the so-called juggling sequences. We characterize juggling sequences mathematically. Also, we count these sequences, that is, the simple juggling patterns, for any given number of balls and given maximal height of throws.
The first theorems in the Mathematics of Juggling are due to two very famous mathematicians, Claude E. Shannon (also a computer scientist, 1916-2001) and Ronald L. Graham (president both of the American Mathematical Society in 1993, and the International Juggler's Association, 1972; 28 joint papers with Paul Erdős). This lecture is based on Burkard Polster's book "The Mathematics of Juggling", 2003, but only some mathematically easy questions will be discussed.
Sometimes, we would like to, or have to, convince outsiders that mathematics is useful, interesting and beautiful. The talk offers a possible way to do so, because it tries to follow the following scheme:
- start with a topic outside mathematics that is sufficiently interesting to many non-mathematicians,
- disregard details of little importance,
- set up a mathematical model that is at least partially clear for outsiders,
- find and prove mathematical theorems in the model that are more or less clear for outsiders,
- draw non-mathematical conclusions for the original topic that are very clear to anyone.
In our case, the non-mathematical conclusion was the discovery of a simple juggling patterns, not known by professional jugglers before their juggling sequences were found. (Perhaps, one of these juggling patterns will be shown.)
Thursday at 17:00, at Eotvos University, (Pazmany Peter setany
1/A - north building, "Északi tömb" - room 1.71; see remark below)
Prof. András Szűcs, Eötvös University: Soups and hedgehogs
Abstract: “It is a mystery why mathematics is such an efficient tool in the hands of scientists in understanding the world” - wrote a Hungarian-American Nobel prize winner physicist, Eugene Wigner. Probably the clue to this mystery is that mathematical abstraction helps us to discover the same essence behind many, seemingly different phenomena. The talk will show examples demonstrating this statement:
1. “The soup can not be mixed properly”, i.e. there always will be a particle which returns to its original position.
2. ‘”A hedgehog can not be combed”. In mathematical terms: there is no nowhere vanishing, continuous, tangent vector field on the 2-dimensional sphere. 3. “The Fundamental Theorem of Algebra”, i.e any polynomial (of degree at least 1 over the complex field) has a root.
It turns out that all these statements (and many more) can be proved using the same elementary notion, the so called
You find the Eotvos University campus by taking trams 4 or 6 southbound from Blaha Lujza, go with them across the Danube and leave the trams immediately on the Buda side. Walk along the Danube southbound until you reach the first of the two huge buildings of the Faculty of Sciences (North building)
A more detailed map of the immediate neighborhood .
The timing will allow all of you to reach the place.
The room is on the first floor. On this plan of the building the red cross shows the location of the room. You need to find an elevator (X) or staircase to go one floor up.
Thursday at 16:30, at the Central European University (Zrinyi utca 14. 3. floor, room 310/A , Budapest, Hungary)
Prof. László Csirmaz, Central European University and Rényi Institute: Gentle introduction to elliptic curves
Abstract:Elliptic curves are playing an important role in modern cryptography. Their most important property is to admit an operation -- addition -- on their points, which is then used to hide information, send secret messages between parties. During the lecture we'll look at those interesting curves. Study their connections with Pappos theorem in projective geometry, with Bezout theorem in algebraic geometry, and find out how the above operation is defined, and why it forms a group. If time permits, we show some interesting cryptographic applications.
This will be an excellent opportunity to meet the students at CEU - some of them BSM alumni - and chat with them about the program.
Thursday at 16:15, at BSM, in Room 102, Bethlen tér
Prof. Tibor Beke, University of Massachusetts, Lowell: The sign pattern theorem
Abstract:This talk is about an unexpected occurrence of algebraic topology in combinatorics or, if you like, combinatorics in algebraic topology. The good thing about it is that one does not need a lot of mathematical machinery to appreciate it! Much of it is very visual.
On the topological end, there is the Brouwer fixed point theorem: any continuous map of the n-dimensional ball into itself will have a fixed point, i.e. a point not moved by the mapping. This statement is surprising even for the 2-dimensional "ball", that is, the disk.
On the combinatorial end: if a string of + and - symbols begins with `+' and ends with `-', then it contains adjacent + and - symbols somewhere. The sign pattern theorem is the analogue of this trivial observation for matrices whose entries are sign-pairs "++", "+-", "-+" or "--": if the matrix satisfies certain boundary conditions then it contains a 2x2 submatrix with a specific sign pattern. (Come to the talk to hear what it is!) There is an n-dimensional version, concerning n-dimensional matrices whose entries are strings of + and - symbols of length n.
Via an easy application of compactness, the sign pattern theorem implies a vector-valued form of the intermediate value theorem, which in turn implies the Brouwer fixed point theorem. Though the statement of the sign pattern theorem is completely combinatorial, all the proofs I know secretly use ideas from algebraic topology. Curiously, while the Brouwer fixed point theorem is classical and well understood, there are open questions about the combinatorics of sign patterns, for example, the computational complexity of finding them.
February 21Thursday 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, 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.
February 14Thursday 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.