Bielefeld Graduate School in Theoretical Sciences

Alexandros Galanakis
(Mathematics)

Congruent Number Problem: From Diophantus to a Millenium Problem

In an attempt to highlight how number theory has evolved over the centuries, we will discuss a well-known problem, the congruent number problem. A simple question about rational right triangles, the complete answer of which, depends on the truth of one of the most important conjectures in modern mathematics.

Eduardo Garnacho
(Physics)

The (not so) strange theory of (not so) small things

Quantum is, closely followed by strings, the word that more interest causes in newcommers in physics. This adjective inmediately grants any discipline of some misterious and seductive aura: Quantum Optics, Quantum Computing, Quantum Information... In this talk we will give a basic introduction to the baseline of all this branches: Quantum Mechanics (QM). Usually calificated as weird and difficult, QM is a fundamental part of the world we live in. We will go over some of the most basic yet counterintuitive concepts and experiments in QM in a relax and interacting way, so everybody can get a grasp of the fascinating ideas behind the quantum world and the role it plays in our society. 

Felix Dammann
(Economics)

The fair price of an olive press option

Legend has it that Thales, one of the oldest Greek mathematicians and  philosophers, predicted a large olive harvest for the coming year and  thus bought the right to rent all the olive presses in the city of  Miletus in the coming autumn. When the  harvest turned out to be as large as expected, he used this right and  made a fortune - making him one of the first historically known  inventors of an option contract. Together, we take a look at perhaps the most  famous stochastic model in financial mathematics, the Black-Scholes  model, and the fair price it assigns to contracts like these.

Dean Valois
(Physics)

The strong puzzle

No more than 60 years ago, scientists were asking how atoms could even exist. If nuclei, like in the helium or the carbon atom, contain positively charged particles called protons, why are atoms stable? Why don't they disintegrate through electromagnetic repulsion? These questions led to the discovery of one of the four fundamental forces of nature: the strong force. That force and three others together with the particles from the so-called Standard Model of Particle Physics, so far our best description of the fundamental laws of nature, encompass everything we know about the universe. In order for the strong interaction to make sense, new particles, now called quarks and gluons, had to be postulated and experimentally detected. The road that led to such breakthrough is far from trivial and disclosed the most intriguing and challenging puzzle in physics. This is the story of that puzzle.

Curves in the projective plane

Abstract: One of the best studied examples in algebraic geometry is the projective space. We will focus on the projective plane which parametrizes one dimensional subspaces of a three dimensional vector space. Although the geometry of the projective plane seems to be simple, it turns out that describing curves inside the plane is a nontrivial task. We will discuss the main tools how to describe curves passing through a specified collection of points in the plane and highlight open conjectures in that field.