Below you can find the schedule of the symposium on the 17th of January 2018, note that it is recommended to be at the location 15 minutes prior to the first talk:
Sjoerd Verduyn Lunel, UU
Klaas Pieter Hart, TU Delft
Frits Beukers, UU
Ale Jan Homburg, UvA
Marcel Vonk, UvA
Hall Ruppert Wit does have a lecture
How can one prove the Twin Prime Conjecture?
In the spring of 2013 the Chinese-American mathematician Yitang Zhang took the mathematical world by storm by announcing his proof that an integer A exists such that there exist an infinite amount of pairs n,n+A which are prime numbers. If A had equaled 2 this would have been a proof of the well-known twin prime conjecture. This conjecture is probably as old as number theory itself. The proof and its optimizations imply something weaker though, namely that A is less than 246. Nonetheless the proof Zhang provided was one of a kind and thusfar other experts in analytical number theory had thought such a proof to be impossible. In this presentation we will discuss the problem of the twin primes, and give an impression of the proof of Zhang and the person behind it.
The Axiom of Choice
The axiom of choice caused quite some commotion at its first use. Many mathematicians did not like it. This was due to the non-constructive nature of the statement "There is always a choicefunction". In this presentation I will discuss how the axiom of choice entered mathematics and what that non-constructive nature actually is. We will also see how it is used in several areas of mathematics, also in the first year's analysis. To reassure the users of the axiom I will also indicate why the axiom does not create any contradictions; and, maybe letting down those same users, also why the axiom of choice is an axiom and not a theorem.
Coincidence and chaos
By means of elementary examples I show how closely interwoven random processes and chaotic dynamics are. I discuss examples of so-called iterated function systems. Previously they were studied to understand fractals, nowadays as models for stochastic and chaotic dynamics. We will see how a bit of coincidence (or chaos) can cause synchronization. And intermittence. And nightmares.
Resurgence: what is 1 + 2 + 6 + 24 + 120 + ...?
Real-world mathematical problems, like the ones appearing in physics, are often virtually impossible to solve exactly. One way to approach computations that cannot be performed exactly is to apply perturbation theory: start from a "nearby" problem that can be solved, and compute the solution of the actual problem order by order in some deformation parameter. Unfortunately, this approach often leads to asymptotically divergent formal series. The relatively new and surprisingly efficient toolkit of resurgence allows one to deal with such asymptotic series, and to obtain finite answers from them. I will briefly describe the "magic of resurgence", how it deals with sums like the one in the title, and how it may become an invaluable tool for future physics and mathematics.
Deep learning is currently going through rapid development and has lead to breakthroughs in speech and image recognition. But what exactly is deep learning? Deep learning is a concrete instance of the classic mathematical problem: For a given set of data and a given set of functions, find which function describes the data most accurately. In this presentation I will explain how deep learning is related to this classic problem and that the use of deep learning is an application of the trusted chainrule. To become familiar with deep learning we'll have to learn function fitting, Fourier and wavelet transforms and architectures. With this knowledge we will then work out an example.
The Marinus Ruppertbuilding, hall Wit and D, Leuvenlaan 21, 3584 CE Utrecht.
The student association for Computer Science, Physics and Mathematics.
The committee of A-Eskwadraat that organizes this symposium.