TopMath School of Advanced Mathematics for Young Students
TopMath Summer School takes place on 17 - 21 September, 2018, at Technical University Munich at Garching Businesscampus.
The TopMath School of Advanced Mathematics for Young Students aims at presenting advanced topics of mathematics and their applications to a selected group of students before starting their third year of Bachelor studies.
Each year a new aspect or branch of Applied Mathematics is in focus. The goal of the school is twofold: on the one hand to show the incredible breath of Mathematics, starting with its seminal ideas all the way to its most recent advances and novel applications; on the other hand to have students exposed to rigorous mathematical thinking and to foster exercising problem solving skills in dedicated sessions on proofs and exercises.
Topic 2018: Introduction to Harmonic Analysis and Applications
Harmonic analysis starts with a memoir written by Fourier in 1806 on the solution of the heat equation by tensor and trigonometric function decompositions. Despite the fact that his method was presented ad-hoc for the model of heat diffusion, the rigorous understanding of the convergence of such trigonometric function series triggered an incredible amount of further developments in analysis. In particular Lebesgue measure and integration theory, as well as the theory of Hilbert spaces are needed to properly explain Fourier’s original ideas.
Whilst for almost two centuries Fourier analysis found its inspirations and applications in the physical world, not last in quantum mechanics, starting with the work of Gabor on time-frequency analysis in 1946, its spectrum of applications widened to include the analysis of signals. Later, in the 1980s, with the work on time-scale analysis and the proposal of the wavelet transform by Grossmann and Morlet, and then the work of Daubechies and Meyer, new connections between harmonic analysis and digital signal/image processing were further discovered.
The course presents this long journey, from the early results of Fourier analysis to the more recent wavelet theory, illustrating and complementing the theoretical findings with corresponding applications. We conclude the lectures showing one relevant application in the use of computational harmonic analysis for the solution of the problem of the (mathematically based) restoration of one of the most important frescoes of the Italian Renaissance, which was destroyed and reduced to hundreds of thousands of fragments by a bombing during World War II.
On Wednesday afternoon we are offering our Conference Dinner in the Augustiner Keller in Munich, starting at 6 pm.
We will meet at the U-Bahn station in Garching Hochbrück at 5 pm to take public transport to the "Biergarten".
Close to the Hackerbrücke in Munich.
Summer School venue
The venue takes place in the QUANTUM. This lounge is located in the
Lichtenbergstr. 4a, Garching Business Campus.
The Campus can be reached by the tube line U6 from central Munich (station: Garsching-Hochbrück); by bus from the S-Bahn tube stations as Ismaning and Neufahrn, or by car via the exit "Garching Süd" on the A9 motorway.
For tube connections, please use the website of the Munich Public Transport Network MVV.
Registration is mandatory and must be done until the End of July. Please apply using the following registration form below.
Due to compability problems, please send us an email at firstname.lastname@example.org, after you have registered for the summer school. If you have already done this, please send us your email also.