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v 52, 2007

 

Matematiska kollokviet

Wednesday 16 January 2008, Glashuset 13.15-14.15, Mattias Enstedt, Uppsala universitet

Title. Hartree-Fock equations with decreasing external magnetic fields
Abstract. In the presence of a decreasing external magnetic field, we present recent results on existence and non-existence of a ground state within the Hartree-Fock theory of atoms and molecules. The ground state exists provided the magnetic field is decreasing and the total charge $Z$ of $K$ nuclei exceeds $N-1$, where $N$ is the total number of electrons. In the opposite direction, no ground state exists when $N \ge 2Z+K$

Wednesday 23 January 2008, Glashuset 13.15-14.15, Andreas Strömbergsson, Uppsala universitet

Title. The Boltzmann-Grad limit of the periodic Lorentz gas and the distribution of visible lattice points
Abstract. The periodic Lorentz gas describes a particle moving in a periodic array of spherical scatterers, and is one of the fundamental mathematical models for chaotic diffusion in a periodic set-up. In my lecture I will describe the recent solution of a problem posed by Y. Sinai in the early 1980s, on the nature of the diffusion when the scatterers are very small. The problem is closely related to some basic questions in number theory, in particular the distribution of lattice points visible from a given position. The main tool in our approach is measure rigidity, a part of ergodic theory which has recently found important applications in several other problems in number theory and mathematical physics, such as the value distribution of quadratic forms at integers, quantum unique ergodicity and questions of diophantine approximation. (This lecture is based on joint work with Jens Marklof, Bristol.)

Wednesday 30 January 2008, Glashuset 13.15-14.15, Prof. Stefan Rauch-Wojciechowski, MAI

Title. What means to explain the motion of the Tippe Top?
Abstract. The Tippe Top has a shape of a truncated sphere with a peg attached to the flat surface. When spun sufficiently fast on its spherical bottom the tippe top turns up and continues motion on the peg. Research on the Tippe Top has long history since 19-th century and it is presently understood that the gliding friction is responsible for this phenomenon and that it takes place for the values of parameters where measures the eccentricity of the centre of mass.
I shall present results of our work on the phase space picture of TT. It appears that under mild assumptions about the friction force the asymptotic frictionless solutions play a special role, they are periodic and they are global attractors. All solutions tend (in the sense of the LaSalle´ theorem) to one of the asymptotic solutions. We have discussed conditions of their stability and have described what happens to the TT in large for all values the parameters and all initial conditions. But detailed dynamics of the Tippe Top, that is description of how a TT is rising to the inverted spinning state remained unexplained. I shall present my recent results that provide tools to capture mathematically the whole dynamics of inversion.
I shall demonstrate the motion of the Tippe Top and other rigid bodies.

Welcome!

Armen Asratian, Milagros Izquierdo, Vladimir Kozlov, Stefan Rauch-Wojciechowski

 

Presentation av examensarbete i tillämpad matematik

Torsdag den 20 december kl. 14.00 i Kompakta Rummet presenterar Andreas Johansson sitt examensarbete.

Title: A potential for the Ricci tensor in the Reissner-Nordström spacetime

Abstract: In their 2006 paper A weighted de Rham operator acting on arbitrary tensor fields and their local potentials Edgar and Senovilla proved the existence of a local potential for the traceless part of the Ricci tensor. We here construct a concrete instance of this kind of potential, namely a potential for the (traceless) Ricci tensor in Reissner-Nordström spacetime, valid for the entire region outside the event horizon.

Välkomna!

Göran Bergqvist

 

Graduate course

NONLINEAR OPTIMIZATION, EQUATIONS AND LEAST SQUARES - a course for graduate students (MAI008)
http://www.mai.liu.se/~olbur/kurser/PHD/info.html

This course is given every year since 2000. It is recommended by LiTH FoFu-nämnden as "Fakultetsgemensamma forskarutbildningskursen". The course start on Wednesday, week 3, and will take about 16-17 weeks (one seminar per week). Each topic is covered twice - first by the lecturer, then at the next meeting by a couple of students. Their presentation is followed by discussions.

The course is worth 6 points. Examination: active participation (at least 85% attendance), presentation of the course topics.

The main topics: unconstrained optimization, constrained optimization, systems of simultaneous nonlinear equations, nonlinear least squares.

Students will get acquaintance with the most effective numerical methods in nonlinear optimization, equations and least squares, many of which have been developed only in recent years. The course responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems.

The basic book is: Jorge Nocedal and Stephen J. Wright. Numerical Optimization, Springer, 1999. For more information about the book see: http://www.ece.northwestern.edu/~nocedal/book/

Students background: basic calculus, numerical linear algebra and optimization. Any gap in the background can be closed by students at the beginning of the course by intensive self-study with a help of the lecturer.

Welcome!

Oleg Burdakov

 

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Material skickas till litemat@mai.liu.se senast torsdagar kl. 12.