# Mirimanoff Lectures 2015

The Math department of the University of Geneva together with NCCR SwissMAP are organising the Mirimanoff Lectures 2015.

The lectures will take place on the **10th of December** 2015, in the **Stückelberg auditorium** (Physics department, 24 quai Ernest Ansermet).

__The Speakers: __

**Israel Michael Sigal (University of Toronto and ETHZ) **

Israel Michael Sigal is a Canadian mathematician specializing in mathematical physics. He holds the Norman Stuart Robinson Chair in Applied Mathematics at the University of Toronto Department of Mathematics. He was an invited speaker at International Congress of Mathematicians, Kyoto—1990 and in International Congress on Mathematical Physics, Lausanne—1979, W. Berlin—1981, Marselle—1986. His research interests include: partial differential equation of quantum physics, quantum mechanics and quantum information theory, quantum field theory, statistical mechanics, non-linear equations, mathematical biology and pattern recognition.

He has received the John L. Synge Award and the CRM-Fields-PIMS prize, and is a fellow of the Royal Society of Canada and the AMS.

** Juerg Froehlich (ETHZ) **

Jürg Martin Fröhlich is a Swiss mathematician and theoretical physicist. Since 1982 he has been a professor for theoretical physics at ETHZ, where he founded the Center for Theoretical Studies. In 1978, Fröhlich gave an invited address to the International Congress of Mathematicians in Helsinki and in 1994 a plenary talk at the ICM in Zurich. He also co-authored a book on quantum triviality. His research interests include: quantum field theory, precise mathematical treatment of models of statistical mechanics, theories of phase transition, the fractional quantum Hall effect, and non-commutative geometry.

He has received the Dannie Heineman prize, Marcel Benoist Prize, Max Planck Medal and the Henri Poincaré Prize, and is a fellow of the AMS, Academia Europaea and the Berlin-Brandenburg Academy of Sciences and Humanities.

__The Program:__ Thursday, December 10

**14:30 - 15:30 ****Israel Michael Sigal (University of Toronto and ETHZ) **

Title: Magnetic Vortices, vortex lattices and automorphic functions

Abstract:

The Ginzburg - Landau theory was first developed to understand behaviour of superconductors, but has had a profound influence on physics well beyond its original area. It had the first demonstration of the Higgs mechanism and it became a fundamental part of the standard model in the elementary particle physics. The theory is based on a pair of coupled nonlinear equations for a complex function (called order parameter or Higgs field) and a vector field (magnetic potential or gauge field). They are the simplest representatives of a large family of equations appearing in physics and mathematics.

Besides of their importance in physics, the equations contain beautiful mathematics (some of the mathematics was discovered independently by A. Turing in his explanation of patterns of animal coats). In this talk I will review recent results involving key solutions of these equations - the magnetic vortices (called Nielsen-Olesen or Nambu strings in the particle physics) and vortex lattices, their existence and stability and how they relate to the modified theta functions appearing in number theory and algebraic geometry. Certain automorphic functions play a key role in the theory described in the talk.

**Coffee break**

**16:00 - 17:00 Juerg Froehlich (ETHZ)**

Title: The Arrow of Time

Abstract:

Several examples of "effective quantum dynamics" of large open (but isolated) systems are discussed - among them: Heat transport between thermal reservoirs and heat engines, (derivation of the 2nd Law of Thermodynamics); quantum friction of particles moving through a gas, quantum Brownian motion; and the dynamics of quantum systems under repeated measurements. The theme common to these and other examples is the appearance of an "arrow of time", in the sense that they exhibit dynamical phenomena that are irreversible. Different sources of irreversibility are revealed and discussed.

Dmitry Mirimanoff (1861 - 1945) was born in Pereslavl-Zalessky in Russia. He received his Ph.D. degree in 1900 at the Department of Mathematics, University of Geneva. Later, he became a Professor in Mathematics at UniGe. He made significant contributions in Set Theory and Number Theory, and he had interests in Theoretical Physics, in particular, in the Theory of Relativity.