Recent and Future Excitements

It is very hectic around here and on top of the eight or so regular research seminars at math (and quite a few more at CS) we have many visitors as school terms at the US are over.

A week ago there was a beautiful talk about prejudices in physics in the Friday Rationality series given by an old friend Eliezer Rabinovici who did a great job. He wrote a single formula on the blackboard (of some Lagrangian) and explained various truths about physics that were shattered over the years. (Mainly in connection with string theory.) This Friday Nancy Cartwright is going to talk about causality.

Also Ron Donagi, who was a star math Olympiad boy in our youth and whom I first met 37 39 years ago came to town and the two abstracts of his talks today and tommorow are quite amazing. I am not sure I will be able to tell you more after the talks so have a look now:

Ron’s first lecture (today at 16:00):

Title: The Geometric Langlands Conjecture

Abstract: We will describe the Langlands program, in its arithmetic and geometric incarnations, as a conjectural non abelian analogue of well known  “abelian” results: class field theory on the arithmetic side, and the Abel-Jacobi theory of Riemann surfaces and their Jacobians on the geometric side. One powerful approach to the geometric Langlands conjectures involves abelianization via Hitchin’s integrable system and its spectral curves. Recent input from physics suggests that this  geometric Langlands conjecture can be viewed as a statement in quantum field theory. This has a classical limit which has now been proved, at  least generically. The relationship between the classical and quantum versions is deep and mysterious. The quantum version can of course be studied as a deformation of the classical one.  But there is tantalizing evidence – from quantum field theory as well as non abelian Hodge theory – that the full quantum version can also be understood as a twistor  rotation of the classical version.

Ron’s second lecture (tommorow 17:15)

Title: From Strings to the Standard Model via Algebraic Geometry

Abstract: The Standard Model of particle physics is the extremely successful  theory of all known matter particles and the three forces that act on  them: electromagnetism and the weak and strong nuclear forces. String theory is an attempt to incorporate also the fourth force, gravity.  It produces a bewildering array of possible physical universes – on the order of 10^500, according to some estimates. A long standing question has been whether any of these models can look anything like  the real world. This means that it should produce the same spectrum  of particles and forces as are known from the MSSM (the Minimal  Supersymmetric Standard Model), as well as the same interactions  among them and the correct values for various constants in the theory. Using techniques from algebraic geometry, the first known  string model with precisely the MSSM spectrum and with realistic  interactions has been constructed recently. This talk is meant for  mathematicians – no familiarity with the physics is assumed. We will  translate the basic physics concepts into mathematical language, and  will outline the tools used in the recent solution – these come from representation theory, topology, and especially algebraic geometry.

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