Triangle Seminars

Abstract:
These will be introductory lectures surveying GW, MNOP and GV invariants – all different ways of counting curves.

For a string theorist this involves seeing the curve as, respectively, the world sheet of a string, a D-brane, or a BPS thingummy.

I will describe a 4th way via stable pairs, which in effect means counting D-branes (or stable objects of the derived category, to mathematicians) after a change of stability condition.

Abstract:
Quantum graphs have become a paradigm for quantum chaos. It is indeed known that universal interference effects can be observed in the statistics of their spectra. Here, we investigate the possibility for the modulus of the high energy eigenfunctions to become uniformly spread over the graph - a property known as quantum ergodicity. A field
theoretical method enables to identify the class of quantum ergodic graphs, and to predict the rate with which quantum ergodicity is obtained.

Abstract:
This seminar deals with integrable models on graphs. After some
motivations for studying such systems, I give the proof of the integrability of
a Calogero model on a star graph (see J.Phys. A 40 (2007) 5491 and
math-ph/0609057). I also discuss its symmetry. In particular, I emphasise the links
with the complex reflection groups and twisted algebra. I finish with
open problems in this quite recent domain of integrable models.

Abstract:
I will discuss several constructions of superalgebras associated to the Killing spinors of a supergravity background, with special emphasis on the ten- and eleven-dimensional supergravities.

Abstract:
Various holographic approaches to QCD in five dimensions are explored using input both from the perturbative five-dimensional non-critical string theory as well as QCD. It is argued that a gravity theory in five dimensions coupled to a dilaton and an axion may capture the important qualitative features of pure YM theory. A part of the effects of higher a'-corrections is resummed into a dilaton potential. The potential is shown to be in one-to-one correspondence with the exact beta-function of QCD, and its knowledge determines the full structure of the vacuum solution. The geometry near the UV boundary is that of AdS5 with logarithmic corrections reflecting the asymptotic freedom of QCD. The IR confining geometries are classified and analyzed. Near the singularity the 't Hooft coupling is driven to infinity. The glueball spectra are gapped and discrete, and they favorably compare to the lattice data. Quite generally, confinement and discrete spectra imply each other. Asymptotically linear glueball masses can also be achieved. Asymptotic mass ratios of various glueballs with different spin also turn out to be universal. Meson dynamics is implemented via space filling D4-anti D4 brane pairs. The associated tachyon dynamics is analyzed and chiral symmetry breaking is shown. The dynamics of the RR axion is analyzed, and the non-perturbative running of the QCD theta-angle is obtained. It is shown to always vanish in the IR. The finite temperature structure is also analyzed and phase diagram is studied. Our preliminary results show a first order deconfining transition to a QGP phase with a transition temperature in agreement with lattice data.