Venue: Ramanujan Auditorium, Time: 9:30 am to 4:30 pm, Date: 14/3/12.
Romesh K Kaul (IMSc), A P Balachandran (Syracuse University, IMSc), V. Parameswaran Nair (City college of CUNY), R Shankar (IMSc), Suresh Govindarajan (IITM).
|14 March||A P Balachandran||coffee||R K Kaul||Suresh Govindarajan||lunch||V Parameswaran Nair||coffee||R Shankar||coffee|
|THE ABOVE IS A TENTATIVE PROGRAM. EFFORTS WILL BE MADE TO AVOID CHANGES. ALL THE LECTURES WILL BE HELD AT RAMANUJAN AUDITORIUM, IMSc, CHENNAI|
Abstract: Conventional approaches to the emergence of mixed from pure states are based on taking partial traces. This approach has limitations for example in the treatment of fermions and bosons where N-particle pure states contain irreducible multi-particle correlations. A new approach based on states on algebras of observables and their restrictions to subalgebras is presented here. The subalgebra here refers to the subsystem being observed. It agrees with the usual answers for bipartite systems of nonidentical particles, but that is not the case in general. For example there exist two fermion state vectors with Schmidt number 1 for which partial trace gives 1 as entropy. The GNS approach instead gives zero, a very reasonable answer. The GNS approach seems very general and can be applied for example to systems obeying braid statistics.
Romesh K Kaul: Topological Quantum Field Theories: Knots and Links in Three-dimensions and Black Holes in 3+1 Dimensions
Suresh Govindarajan: Aspects of Higher Dimensional Partitions
Abstract: Several combinatorial problems in physics, mathematics and computer science lead to a natural generalisation of the partitions of integers -- these are called higher-dimensional partitions and were first introduced by MacMahon. Two-dimensional or plane partitions have a nice generating function like the one due to Euler for usual partitions. No simple generating function exists for dimensions greater than two. We discuss two aspects of these partitions -- their exact enumeration and their asymptotic behaviour. We show the existence of transforms that show that the problem of exact enumeration becomes somewhat easier than expected. The transforms come with combinatorial interpretations and enable us to compute partitions of all integers <=25 in any dimension. We also discuss the asymptotic behaviour of these partitions focusing on the three-dimensional (solid) partitions for concreteness.
V Parameswaran Nair: The gauge orbit space and mass gap: Considerations from lower dimensions.
Abstract: The topology and geometry of the gauge orbit space (space of physically relevant configurations) are expected to play a crucial role in the question of a nonzero mass gap for Yang-Mills theories. Earlier attempts in developing this point of view were vitiated by the discovery of the so-called spikes. I shall review the spikes and the existence of a volume measure on the gauge orbit space and relate it to the mass gap for 3 dimensional gauge theories. More recent results will also include the extension of these ideas to extended supersymmetric theories.
R Shankar: Topology of incompressible fermionic quantum fluids
Abstract: We will review the use of topology to understand the physics of quantum Hall systems and topological insulators. We then discuss the concept of topological order in an exactly solvable 2-dimensional spin-1/2 model, the Kitaev honeycomb model. Finally we present some results from the ongoing work at IMSc on Hubbard type models which have phases with topological order.