Triangle Seminars

Abstract:
After a brief introduction to the basic concepts of
entanglement in discrete and continuous systems
I will outline various results of our recent work in these
areas. In particular, I will present a scaling relation
for the entanglement of a subsystem with respect
to the rest of the lattice in the size of the regions.

Abstract:
We shall discuss aspects of how internal manifolds evolve during cosmology, paying particular attention to the regions where the manifold changes topology.

Abstract:
I will present an overview over work on the construction of Baxter's Q-operator. The latter is a an auxiliary tool in diagonalizing the Hamiltonian of integrable spin-chains. This is an alternative approach to the Bethe ansatz and has several advantages over the latter. I will highlight the representation theoretic construction of the Q-operator and discuss how this approach leads to a difference equation (called the quantum Wronskian) which is sufficient to determine the spectrum of the spin-chain Hamiltonian. In contrast to the Bethe ansatz equations which are of polynomial order (= number of sites of the chain) the quantum Wronskian leads to a system of quadratic equations. I will also briefly discuss how the Q-operator allows for an alternative description of the trace functional used in the recent discussion of correlation functions by Boos, Jimbo, Miwa, Smirnov and Takeyama.

Abstract:
The random planar curves that occur, for example, as the boundaries of spin clusters in the Ising model or of percolation clusters in two dimensions have the special property of being conformally invariant in the scaling limit. I describe a new approach, called tochastic Loewner evolution (SLE), to describing the measure on such curves and to computing many of their properties.

Abstract:
TBA

Abstract:
Mary Cartwright lecture of the London Mathematical Society.

Abstract:
Mary Cartwright lecture of the London Mathematical Society.