We present calculations for the effective action of string world sheet in R 3 and R 4 utilizing its correspondence with the constrained Grassmannian σ-model. Minimal surfaces describe the dynamics of open strings while harmonic surfaces describe that of closed strings. The one-loop effective action for these are calculated with instanton and anti-instanton background, representing N-string inte...

The goal of this seminar is to understand the Nekrasov partition function introduced by Nekrasov in 2003 [Nek03]. This is a generating function for correlation functions in an N = 2 supersymmetric gauge theory, so my goal today is to explain what N = 2 gauge theory is and why we might find it interesting. We begin with the latter question, why is this interesting? There are two intertwined answ...

We introduce a core-based stability concept for networks with widespread externalities. The model is a generalisation of the recursive core for partition function form games. We present a simple example of a favour network and show that the core is nonempty when players must pay transfers to intermediaries. This simple setting also models economic situations such as airline networks. Subject cl...

Improving on some results of J.-L. Nicolas [15], the elements of the set A = A(1+ z+ z + z + z), for which the partition function p(A, n) (i.e. the number of partitions of n with parts in A) is even for all n ≥ 6 are determined. An asymptotic estimate to the counting function of this set is also given.

All of the thermodynamic information on a statistical mechanical system is encoded in the locus and density of its partition function zeroes. Recently, a new technique was developed which enables the extraction of the latter using finite-size data of the type typically garnered from a computational approach. Here that method is extended to deal with more general cases. Other critical points of ...

In celebration of G.E. Andrews' 60 th birthday.

Abstract We use Fermi coordinates to calculate the canonical partition function for an ideal gas in a circular geodesic orbit in Schwarzschild spacetime. To test the validity of the results we prove theorems for limiting cases. We recover the Newtonian gas law subject only to tidal forces in the Newtonian limit. Additionally we recover the special relativistic gas law as the radius of the orbit...

We prove that the open topological string partition function on aD-brane configuration in a Calabi-Yau manifoldX takes the form of a closed topological string partition function on a different Calabi-Yau manifold Xb. This identification shows that the physics of D-branes in an arbitrary background X of topological string theory can be described either by open+closed string theory in X or by clo...

It has been recently pointed out that a definition of the geometric entropy using the partition function in a conical space does not in general lead to a positive definite quantity. For a scalar field model with a non-minimal coupling we clarify the origin of the anomalous behavior from the viewpoint of the canonical formulation.

We derive the dominant asymptotic form and the order of the correction terms of the finite-perimeter partition function of self-avoiding polygons on the square lattice, which are weighted according to their area A as q, in the inflated regime, q > 1. The approach q → 1+ of the asymptotic form is examined.