On Some Developments in Non-local Field Theory

Some Developments in Ramsey Theory

Ramsey Theory is a part of combinatorial mathematics that studies the behaviour of structures under partitions. Many Ramsey type results assert that complete disorder is impossible they find some regular substructures in general combinatorial structures. Generic results are due to F.P. Ramsey [R3] and B.L. van der Waerden [V]. The systematic study of these and related statements was initiated b...

Recent Developments in Non-perturbative Quantum Field Theory

In the last couple of years we have been witnessing a series of impressive results in the framework of two different but related types of quantum theories: supersymmetric Yang–Mills theories in four dimensions and superstrings. They have in common space-time supersymmetry. They also share the property that a formal perturbative expansion can be defined for these theories, and “renormalization” ...

Developments in Random Field Theory

Random field theory is used in the statistical analysis of SPM’s whenever there is a spatial component to the inference. Most important is the question of detecting an effect or activation at an unknown spatial location. Very often we do not know in advance where to look for an effect, and we are interested in searching the whole brain, or part of it. This presents special statistical problems ...

Some Recent Developments in Additive Number Theory

Some Recent Developments in Chiral Perturbation Theory∗

The first part of this talk concerns the application of chiral perturbation theory (CHPT) at unphysical quark masses. More precisely, lattice QCD (LQCD) allows one in principle to calculate hadronic matrix elements ab initio using capability computing on a discretized space-time. To connect to the real world, various extrapolations are necessary: LQCD operates at a finite volume V , at a finite...