Talks

I will describe antiferromagnets and superconductors near quantum phase transitions. There is a remarkable analogy between their dynamics and the holographic description of Hawking radiation from black holes. I will show how insights from this analogy have shed light on experiments on the cuprate high temperature superconductors.

I will show how to construct very general ERG equations, and will use this as the starting point for a discussion of Polchinski\'s equation and its cousins. I will introduce diagrammatics and an associated universal calculus, which will be illustrated with a simple calculation.

The dynamics of particles moving in a medium defined by its relativistically invariant stochastic properties is investigated. For this aim, the force exerted on the particles by the medium is defined by a stationary random variable as a function of the proper time of the particles. The equations of motion for a single one-dimensional particle are obtained and numerically solved. A conservation law for the drift momentum of the particle during its random motion is shown. Moreover, the conservation of the mean value of the total linear momentum for two particles repelling each other according to the Coulomb interaction also follows. Therefore, the results indicate the realization of a kind of stochastic Noether theorem in the system under study.

We introduce a formalism allowing us to localize a certain class of theories with an infinite number of derivatives (nonlocal), which include effective actions of string field theory. The number of degrees of freedom is finite and the Cauchy problem, Hamiltonian and quantization are all well-defined. As applications, the rolling tachyon of cubic string field theory and some cosmological toy models are considered.

Geometries produced by brane intersections preserving eight supercharges are constructed. Typical examples of such configurations are given by fundamental strings ending on D branes and by brane webs. Consistency conditions of supergravity are shown to impose certain requirements on the locations of the sources, and these restrictions are found to be in a perfect agreement with results of the probe analysis. This agreement serves as a nontrivial test of the duality between open and closed strings. Some applications to AdS/CFT correspondence are also discussed.

Graphene, a single atomic layer of graphite, was created only a few years ago. It is a remarkable system, whose law energy effective theory has a lot in common with relativistic 2 + 1 dimensional ones. Graphene allows tabletop experiments for observing nonperturbative relativistic phenomena, most notably spontaneous chiral symmetry breaking both in vacuum and in an external magnetic field. The latter is in turn crucial for the dynamics of Quantum Hall effect in this system. I will review the basic physics and the latest results obtained both in the experimental studies and the theory of graphene.

In this lecture, I will discuss Wilson's picture of renormalization and its relation to the Exact Renormalization Group (ERG). In particular, I will focus on how one can understand, in a physically intuitive way, what it is for a quantum field theory to be nonperturbatively renormalizable.

F-theory compactifications on Calabi-Yau fourfolds provide one way to obtain N=1 supersymmetric grand unified models of particle physics from string theory. With this motivation in mind, I will consider F-theory on a particularly simple class of local Calabi-Yau fourfolds, for which a low-energy analysis based upon topological gauge theory is valid. For these models, I will explain how the geometry of the fourfold determines the spectrum of massless charged matter and the effective superpotential in four dimensions. If time permits, I will also discuss the relation between certain surface operators in gauge theory and brane recombination in F-theory.