We study the conditions under which an algebraic curve can be modelled by a Laurent polynomial that is nondegenerate with respect to its Newton polytope. Such nondegenerate polynomials have become popular objects in explicit algebraic geometry, owing to their connection with toric geometry; however, despite their ubiquity, the intrinsic property of nondegeneracy has not seen much detailed study. We prove that every curve of genus $g \geq 4$ over an algebraically closed field is nondegenerate in the above sense. More generally, let $\mathcal{M}_g^{\textup{nd}}$ be the locus of nondegenerate curves inside the moduli space of curves of genus $g \geq 2$. Then we show that $\dim \mathcal{M}_g^{\textup{nd}} = \min(2g+1,3g-3)$, except for $g=7$ where $\dim \mathcal{M}_7^{\textup{nd}} = 16$; thus, a generic curve of genus $g$ is nondegenerate if and only if $g \geq 4$

T-duality has long been well understood locally via the Buscher rules. Global T-duality in the presence of an arbitrary background is much more involved. It relates backgrounds of different topology and can be seen to map 'regular' or commutative geometries to noncommutative ones. I will give a brief overview of these attempts at studying T-duality and show how T-duality acts very naturally in the context of Hitchin's generalized geometry. I will show that T-duality is an automorphism of the Courant bracket in the most general sense and give an example. If time permits, I will discuss applications to Poisson-Lie T-duality.

For nearly 25 years Calabi-Yau spaces have played a central role in string theory, yet no explicit metric was known. I will outline ideas pioneered by Donaldson and Yau that lead to such metrics numerically; then extend this approach to solving the hermitian Yang-Mills equation, and also obtain metrics on moduli spaces. Knowledge of these quantities is unavoidable for physical predictions.

This is the first of a series of lectures on F-theory. The lectures will present the theory of elliptically fibered Calabi-Yau manifolds in considerable detail, explain how these manifolds are used to produce string vacua by means of the ``F-theory'' construction, and how various properties of these string vacua are determined by the corresponding Calabi-Yau manifolds.

I discuss recent work attempting to construct stable vacua of string theory without supersymmetry.

The talk will begin with a review of some recent progress in non-supersymmetric string theory, motivating a careful study of such backgrounds. Many non-supersymmetric closed string theories have negative modes (``tachyons''). I will describe an approach to understanding the result of tachyon condensation using configurations in string theory of effectively negative but finite tension (such as orientifold planes and their S-duals).

One of the most fundamental unresolved questions in particle physics and cosmology is the origin of the cosmic baryon asymmerty, a necessary ingredient for galaxy formation. There are three known conditions for baryogesis, the Sakharov conditions: (1) Baryon number violation; (2) CP, C violation; (3) (1) & (2) must simulatneously occur out of equilibrium with the rest of the universe. Over the last 25 years it has been a challenge to realize these conditions and the precise number (n/s \sim 6.04 \times 10^{-10}) for baryon asymmetry within the framework of the standard model of particle physics and cosmology. In this seminar we show that the baryon asymmetry can be generated, unifying all three Sakharov conditions, during the epoch of cosmic inflation. The Sakharov conditions are realized in one physical proccess, the quantum generation of elliptically polarized gravitons. We further, show that this mechanism is realized concretely and in a compactification independent manner in superstring theory. We construct a Heterotic model of this inflationary baryogenesis mechanism and observationally constrain(postdict) the string length scale from a cosmological observable. Key to this result is the universality of the model independent axion and the Green-Schwarz mechanism. We report on future work w.r.t a heterotic version of the KKLT mechanism via. geometric transistion.

It is proposed that conformality at the TeV scale be used to solve the hierarchy problem and to restrict fields additional to those of the standard model. This idea provides rigid predictions.

The connection between large N gauge theories and string theories is typically made perturbatively. Namely, the Taylor expansion in 1/N corresponds to the genus expansion in string theory. Instanton effects in the gauge theory, however, go like exp(-N) and correspond to non-perturbative effects in the string theory. I will argue, in the context of the N=4 super Yang-Mills theory, how very non-trivial large N non-renormalization theorems in this instanton sector follow simply from the dual string description. The argument assumes little other than the existence of a derivative expansion in string theory. As a particular example, one can explain the striking agreement found by Dorey et al between certain weak coupling instanton calculations and the strong coupling predictions of supergravity.