## John Voight : On Moduli of Nondegenerate Curves

- String Theory ( 244 Views )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 $g \geq 4$

## Anja Sturm : Coexistence and convergence for voter model with selection

- String Theory ( 238 Views )We consider variations of the usual voter model, which favor types that are locally less common. Such voter models with selection are dual to systems of branching annihilating random walks that are parity preserving. We consider coexistence of types in the voter models which is related to the survival of particles in the branching annihilating random walk. We find conditions for the uniqueness of a homogeneous coexisting invariant law as well as for convergence to this law from homogeneous and coexisting initial laws. For a particular one dimensional model we also show a complete convergence result for any initial condition. This is based on comparison with oriented percolation of the associated branching annihilating random walk.

## Lenya Ryzhik : How an incompressible flow helps diffusion to mix things

- String Theory ( 237 Views )I will describe some recent results that concern various aspects of the mixing properties of a strong incompressible flow acting together with a diffusion. In particular, we will discuss the short-time decay of solutions of the corresponding initial value problem, asymptotics of the principle Dirichlet eigenvalue and the behavior of the explosion threshold in the Zeldovich problem when the incompressible flow is strong. When the flow is prescribed, the "enhancement" of these characteristics comes from the geometric properties of the flow. We will also show that flows arising from the Stokes-Bousisnesq problems possess these "enhancement" features.

## Josh Garretson : T-duality and Generalized Geometry

- String Theory ( 230 Views )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.

## Robert Karp : A convex optimization problem in string theory

- String Theory ( 229 Views )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.

## Mainak Patel : Temporal Binding Emerges as a Rapid and Accurate Encoding Tool Within a Network Model of the Locust Antennal Lobe

- String Theory ( 224 Views )The locust olfactory system interfaces with the external world through antennal receptor neurons (ORNs), which represent odors in a distributed, combinatorial manner. ORN axons bundle together to form the antennal nerve, which relays sensory information centrally to the antennal lobe (AL). Within the AL, an odor produces a stimulus-specific temporal progression of neuronal spiking, inspiring the hypothesis that the AL encodes odors through dynamically evolving ensembles of active cells. Such a coding strategy, however, requires higher olfactory centers to integrate a prolonged dynamic profile of AL signals prior to stimulus assessment, a process that is likely to be slow and inconsistent with the generation of quick behavioral responses. Our modeling work has led us to propose an alternate hypothesis: the dynamical interplay of fast and slow inhibition within the locust AL induces transient correlations in the spiking activity of an odor-dependent neural subset, giving rise to a temporal binding code and allowing rapid stimulus detection by downstream elements.

## Mark Jackson : Superstring Cosmology: New Physics in the Sky

- String Theory ( 222 Views )Striking advances in observational cosmology over the past two decades have ushered in a golden era in cosmology, where our focus has turned from what the universe is made of to why it has the form we observe. The leading theory capable of answering such a question, Superstring Theory, does not appear capable of being tested using conventional accelerator-based experiments, forcing us to be more creative in our goal to verify or dismiss it. Focusing on brane inflation as a string theory-inspired model of inflationary cosmology, I will review how the cosmic microwave background (CMB) will provide a deluge of high- precision data into otherwise inaccessible energy scales. These data include possible "Transplanckian" signatures in the power spectrum, indications of variable sound speed or extra dimensions in non- Gaussianity, or constraining the inflation model parameter space using polarization. I then describe how the production of cosmic (super)strings in brane inflation would provide an additional means to verify superstring theory, and which would yield much detailed information about the underlying theory parameters.

## Ronen Plesser : `Toric duality is Seiberg duality

- String Theory ( 31 Views )We study four N=1 SU(N)^6 gauge theories, with bi-fundamental chiral matter and a superpotential. In the infrared, these gauge theories all realize the low-energy world-volume description of N coincident D3-branes transverse to the complex cone over a del Pezzo surface dP_3 which is the blowup of P^2 at three generic points. Therefore, the four gauge theories are expected to fall into the same universality class--an example of a phenomenon that has been termed "toric duality." However, little independent evidence has been given that such theories are infrared-equivalent. In fact, we show that the four gauge theories are related by the N=1 duality of Seiberg, vindicating this expectation. We also study holographic aspects of these gauge theories. In particular we relate the spectrum of chiral operators in the gauge theories to wrapped D3-brane states in the AdS dual description. We finally demonstrate that the other known examples of toric duality are related by N=1 duality, a fact which we conjecture holds generally.

## Eva Silverstein : An Approach to Tachyon Dynamics in Closed String Theory

- String Theory ( 29 Views )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).

## Albion Lawrence : D-Branes on Calabi-Yau Threefolds

- String Theory ( 26 Views )D-branes on Calabi-Yau threefolds are interesting both as alternative probes of quantum geometry, and as nontrivial realizations of gauge theories with four supercharges. Of course, these issues are not independent. In this talk I will briefly discuss the former by describing and characterizing D-brane states at the Gepner point in the moduli space of the quintic. I will then use such D-branes to realize d=4 N=1 SUSY gauge theories, and discuss the computation of the superpotential of these theories, particularly for those realized by D6-branes wrapped around special Lagrangian submanifolds of the threefold. I will close with some speculations on the implications of mirror symmetry for these superpotentials.

## Rajesh Gopakumar : exp(N)

- String Theory ( 25 Views )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.