FRG Workshop "Algebraic Geometry, Symplectic Geometry and Theoretical Physics: a conference celebrating the contribution of women researchers", Philadelphia, May 2005







I. Arefeva, Stringy Models of Cosmological Dark Energy
Recent astronomical observations show that the Universe is presently expanding with acceleration. This remarkable discovery suggests that the bulk of energy density in the Universe is gravitationally repulsive and appears like an unknown form of energy (dark energy) with negative pressure. It is believed that a new particle and/or gravitational physics is required to explain the acceleration of of the Universe. There are various phenomenological models of the dark energy but there was not a model based on fundamental principles. I will consider a model for the dark energy which is derived from the string field theory describing the non-BPS brane decay. In this model the acceleration of the Universe is driven by a nonlocal stringy Higgs mechanism.

M. Becker, Flux Compactifications, Cosmology and
the Standard Model of Elementary Particles

In this talk I shall discuss flux compactifications of M-theory and string theory and study their implications for Cosmology, the Standard Model of Elementary Particles and Mathematics.

R. Britto, Singularities of Particle Interactions
Elementary particle interactions are measured by complex functions that are strongly constrained by unitarity. Study of their analytic structure reveals new relations among particle processes. These relations greatly simplify computations and expand our understanding of quantum field theory.

L. Caporaso, Neron models and moduli theory
Neron models are universal objects that have been extensively studied and used in arithmetic algebraic geometry (during the second half of the twentieth century). We introduce them in connection with the moduli theory of curves and indicate some further applications of a more geometric character.

A. Ceresole, Geometric Tools in Supergravity and String Theory
Supergravity, the gauge theory of the SuperPoincare algebra, is the low energy effective field theory of Superstrings. There are many supergravity models depending on the spacetime dimension D, the number N of supersymmetry generators and the coupling to matter multiplets. They are highly constrained by physical, geometrical and algebraic principles. I will illustrate some of these principles, emphasizing the mathematical tools that are guiding our progress towards the understanding of M-theory.

E. Cheung, Strings in gravimagnetic field Closed string theory in Nappi-Witten model--a background of plane-polarized gravitational waves supported by a null NS flux--is proved to be exactly solvable via wakimoto free fields. not only the complete string tree-level interaction amplitudes for the scattering of an arbitrary number of particles can be determined but also the quantum string vertex operators can be constructed explicitly. i will present the classical geodesic and the semi-classical wave-function analysis before introducing the abstract conformal field theory techniques.

A. Degeratu, The Positive Mass Conjecture for Non-Spin Manifolds.
The Positive Mass Conjecture states that the total mass of an asymptotically flat manifold with positive scalar curvature is never negative. For 3-manifolds this was proved first by Schoen and Yau using minimal surfaces techniques. Subsequently, Witten gave another proof based on the properties of the Dirac operator. In this talk I will present the proof of the Positive Mass Conjecture for large classes of asymptotically flat non-spin manifolds. This is joint work with Mark Stern.

X. De la Ossa, Arithmetic of Calabi-Yau Manifolds

L. Dolan, Conformal Operators and Partially Massless Fields

B. Fantechi, On moduli spaces with selfdual obstruction theories
This is joint work in progress with Kai Behrend, UBC Vancouver. Let $X$ be a moduli space; we say that it has an obstruction theory of expected dimension $d$ if at every point $x$ we are given an obstruction space $T^2_xX$ such that $\dim T_xX-\dim T^2_xX=d$. The theory is selfdual if $T^2_xX$ is naturally dual to $T_xX$ (which implies $d=0). This happens for instance to the Donaldson Thomas moduli space of stable sheaves of fixed determinant on a Calabi-Yau 3fold. We prove that being selfdual restricts the possible singularities of $X$. We give some evidence for the following conjectures: 1) such an $X$ can be locally described as zero locus of a closed one-form on manifold $M$; 2) the virtual degree, defined only for $X$ compact, extends to a virtual Euler characteristic defined for arbitrary $X$ and additive over open covers.

Y. Ito, The McKay correspondence
The McKay correspondence shows us a bridge between algebra and geometry for a resolution of quotient singularities. It was observed in dimension two in 1979 mathematically. The generalized McKay correspondence was developed around 1995 based on the results in the superstring theory. After that, Physicists used the correspondence in physically to explain mirror symmetry. Now we can also see some bridges between mathematics and physics. I would like to show you these interesting relations in this talk.

R. Kallosh, Flux vacua and the index of the Dirac operator on the brane

C.C. M. Liu, Marino-Vafa Formula of One-Partition Hodge Integrals
I will describe applications and proof of a formula of Hodge integrals conjectured by Marino and Vafa based on joint works with Kefeng Liu and Jian Zhou.

D. McDuff, Symplectic Geometry: a meeting ground

C. Nappi, Yangians in strings and gauge theories

S. Paban, Evolution of Gravitationally Unstable de Sitter Compactifications

A. Peet, Stringy resolution of spacetime singularities

R. Piene, Counting curves on a surface
To solve a problem in enumerative algebraic geometry: how many geometric objects of a given type satisfy certain given conditions? there are two obvious methods: specializing the objects and/or the conditions so that the answer becomes "obvious" from a combinatorial point of view, or using intersection theory on a suitable parameter space. In this talk the objects will be curves lying on a surface, and I will show how the shape of the generating function for such a problem can be understood via the two methods.

L. Randall, To be confirmed

S. Salur,

N. Saulina, BPS Black Holes,Topological Strings and q-deformed Yang-Mills,
I will first review recent connection between the black hole entropy and the topological string partition sum. Then, I will talk about counting of bound states of BPS black holes on local Calabi-Yau 3-folds involving a Riemann surface of genus g. I will explain how this counting problem reduces to computing q-deformed U(N) Yang Mills partition sum on Riemann surface. Finally, I will demonstrate how in the large N limit this partition sum is expressed in terms of topological string amplitudes.

E. Silverstein, The Uses of Tachyons
General relativity breaks down near singularities and other regions where small features appear in the spacetime geometry. In these regimes, extra degrees of freedom can become important and affect the dynamics of the spacetime. In the framework of string theory, one of the simplest such modes is a string wound around a small circle in the geometry, which can develop a negative mass squared leading to an instability. I will review how the dynamics of such modes provides simple examples of topology changing processes and resolution of conical singurities in spacetime (including ongoing application to spacelike singularities). Although our physical methods of analysis are not mathematically rigorous, it is also interesting to note that the topology changing dynamics has some intriguing similarities to methods used in classifying 3-manifolds (Ricci flows applied to the geometrization conjecture).

M. Symington, Making a smooth torus action symplectic, or almost...
Some of the most powerful tools for understanding the topology of symplectic four-manifolds, in particular the theory of pseudo-holomorphic curves and Lefschetz fibrations, are inspired by complex algebraic geometry. Recent works of Taubes, Donaldson, Auroux and Katzarkov show that these techniques can be generalized to apply to an easily identified class of smooth four-manifolds that includes "almost all" closed manifolds. The manifolds in question are called near-symplectic. The presence of torus actions on a manifold should aid in the determination of moduli spaces of (non-compact) pseudo-holomorphic curves. I will explain this motivation and present a simple classification of toric near-symplectic manifolds in terms of generalized moment map images. This is joint work with David Gay.


Physics Department

Math Department