| Lara Anderson. | Heterotic and F-theory Compactifications and Geometry
| We systematically analyze a broad class of dual heterotic and
F-theory models that give rise to six- and four-dimensional supergravity
theories, and compare the geometric constraints on the two sides of the
duality. In this talk we will demonstrate that both theories together
give new insight into the space of possible effective theories arising
from string theory. We will describe recent explicit constructions of
all dual F-theory/heterotic pairs in a broad class and discuss aspects
of G-flux in F-theory.
|
| Katrin Becker. | M-theory and G_2 manifolds | This is an
introduction to M-theory which is a theory of quantum gravity. It unifies
general relativity with quantum field theory. M-theory includes besides
all string theories eleven-dimensional supergravity. In a Kaluza and Klein
approach to unification, a four-dimensional theory can be obtained by
assuming the additional seven dimensions to be small and compact. Unbroken
supersymmetry requires that the seven dimensional manifold admits a G2
holonomy metric. We will discuss how these classical solutions become
solutions of the quantum theory.
|
| Melanie Becker. | The alpha' Expansion of Calabi-Yau Compactifications
| We consider alpha' corrections to Calabi-Yau compactifications
of string theory. These were discussed many years ago in terms of
non-linear sigma models by Nemeschansky and Sen. Using the effective
field theory approach we show that SU(3) holonomy manifolds become SU(3)
structure manifolds once such corrections are included.
|
| Jonathan Heckman. | Higher Derivative Holography, E-strings, and a 6D
Conformal Anomaly | In this talk we show how to use a recently
proposed formula for the conformal anomaly a_{6D} of 6D superconformal
field theories to probe the structure of higher derivative corrections
to 11D supergravity in the presence of non-trivial four-form fluxes and
a Horava-Witten 9-brane.
|
| Sheldon Katz. | The partition function of elliptically fibered
Calabi-Yau threefolds and Jacobi forms | I give evidence that the
all genus amplitudes of topological string theory on compact elliptically
fibered Calabi-Yau manifolds can be written in terms of meromorphic Jacobi
forms whose weight grows linearly and whose index grows quadratically
with the base degree. This talk is based on joint work with Albrecht
Klemm and Minxin Huang.
|
| Siu-Cheong Lau. | Modular properties of SYZ mirrors | In this
talk we will construct the SYZ mirrors of certain infinite-type toric
Calabi-Yau manifolds and their quotients, and investigate their properties
under modular transformations of the global moduli. We will also study
the generalized SYZ mirrors of elliptic curve quotients. While an SYZ
mirror is a priori defined over a formal neighborhood around the large
volume limit, the study in all these cases suggests that it is indeed
the tip of the iceberg over the global moduli space.
|
| Bong Lian. | Differential zeros of generalized hypergeometric
functions | I will discuss a new way to compute zero locus
of certain differential polynomials of period integrals of families
of algebraic varieties, including Calabi-Yau and general type
hypersurfaces in a G-space. These zero locus generalizes zeros of
classical hypergeometric functions in one variable. The method is based
on a new algebraic description of Picard-Fuchs systems for the period
integrals, and generalized hypergeometric functions in particular. The
talk is based on joint work with J. Chen, A. Huang, S.-T. Yau, and X. Zhu.
|
| Laura Schaposnik. | Higgs bundles, branes, and applications.
| Higgs bundles (introduced by N. Hitchin in 1987) are
pairs of holomorphic vector bundles and holomorphic 1-forms taking
values in the endomorphisms of the bundle. The moduli space of Higgs
bundles carries a natural Hyperkahler structure, through which we
can study A-branes (Lagrangian subspaces) or B-branes (holomorphic
subspaces) with respect to each structure. We shall begin the talk by
first introducing Higgs bundles for complex Lie groups and the associated
Hitchin fibration, and recalling how to realize Langlands duality through
spectral data. We will then look at a natural construction of families
of subspaces which give different types of branes, and explain how the
topology of some of these branes can be completely determined via the
monodromy action of the Hitchin system. Finally, we shall give some
applications of the above approaches in relation to Langlands duality
and the study of character varieties. Some of the work presented during
the talk is in collaboration with David Baraglia (Adelaide).
|
| Paul Seidel. | Fukaya categories and the enumerative geometry of
Lefschetz pencils | I will describe the conjectural interplay
between Fukaya categories of Lefschez fibrations and mirror maps for
Calabi-Yau hypersurfaces.
|
| Nick Sheridan. | Counting curves using the Fukaya category |
In 1991, string theorists Candelas, de la Ossa, Green and Parkes made a
startling prediction for the number of curves in each degree on a generic
quintic threefold, in terms of periods of a holomorphic volume form on a
`mirror manifold'. Givental and Lian, Liu and Yau gave a mathematical
proof of this version of mirror symmetry for the quintic threefold
(and many more examples) in 1996. In the meantime (1994), Kontsevich
had introduced his `homological mirror symmetry' conjecture and stated
that it would `unveil the mystery of mirror symmetry'. I will explain
how to prove that the number of curves on the quintic threefold matches
up with the periods of the mirror via homological mirror symmetry. I
will also attempt to explain in what sense this is `less mysterious'
than the previous proof.
|
| Cumrun Vafa. | Topological Strings and Black Holes | We
discuss the connection between topological string on elliptic Calabi-Yau
three folds and 5-dimensional spinning black holes. Recent results,
using insights from the structure of meromorphic Jacobi forms, lead to
unexpected new insights about spinning black holes.
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