Physics Around Mirror Symmetry

Physics Around Mirror Symmetry

 

Friday Oct 25, 2013
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Friday Oct 25, 2013
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G_2 manifolds play
the analogous role in M-theory that Calabi-Yau manifolds play in string
theory. There has been work in the physics community on conjectural
"mirror symmetry" in this context, and it has also been observed that
singularities are necessary for a satisfactory theory. After a very
brief review of these physical developments (by a mathematician who
doesn't necessarily understand the physics), I will give a mathematical
introduction to G_2 conifolds. I will then proceed to give a detailed

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Thursday Oct 24, 2013
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Chiral gauge theories in two dimensions with (0,2) supersymmetry admit a
much broader, and more interesting, class of vacuum solutions than
their better studied (2,2) counterparts. In this talk, we will explore
some of the possibilities that are offered by this additional freedom by
including field-dependent theta-angles and FI parameters. The moduli
spaces that will result from this procedure correspond to heterotic
string backgrounds with non-trivial H-flux and NS-brane sources. Along

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Thursday Oct 24, 2013
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Thursday Oct 24, 2013
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Wednesday Oct 23, 2013
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I
will describe a new method for understanding a large class of

generalized complex manifolds, in which we view them as usual

symplectic structures on a manifold with a kind of log structure. I

will explain this structure in detail and explain how it can be used

to prove a Tian-Todorov unobstructedness theorem as well as

topological obstructions for existence of nondegenerate generalized

complex structures.

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Wednesday Oct 23, 2013
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The concept of wall-crossing structure (WCS for short) was introduced
recently in my joint work with Maxim Kontsevich. WCS appear in different
disguises in the theory of Donaldson-Thomas invariants of Calabi-Yau
3-folds, quiver representations,integrable systems of Hitchin type,
cluster algebras, Mirror Symmetry, etc.
I plan to discuss the
definition of WCS and illustrate it in several well-known examples. If
time permits I will speak about a special class of WCS called rational

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Tuesday Oct 22, 2013
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Hermitian matrix models have been used since the early days of 2d
quantum gravity, as generating series of discrete surfaces, and
sometimes toy models for string theory. The single trace matrix models
(with measure dM exp( - N Tr V(M)) have been solved in a 1/N expansion
in the 90s by the moment method of Ambjorn et al. Later, Eynard showed
that it can be rewritten more intrinsically in terms of algebraic
geometry of the spectral curve, and formulated the so-called topological
recursion.

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Tuesday Oct 22, 2013
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I will review some ongoing work on the low energy properties of D-branes/boundary conditions in massive two-dimensional field theories with (2,2) supersymmetry.

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