All talks will take place in room B3.02 of the Mathematics Institute at the University of Warwick.
Murad Alim: Polynomial Structure of the (Open)
Topological String Partition
Function
The polynomial structure of the topological string partition
function found by Yamaguchi and Yau for the quintic is shown to hold for
arbitrary Calabi-Yau manifolds with any number of moduli. Furthermore
the structure is generalized to the open topological string partition
function as discussed by Walcher.
Giulio Bonelli: Observations on
gauge/string correspondence and mirror symmetry
Vincent Bouchard: Open B-model on non-compact
Calabi-Yau threefolds
Andrea Brini: Exact results for topological strings on resolved
Yp,q singularities
Mirror symmetry has been a most powerful tool in the study of
topological string theory away from its geometric phase; the research
in this sense for the case of toric Calabi-Yau threefolds as A-model
target spaces has recently received much impetus. I will show how, for
a large family of such toric CY's, closed-form computation on the
mirror side allow for a detailed analysis of the B-model moduli space
and for a rather straightforward computation of open and closed genus
zero amplitudes beyond the large radius expansion. Applications to
orbifolds and some possible extensions will be described as well.
Vicente Cortes: Aspherical Kähler manifolds with solvable
fundamental group
I will survey recent developments which led to the
solution of the Benson-Gordon conjecture on Kähler quotients of
completely solvable Lie groups and to the classification of compact
aspherical Kähler manifolds with (virtually) solvable fundamental
group up to biholomorphic equivalence. The talk is based on
arXiv:math/0601616.
Duiliu-Emanuel Diaconescu:
Local Donaldson-Thomas Theory via ADHM Sheaves
Ezra Getzler: Deligne-Mumford moduli spaces and Topological
Field Theory
There is a stratification of the Deligne-Mumford moduli space
Mbar(g,n) such that the inclusion of Mbar(g,n)
k into Mbar(g,n) is
k-connected. (This stratification happens to be the same one considered by
Graber and Vakil in their study of the the tautological ring. Also, it is
compatible with the modular operad stucture on Mbar.) There are
generalizations of this result to the G-equivariant case (G a finite group),
to the moduli spaces arising in the study of open/closed topological field
theory, and to the case of moduli spaces of unoriented surfaces. There is
also a variant where Mbar(g,n) is replaced by Mhat(g,n), the real blowup of
Mbar(g,n) along its boundary divisor. (In other words, we remember an angle
at each node.)
For k=1, these theorems give a variant approach to the results of Alexeevski
and Natanzon, Lauda and Pfeiffer, Moore and Segal, Turaev and others, on 2d
TFT. For k=2, they generalize the theorem of Moore and Seiberg (proved by
Bakalov and Kirillov and by Funar and Geica) on modular functors.
Victor Ginzburg: Noncommutative del Pezzo surfaces
Manfred Herbst: Phases of N=2 theories in 1+1 dimensions with
boundary
We consider B-type D-branes in N=2 supersymmetric sigma
models, which describe the internal part of type II string
compactifications to four dimensions. Such theories have a rich phase
structure over Kaehler moduli space. In particular, non-geometric phases
containing Gepner models come along with geometric ones, corresponding
to smooth CY manifolds. We develop an effective tool to transport
D-branes between different phases. In that way we can for instance
relate the derived category of coherent sheaves on a CY-hypersurface to
matrix factorzations of corresponding hypersurface polynomial.
Hiroshi Iritani: Integral structures in quantum cohomology
Ludmil Katzarkov: Generalized HMS for
Fano manifolds
Yukiko Konishi: Higher genus Gromov-Witten invariants of the Grassmannian, and the
Pfaffian Calabi-Yau threefolds
Andy Neitzke: Wall crossing in two and four dimensions
Masa-Hiko Saito: Deligne-Hitchin-Simpson's Twistor space for non-compact case and a
degeneration of Painlevé equations
In this talk, we will discuss about Deligne-Hitchin-Simpson's twistor
space related to the moduli space of λ-connections on a smooth
projective curve with at most regular singularities. From results of
Inaba-Iwasaki-Saito and Inaba, we can obtain good moduli spaces of stable
λ-parabolic connections with regular singularities
with fixed local exponents, as smooth quasi-projective varieties with
canonical holomorphic symplectic structures and natural compactifications.
Varying λ, we obtain a family MHod → C
of moduli spaces over C. The twistor space can be obtained by
patching two copies of this family via Riemann-Hilbert correspondences
twisted by the complex conjugation. We note that the fiber over
λ=0
is the moduli space of parabolic Higgs fields.
Painlevé equations of type VI is obtained by isomonodromic deformations
of linear connections of rank 2 over the projective line with 4-singular
points at {0, 1, t, ∞ }. We will explain
how Painlevé VI equations are degenerating to the
Hitchin's integrable systems in our twistor spaces.
Emanuel Scheidegger:
Topological strings on K3 fibrations
Christian Sevenheck: Twistor structures and singularity theory
Sergey Shadrin: Applications of the Givental group action on
CohFT
Duco van Straten: Classical & Quantum
Integrability
Atsushi Takahashi: Homological Mirror Symmetry of Isolated Hypersurface Singularities
Johannes Walcher: Mirror Symmetry and Extended Holomorphic Anomaly