Workshop

on

The geometry and integrability
of topological QFT and string theory



  09:15-10:15 11:00-12:00 14:00-15:00 15:30-16:30  
Mon, March 31
Tue, April 1
conference dinner
Wed, April 2
excursion
excursion
excursion
Thu, April 3
Fri, April 4
drinks and snacks
Sat, April 5
 
 


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 MHodC 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