April 11, 2019
TITLE: Hidden Sectors and Associated Physics — Supersymmetry Breaking, Dark Matter, de Sitter Vacuum
ABSTRACT: Compactifications on G2 manifolds lead to theories that describe the world well. As we understand G2 manifolds better we can test and improve this situation. Hidden sectors generically accompany G2 manifolds, and in turn lead to important physics – in particular supersymmetry breaking, De Sitter vacua, and candidates for the dark matter of the universe.
Slides of Lecture
- 4/08/2019: K3 Metrics from Little String Theory
April 8, 2019
TITLE: K3 Metrics from Little String Theory
ABSTRACT: I explain how one can find formulae for Ricci flat metrics on K3 surfaces by using data about the BPS spectrum of an auxiliary (compactified) little string theory. Well known approximations to such metrics, like the semi-flat approximation and the Gross-Wilson metric, arise as limits of this formalism.
April 12, 2019
TITLE: F-Theory and Spin7 Manifolds
We discuss some recent progress in understanding 4D vacua obtained from F-theory on Spin(7) manifolds. Such backgrounds provide a potentially attractive way to avoid fine-tuning to cancel zero point energies. We present a general proposal for cosmological solutions in this framework, and also develop the physical formalism of local Spin(7) geometries containing a four-manifold of ADE singularities.
Based on work with C. Lawrie, L. Lin, and G. Zoccarato, hep-th/1811.01959
and C. Lawrie, L. Lin, J. Sakstein and G. Zoccarato, hep-th/1901.10489.
January 9, 2019
TITLE: Prime Fano 3-folds and BN-general K3s
ABSTRACT: Fano 3-folds with 2nd Betti number one are classified into 17 deformation types. The anti-canonical degree 2g-2 and the 3rd Betti number 2p are their basic numerical invariants. The sum g+p varies from 12 to 54, and the minimum 12 is attained in 3 cases. In this talk I will explain the linear section theorem in the case (g,p)=(10,2): a prime Fano 3-fold of g=10 is obtained from the (5-dimensional) G2-adjoint variety by taking hyperplane section p=2 times. The basic tool is a rigid, or spherical, vector bundle on a K3 surface S in the anti-canonical linear system. The key property of S used in the proof is the BN-genericity.
- 01/07/2019: Polarized tropical manifolds and Lagrangian torus fibrations
- 01/09/2019: Conifold transitions and deformations of polarized tropical manifolds
January 7, 2019
TITLE: Polarized tropical manifolds and Lagrangian torus fibrations
ABSTRACT: I will review the notion of polarized tropical manifolds which are the basic combinatorial objects in the Gross-Siebert program. These can be viewed as the basis of a Lagrangian torus fibration on a symplectic Calabi-Yau manifold, but via the Legendre tranfsform they also provide the starting data for the reconstruction of the mirror family using the Gross-Siebert algorithm.
January 9, 2019
TITLE: Conifold transitions and deformations of polarized tropical manifolds
ABSTRACT: Conifold singularities have a nice description in terms of polarized tropical manifolds. I will describe a result where the obstructions to the existence of symplectic resolutions (Smith-Thomas-Yau) and of the complex smoothings on the mirror (Friedman-Tian) can be both read in terms of certain tropical cycles. This suggests an approach, via the Gross-Siebert program, to Morrison’s Conjecture stating that the mirror of a resolution is a smoothing of the mirror. In a joint work with Helge Ruddat this idea leads to the notion of a deformation of a polarized tropical manifold induced by a tropical cycle.
April 9, 2019
TITLE: Selected topics about 5d theories and geometry
January 11, 2019
TITLE: Aspects of 5d SCFTs and their gauge theory phases
ABSTRACT: In this talk I will revist the geometric engineering of five-dimensional supersymmetric conformal field theories (SCFTs) in M-theory after Intrilligator, Morrison and Seiberg. This esablishes a conjectural bijection assigning to each local isolated Calabi-Yau three-fold singularity a five-dimensional superconformal field theory and viceversa. Focusing on the toric case, I will discuss applications of IIA/M-theory fiberwise duality (i.e. a peculiar instance of collapse) to characterizing the possible gauge theory phases of these systems. This geometric setup clarifies the notion of “UV duality” for such theories. Along the way, I will provide a novel gauge theoretical expression for the 5d prepotential, accounting correctly for the 5d parity anomaly. Based on the preprint arXiv:1812.10451, with Cyril Closset and Vivek Saxena.
January 8, 2019 and January 9, 2019
TITLE: The essential skeleton of a Calabi-Yau degeneration
ABSTRACT: To any meromorphic degeneration of complex projective varieties corresponds a projective variety over the field of Laurent series, and hence a non-Archimedean analytic space in the sense of Berkovich. This applies in particular to a degeneration of polarized Calabi-Yau manifolds, and has been used in recent years by Nicaise, Xu and their collaborators to approach a version of the Ströminger-Yau-Zaslow conjecture due to Kontsevich-Soibelman. I will provide a gentle introduction to this circle of ideas, mostly based on a joint work with Jonsson, in which the limit of Calabi-Yau volume forms in the associated Berkovich space is analyzed.