Week 1

  1. On Monday 10th at 10:00,
    Sven Krippendorf
    GANs for generating EFT models
    Abstract: In this talk I present recent work on generating novel models by the computer, satisfying both experimental and theoretical constraints. In particular, I present a framework which allows the generation of effective field theories. We use Generative Adversarial Networks (GANs) to generate these models and we generate examples which go beyond the examples known to the machine. As a starting point, we apply this idea to the generation of supersymmetric field theories. In this case, the machine knows consistent examples of supersymmetric field theories with a single field and generates new examples of such theories. In the generated potentials we find distinct properties, here the number of minima in the scalar potential, with values not found in the training data. I comment on potential further applications of this framework, particularly interesting for string model building and compactifications of string theory.

  2. On Monday 10th at 14:00,
    James Gray
    Aspects of F-theory from CICYs
    Abstract: I will review some recent work describing both multiple fibration and multiple fiber structures in F-theory. The discussion will be illustrated throughout with concrete examples based upon Calabi-Yau manifolds described as simple complete intersections in products of projective spaces.

  3. On Tuesday 11th at 10:00,
    David Andriot
    Classical de Sitter solutions, dimensional reduction and the swampland
    Abstract: I will first discuss the search for a controlled stringy de Sitter vacuum, and the related swampland criterion, in the present cosmological context. I will then review the most recent constraints on 10d classical de Sitter solutions. I will finally connect to the required study of dimensional reductions on curved manifolds (e.g. group manifolds). I will present the spectrum of the Laplacian and various truncations on a nilmanifold.

  4. On Tuesday 11th at 14:00,
    Antonella Grassi
    Singularities in F-theory
    Abstract: I will discuss recent results about F-theory compactified on elliptic varieties with singularities. I will also discuss the extension of Kodaira's classification of singular fibers on elliptic surfaces to higher dimension and applications.

  5. On Wednesday 12th at 10:00,
    Lara Anderson
    Heterotic/Heterotic and Heterotic/F-theory Duality
    Abstract: I will review some recent progress on understanding dualities of heterotic string compactifications (inherited from target space dualities of (0,2) GLSMs) and the consequences of these for heterotic/F-theory duality.

  6. On Wednesday 12th at 14:00,
    Fabian Ruehle
    Calabi-Yau Manifolds and SU(3) Structure
    Abstract: Compactifications of string theory most commonly considered are on Calabi-Yau manifolds. Nevertheless, backreactions of the string background can require compactification on an SU(3) structure manifold rather than a Calabi-Yau manifold. In this talk, we explain how to construct a large class of SU(3) structure manifolds relevant for string theory. Starting from Complete Intersection Calabi-Yau manifolds, we show that all these manifolds carry a Strominger-Hull system, which is relevant for Heterotic and Type II string theory. These constructions allow us to study string compactifications for which the metric is known explicitly and analytically.

  7. On Thursday 13th at 10:00,
    Gil Cavalcanti
    Lefschetz fibrations and symplectic structures.
    Abstract: I will recall the near correspondence between symplectic structures and Lefschetz fibrations proved by Gompf and Donaldson. Then I will introduce log-symplectic structures and stable generalized complex structures, explain how they share many features of symplectic manifolds and how the existnece of Lefschetz fibrations-like maps induces these structures on certain manifolds. This allows us to produce many examples for which we have a concrete handle on the geometric structure.

  8. On Thursday 13th at 14:00,
    Magdalena Larfors
    Instanton corrections to M theory on G2 manifolds
    Abstract: In this talk, I will discuss non-perturbative corrections to the superpotential of M theory compactified on certain twisted connected sum (TCS) G2 manifolds. The corrections arise from M2 instantons on infinitely many inequivalent three-cycles, which are conjectured to be associative. To reach this conclusion, we use a recently conjectured duality chain between M theory on G2 manifolds, the E8xE8 heterotic string compactified on the split bicubic and F theory on a K3 fibered Calabi Yau fourfold. The latter is known to have an infinite number of instanton corrections that we trace through the duality chain back to the G2 compactification.

  9. On Thursday 13th at 16:00,
    Andrei Constantin
    Formulae for Line Bundle Cohomology on Calabi-Yau Threefolds
    Abstract: I discuss about the existence of closed form expressions for the ranks of all cohomology groups of holomorphic line bundles on Calabi-Yau threefolds realised as complete intersections in products of projective spaces. The formulae have been obtained by systematising and extrapolating concrete calculations on several manifolds and they have been checked computationally. Although the intermediate calculations often involve laborious computations of ranks of Leray maps in the Koszul spectral sequence, the final results for cohomology follow a simple pattern. The space of line bundles can be divided into several different regions, and in each such region the ranks of all cohomology groups can be expressed as polynomials in the line bundle integers of degree at most three. The number of regions increases and case distinctions become more complicated for manifolds with a larger Picard number. We also find explicit cohomology formulae for several non-simply connected Calabi-Yau threefolds realised as quotients by freely acting discrete symmetries. More cases may be systematically handled by machine learning algorithms.

  10. On Friday 14th at 10:00,
    Mohamed Elmi
    Attractor Points and Zeta Functions

    On Friday 14th at 10:30,
    Callum Brodie
    NS5-branes and Line Bundle Models in Heterotic/F-Theory Duality

  11. On Friday 14th at 14:00,
    Tristan Hubsch
    Evidence for Infinitely Diverse Non-Convex Mirrors
    Abstract: Calabi-Yau hypersurfaces in non-Fano varieties are now a little over three years young, their toric siblings a year younger. Their defining polynomials include rational monomials, and are encoded by non-convex polytopes. Nevertheless, the phases of the corresponding gauged linear sigma models and an increasing number of their classical and quantum characteristics are found to be just as computable. This survey will focus on Batyrev-Hodge numbers, transposition mirror models and discriminants, eying also Yukawa couplings and other results within reach. Showcasing Calabi-Yau hypersurfaces in Hirzebruch n-folds shows this class of constructions to be infinitely vast, with infinite diversity for string theory.

    Week 2

    1. On Monday 17th at 10:00,
      Burt Ovrut
      Supersymmetric Higgs-Sneutrino Inflation and Reheating
      Abstract: It is shown that in the phenomenologically realistic supersymmetric B − L MSSM theory, a linear combination of the neutral, up Higgs field with the third family left-and right-handed sneutrinos can play the role of the cosmological inflaton. Assuming that supersymmetry is softly broken at a mass scale of order 10^13 GeV, the potential energy associated with this field allows for 60 e-foldings of inflation with the cosmological parameters being consistent with all Planck2015 data. The theory does not require any non-standard coupling to gravity and the physical fields are all sub-Planckian during the inflationary epoch. It will be shown that there is a “robust” set of initial conditions which, in addition to satisfying the Planck data, simultaneously are consistent with all present LHC phenomenological requirements. The theory of perturbative reheating in the Sneutrino-Higgs cosmology of the B-L MSSM is presented.

    2. On Monday 17th at 14:00,
      Anthony Ashmore
      Moduli and obstructions of N=1 heterotic backgrounds
      Abstract: A recurring problem in heterotic compactifications is the plethora of moduli fields in the resulting low-energy theories which we do not observe in nature. One might be able to lift these moduli by moving to non-Kahler compactifications. The general N=1 heterotic solution with a 4d Minkowski vacuum is described by the Strominger system. The compactification manifold is non-Kahler, there is H flux and one has a non-trivial Bianchi identity to deal with. The moduli of these solutions has been a mystery until recently. I will present work on understanding the moduli of these compactifications to higher orders using the heterotic superpotential. Obstructions to integrating the deformations appear as non-zero Yukawa couplings in the low-energy theory. I will also comment on links to generalised geometry and a generalisation of Kodaira-Spencer gravity.

    3. On Tuesday 18th at 10:00,
      Mario Garcia-Fernandez
      Canonical metrics on holomorphic Courant algebroids
      Abstract: The solution of the Calabi Conjecture by Yau implies that every Kähler Calabi-Yau manifold X admits a metric with holonomy contained in SU(n), and that these metrics are parametrized by the positive cone in H^2(X,R). In this talk I will give evidence of an extension of Yau's theorem to non-Kähler manifolds, where X is replaced by a compact complex manifold with vanishing first Chern class endowed with a holomorphic Courant algebroid Q. The equations that define our notion of "best metric" are motivated by generalized geometry, and correspond to a mild generalization of the Hull-Strominger system. The role of the second cohomology is played by an affine space of "Aeppli classes", naturally associated to Q via secondary holomorphic characteristic classes defi ned by Donaldson. As applications, we will uncover the fundamental degrees of freedom of a heterotic flux compactification with even dimensional internal manifold, and propose a new class of such compactifications with very small moduli. Joint work with R. Rubio, C. Shahbazi and C. Tipler arXiv:1803.01873, arXiv:1807.10329.

    4. On Tuesday 18th at 14:00,
      Chris Hull
      Non-geometric Calabi-Yau Backgrounds in String Theory
      Abstract: String theory duality symmetries can be used to glue together different patches of a solution to construct what have been called ‘non-geometric spaces’; these can be good solutions of string theory even though they would not be allowed in supergravity. In this talk, some recent work with Israel and Sarti will be described that constructs non-geometric analogues of Calabi-Yau manifolds in which patches are glued together with mirror symmetry transformations to construct a ‘mirrorfold'. These solutions preserve the same amount of supersymmetry as Calabi-Yau spaces, but typically have far fewer light moduli and so lead to models with far fewer light particles. .

    5. On Wednesday 19th at 10:00,
      Ruben Minasian
      GCG beyond supergravity
      Abstract: I will review the relations between string/ M-theory corrections and GCG.

    6. On Wednesday 19th at 14:00,
      Marc-Antoine Fiset
      G-structure symmetries and anomalies in (1,0) non-linear sigma-models
      Abstract: A new symmetry of (1,0) supersymmetric non-linear sigma-models in two dimensions with a Fermi sector will be discussed. It is a generalisation of the so-called special holonomy W-symmetry of Howe and Papadopoulos associated with structure group reductions of the target space M. This symmetry allows in particular non-trivial flux and instanton-like connections on vector bundles over M. Time permitting, I will also explain how to derive from the quantum effective action a corrected version of this symmetry. This result should find interesting applications in worldsheet approaches to heterotic compactifications at first order in α′. Based on joint work with Xenia de la Ossa.

    7. On Wednesday 19th at 16:00,
      David Tennyson
      Exceptional Complex Structures and Their Deformations
      Abstract: It is interesting to study a particular substructure of Exceptional Calabi-Yau structures, i.e. backgrounds preserving 8 supercharges, defined by just the (unweighted) J_{3} tensor. We have called these geometries Exceptional Complex Structures (ECS). Here I will define what these structures are, provide a few key properties and give a definition of integrability. I will also explore their linear deformations up to generalised diffeomorphisms. It turns out that there is a natural differential defined by the ECS whose cohomology controls these deformations, provided this differential satisfies a particular property that I will outline. Finally, I will give an explicit example of deformations of conventional Calabi-Yau's.

    8. On Thursday 20th at 10:00,
      Jock McOrist
      The Universal Geometry of Heterotic Vacua.
      Abstract: This talk is about derivatives. We describe how gauge covariance leads to a construction of a universal bundle for the moduli space of four-dimensional heterotic vacua. The resulting geometry unifies tensors for the heterotic theory with tensors on the moduli space. Deformation theory, replete with all its complicated algebraic relations, is recast in terms of simple tensor equations. The surprising fact is that this is a useful thing to do.

    9. On Thursday 20th at 14:00,
      Dave Morrison
      Limits of K3 metrics, with applications to G2 compactification
      Abstract: The detailed study of degenerations of K3 surfaces as complex manifolds goes back more than forty years and is fairly complete. Much less is known about the analogous problem in differential geometry of finding Gromov--Hausdorff limits for sequences of Ricci-flat metrics on the K3 manifold. I will review recent work of L. Foscolo, H.-J. Hein, G. Chen--X. Chen, and J. Viaclosky--S. Sun--R. Zhang on various aspects of this problem, and outline a conjectural complete picture. There are potential applications to the study of manfiolds with holonomy G2 which I shall also describe.

    10. On Friday 21st at 10:00,
      Eirik Svanes
      Counting Associatives in G2 manifolds and Non-Perturbative Superpotentials
      Abstract: By applying the F-theory/heterotic/M-theory duality chain the non-perturbative superpotential in F-theory discovered by Donagi, Grassi and Witten was recently used to conjecture that a certain M-theory G2-manifold contains an infinite number of associative sub-manifolds, i.e. three-cycles calibrated with respect to the G2 three-form. The corresponding M-theory superpotential derives from Euclidean M2 branes wrapping these associatives. I will prove the existence of these associative three-cycles at a certain orbifold point of the G2 manifold, and connect the corresponding F-theroy superpotential through the M-theory/IIA/IIB/F-theory duality chain.

    11. On Friday 21st at 12:00,
      Michaela Petrini
      Deformations of generalised structures and exactly marginal deformations of SCFT's
      Abstract: Generalised Geometry proves very useful in the context of AdS/CFT. In this talk I will apply Generalised Geometry to the analysis of the exactly marginal deformations of N=1 SCFT's in four-dimensions.