### Info

This seminar features recent results at the intersection of high-energy physics, string theory, and geometry and topology.

** Prerequisites:** None. Everyone is welcome. To receive announcements for
this seminar, and for the advertisement of other talks at the intersection of physics and
geometry in Heidelberg,
you may subscribe to the
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** Time and Place:** Regularly: Monday, 2 p.m.s.t., MATHEMATIKON
SR 3

Alternatively: Tuesday or Thursday, 2 p.m.s.t., various locations (or as noted below).

### Schedule

Date | Speaker | Title, Abstract |
---|---|---|

March 18 | Luca Battistella (Bonn) | Reduced Gromov-Witten theory in genus one and singular curves |

The moduli space of genus 0 stable maps to projective space is a smooth orbifold. The quantum hyperplane principle allows us to compute the invariants of a hypersurface as twisted invariants of projective space, hence e.g. by torus localisation. In higher genus the moduli space can be arbitrarily singular. The genus 1 case has been particularly studied: J. Li, R. Vakil, and A. Zinger have desingularised the main component, defined reduced invariants, and compared them with standard ones, providing the first mathematical proof of the BCOV mirror symmetry prediction. Ten years later, we understand their construction in terms of log geometry and singular (worse than nodal) curves, thanks to work of D. Ranganathan, K. Santos-Parker, and J. Wise. I will describe some results in this direction, jointly obtained with F. Carocci and C. Manolache, and N. Nabijou and D. Ranganathan. | ||

Tuesday, April 23 Hörsaal, 2 p.m. |
Martin Cederwall (Göteborg) | Pure spinors and supersymmetry |

I will describe how pure spinors, suitably defined, arise from traditional superspace. In cases of maximal supersymmetry, such as D=10 super-Yang-Mills theory and D=11 supergravity, pure spinor superspace solves the old problem with off-shell formulations, and gives Batalin-Vilkovisky actions. I will also mention some related applications of pure spinors and minimal orbits. | ||

April 29 | N.N. | T.B.A. |

abstract forthcoming | ||

May 6 | Xujia Chen (Stony Brook) | Bounding chains for Welschinger's invariants |

abstract forthcoming | ||

May 13 | no seminar | T.B.A. |

abstract forthcoming | ||

May 20 | Francesca Ferrari (Trieste) | False Theta Functions, Log VOA's and 3-Manifold Invariants |

Since the 1980s, the study of invariants of 3-dimensional manifolds has benefited from the connections between topology, physics and number theory. Recently, a new topological invariant that categorifies the Witten-Reshetikhin-Turaev invariant has been discovered. This is known as the homological block. When the 3-manifold is a Seifert manifold given by a negative-definite plumbing the homological block turned out to be related to false theta functions and characters of logarithmic VOA's. In this talk, I describe the relations between this topological invariant, certain number theoretical objects and the representation theory of logarithmic VOA's. | ||

Tuesday, May 21 Philosophenweg 19, 2pm |
Du Pei (Aarhus/Caltech) | Taming the Non-Unitary Zoo with Wild Higgs Bundles |

We propose a new link between the geometry of moduli spaces of Higgs bundles and quantum topology. The construction goes through a class of four-dimensional quantum field theories that are said to satisfy "property F". Each such theory gives rise to a family of modular tensor categories, whose algebraic structures are intimately related to the geometry of the Coulomb branch. This is based on joint work with Mykola Dedushenko, Sergei Gukov, Hiraku Nakajima and Ke Ye. | ||

Tuesday, June 4 Hörsaal, 2pm |
Marc-Antoine Fiset (Oxford) | Interpolating stringy geometry:
from Spin(7) and G_{2} to Virasoro N=2 |

Spectral flow, topological twists, chiral rings related to a refinement of the de Rham cohomology and to marginal deformations, spacetime supersymmetry, mirror symmetry. These are some examples of features arising from the N=2 Virasoro chiral algebra of superstrings compactified on Calabi-Yau manifolds. To various degrees of certainty, similar features were also established for compactifications on 7- and 8-dimensional manifolds with exceptional holonomy group \(G_2\) and Spin(7) respectively. In this talk, I will explain that these are more than analogies: I will flesh out the underlying symmetry connecting exceptional holonomy to Calabi-Yau surfaces (K3) via a limiting process. | ||

June 10 | No Seminar (Whit Monday) | |

June 17 | Ezra Getzler (Northwestern) | The Batalin-Vilkovisky formalism and supersymmetric particles I |

Recently, I have been studying one-dimensional toy models of the superstring within the BV formalism: these are known respectively as the spinning particle (analogous to the GSO superstring) and the Superparticle (analogous to the Green-Schwarz superstring). The spinning particle turns out to be an AKSZ model, and exhibits some very interesting pathologies: it appears to be the first model to have been investigated that exhibits BV cohomology in all negative degrees. By contrast, the superparticle has a very well-behaved BV cohomology. The action for the superparticle contains a term of topological type (the dimensional reduction of a super-WZWN term), and to handle this, we borrow some ideas from Sullivan's approach to rational homotopy theory. In my third talk, I will turn to quantization: I will show how to generalize Lagrangians in the BV formalism to "flexible Lagrangians", defined chart-by-chart with families of homotopies on the intersections of charts. The work on the superparticle is joint with my graduate student Sean Pohorence. | ||

Tuesday, June 18 SR 00. 200, 2pm |
Ezra Getzler (Northwestern) | The Batalin-Vilkovisky formalism and supersymmetric particles II |

Recently, I have been studying one-dimensional toy models of the superstring within the BV formalism: these are known respectively as the spinning particle (analogous to the GSO superstring) and the superparticle (analogous to the Green-Schwarz superstring). The spinning particle turns out to be an AKSZ model, and exhibits some very interesting pathologies: it appears to be the first model to have been investigated that exhibits BV cohomology in all negative degrees. By contrast, the superparticle has a very well-behaved BV cohomology. The action for the superparticle contains a term of topological type (the dimensional reduction of a super-WZWN term), and to handle this, we borrow some ideas from Sullivan's approach to rational homotopy theory. In my third talk, I will turn to quantization: I will show how to generalize Lagrangians in the BV formalism to "flexible Lagrangians", defined chart-by-chart with families of homotopies on the intersections of charts. The work on the superparticle is joint with my graduate student Sean Pohorence. | ||

Wednesday, June 19 SR 9, 9am ct |
Ezra Getzler (Northwestern) | The Batalin-Vilkovisky formalism and supersymmetric particles III |

Recently, I have been studying one-dimensional toy models of the superstring within the BV formalism: these are known respectively as the spinning particle (analogous to the GSO superstring) and the superparticle (analogous to the Green-Schwarz superstring). The spinning particle turns out to be an AKSZ model, and exhibits some very interesting pathologies: it appears to be the first model to have been investigated that exhibits BV cohomology in all negative degrees. By contrast, the superparticle has a very well-behaved BV cohomology. The action for the superparticle contains a term of topological type (the dimensional reduction of a super-WZWN term), and to handle this, we borrow some ideas from Sullivan's approach to rational homotopy theory. In my third talk, I will turn to quantization: I will show how to generalize Lagrangians in the BV formalism to "flexible Lagrangians", defined chart-by-chart with families of homotopies on the intersections of charts. The work on the superparticle is joint with my graduate student Sean Pohorence. | ||

June 26 | N.N. | T.B.A. |

abstract forthcoming | ||

July 1 | N.N. | T.B.A. |

abstract forthcoming | ||

July 8 | N.N. | T.B.A. |

abstract forthcoming | ||

July 15 | N.N. | T.B.A. |

abstract forthcoming | ||

July 22 | N.N. | T.B.A. |

abstract forthcoming |

### Organizers

Prof. J. Walcher, walcher@uni-heidelberg.de

Dr. Ingmar Saberi,
saberi@mathi.uni-heidelberg.de