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 Mailing List.
Time and Place: Regularly: Monday, 2 p.m.s.t., MATHEMATIKON
Alternatively: Tuesday or Thursday, 2 p.m.s.t., various locations (or as noted below).
|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.|
|May 6||Xujia Chen (Stony Brook)||Lifting Cobordisms and Kontsevich-Type Recursions for Counts of Real Curves|
|Kontsevich's recursion, proved by Ruan-Tian in the early 90s, is a recursion formula for the counts of rational holomorphic curves in complex manifolds. For complex fourfolds and sixfolds with a real structure (i.e. a conjugation), Welschinger (2003) defined invariant signed counts of real rational holomorphic curves. Solomon interpreted Welschinger's invariants as holomorphic disk counts in 2006 and proposed Kontsevich-type recursions for them in 2007, along with an outline for adapting Ruan-Tian's homotopy style argument to the real setting. For many symplectic fourfolds and sixfolds, these recursions determine all invariants from basic inputs. We establish Solomon's recursions by re-interpreting his disk counts as degrees of relatively oriented pseudocycles from moduli spaces of stable real maps and lifting cobordisms from Deligne-Mumford moduli spaces of stable real curves.|
|May 13||no seminar||T.B.A.|
|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, 4pm!
|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
|Marc-Antoine Fiset (Oxford)||Interpolating stringy geometry: from Spin(7) and G2 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 G2 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)||Gluing gauge conditions together in the BV formalism I|
| Tuesday, June 18
SR 00. 200, 2pm
|Ezra Getzler (Northwestern)||Gluing gauge conditions together in the BV formalism II|
| Wednesday, June 19
SR 00. 200, 4pm
|Ezra Getzler (Northwestern)||Gluing gauge conditions together in the BV formalism III|
| Wednesday, June 26
|Brian Williams (Northeastern)||T.B.A.|