Date 
Speaker 
Title, Abstract 
March 18 
Luca Battistella (Bonn) 
Reduced GromovWitten 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. SantosParker, 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 superYangMills theory and D=11 supergravity,
pure spinor superspace solves the old problem with offshell formulations, and gives BatalinVilkovisky 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 3Manifold Invariants 

Since the 1980s, the study of invariants of 3dimensional manifolds has benefited
from the connections between topology, physics and number theory. Recently, a new topological
invariant that categorifies the WittenReshetikhinTuraev invariant has been discovered. This is
known as the homological block. When the 3manifold is a Seifert manifold given by a negativedefinite
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 NonUnitary 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 fourdimensional 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 
MarcAntoine 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 CalabiYau manifolds. To various degrees of
certainty, similar features were also established for compactifications on 7 and
8dimensional 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
CalabiYau surfaces (K3) via a limiting process. 
June 10 
No Seminar (Whit Monday) 
June 17 
Ezra Getzler (Northwestern) 
The BatalinVilkovisky formalism and supersymmetric particles I 

Recently, I have been studying onedimensional 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 GreenSchwarz 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 wellbehaved BV cohomology. The action for the superparticle contains
a term of topological type (the dimensional reduction of a superWZWN 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 chartbychart 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 BatalinVilkovisky formalism and supersymmetric particles II 

Recently, I have been studying onedimensional 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 GreenSchwarz 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 wellbehaved BV cohomology. The action for the superparticle contains a term
of topological type (the dimensional reduction of a superWZWN 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 chartbychart 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 BatalinVilkovisky formalism and supersymmetric particles III 

Recently, I have been studying onedimensional 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 GreenSchwarz 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 wellbehaved BV cohomology. The action for the superparticle contains a term of
topological type (the dimensional reduction of a superWZWN 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 chartbychart with families of homotopies on the intersections of charts.
The work on the superparticle is joint with my graduate student Sean Pohorence. 
Wednesday, August 21 SR 3, 2 p.m. 
Alexey Basalaev (Skoltech) 
Open WDVV equation and ADE singularities Fmanifolds 

abstract forthcoming 