SuperGeometry and SuperModuli: March 27 – May 19, 2023

Participant List

Organized by: Sergio Cacciatori (Università degli studi dell’Insubria), Samuel Grushevsky (SCGP), Alexander Polishchuk (University of Oregon)

A supermanifold is the generalization of a usual manifold when some of the coordinates are even variables, and some are odd. The mathematical foundations of supergeometry were established in the 1970s and 1980s. While much of the motivation for this came from supersymmetric theories in physics, the mathematical study became possible largely due to the development of the language of algebraic and complex geometry in the preceding decades. For the following 30 years or so, the progress of supergeometry was somewhat modest, although there were some substantial developments in other mathematical aspects of supersymmetry (eg. Lie superalgebras). Recently, the interest in supergeometry has revived, from physicists reexamining the foundations of superstring scattering, from the physical interest in mirror symmetry for supermanifols, and from mathematicians finally nearing a rigorous construction and study of the moduli of supercurves, and exploring related foundational questions in algebraic supergeometry. The program will bring together mathematicians and physicists who have been recently working on supergeometry, aiming to create a cohesive community of researchers and to let the physical intuition and mathematical rigour benefit from each other. There is also a workshop associated with this event: SuperGeometry and SuperModuli: March 27-31, 2023

Schedule of Program Talks:
*All talks will be held in room 313 unless otherwise noted

Mon 4/3 at 10:30am Mini-course on moduli of SUSY curves I Alexander Polishchuk  
Tues 4/4 at 1:30pm Universal de Rham/Spencer double complex on a supermanifold Sergio Cacciatori  
Wed 4/5 at 10:30am Mini-course on moduli of SUSY curves II Alexander Polishchuk  
Thurs 4/6 at 1:30pm Towards super Teichmuller spin Osp(1|2) TQFT Nezhla Aghaei Abstract
Fri 4/7 at 10:30am Mini-course on moduli of SUSY curves III Alexander Polishchuk  
Tues 4/11 at 10:30am Supergravity and supergeometry I Pietro Antonio Grassi  
Wed 4/12 at 10:30am Supergravity and supergeometry II Pietro Antonio Grassi  
Thurs 4/13 at 1:30pm SUSY operads Enno Kessler  
Fri 4/14 at 1:30pm Compactification of moduli of SUSY curves Yehao Zhou  
Mon 4/17 at 10:30am CS forms: a consistent formalism for integrals on complex supermanifolds Dmitry Vaintrob  
Wed 4/19 at 10:30am Compactification of moduli of SUSY curves – details of the construction Yehao Zhou  
Mon 4/24 at 10:30am The supermoduli space M_{0,0,n} Alexander Voronov  
Wed 4/26 at 10:30am Volumes of moduli spaces of super hyperbolic surfaces with Ramond punctures. Paul Norbury  
Mon 5/1 at 10:30am Microformal morphisms of supermanifolds and homotopy algebras Theodore Voronov  
Tues 5/2 at 10:30am Log geometry and Log orbifold compactification of the space of superconformal curves Dmitry Vaintrob  
Wed 5/3 at 10:30am Classical Cohomological Field Theory Shuhan Jiang  
Wed 5/3 at 1:30pm in room 102 Microformal morphisms of supermanifolds and homotopy algebras, part II Theodore Voronov  
Thurs 5/4 at 10:30am Super Pluecker map – towards super cluster algebras Ekaterina Shemyakova