Differential Geometry Seminars 2020

School of Mathematical Sciences – The University of Adelaide

Previous years

2019

2018

2017

2016

2015

2014

2013

2012

2011

2010

2009

2008

2007

2006

2005

2004

2003

2002

2001

2000

1999

1998

1997

1996

~ Upcoming talks ~

~ Past talks ~

  • Paolo Rossi (Università degli Studi di Padova)
    Title: Double ramification cycles and integrable systems
    Monday, 17 February 2020 at 2:10pm at Napier 208 Lecture Theatre

    Abstract: The double ramification cycle in the moduli space of smooth algebraic curves with marked points is the locus of curves whose marked points form the support of a principal divisor. A natural Chow class representing the compactification of such locus is the push-forward of the virtual fundamental class of the space of rubber maps to P1 relative to 0 and infinity. In a series of papers with A. Buryak (and, in part, with B. Dubrovin and J. Guéré), we have studied the intersection theory of such cycle with other tautological classes. In particular, inspired by ideas from Eliashberg, Givental and Hofer's Symplectic Field Theory, we have developed a construction using the DR cycle to associate to any cohomological field theory on the moduli space of stable curves an integrable system (of Hamiltonian PDEs) and its quantization, called the DR hierarchy. This turns out to have a deep relation, via a more classical construction of Dubrovin and Zhang, with Gromov-Witten theory, mirror symmetry and the structure of the tautological ring. I will try to introduce in a simple way the main ideas and features of this construction and showcase some of its applications.