【学术报告】An explicit formula for the full Gromov-Witten potential of an elliptic curve.

• 主讲人：Alexander Buryak
• 举办方： Beijing-Novosibirsk Seminar on Geometry and Mathematical Physics
• 时间： 2022-03-31 17:00 - 2022-03-31 18:00
• 地点： online

Video: https://disk.pku.edu.cn:443/link/00D78290DBF63E607B728CC1D34FCC31
Valid Until：2026-05-31 23:59

 

Abstract: A algorithm to determine all the Gromov-Witten (GW) invariants of any smooth projective curve was obtained by Okounkov and Pandharipande in 2006. They identified stationary invariants with certain Hurwitz numbers and then presented Virasoro type constraints that allow to determine all the other GW invariants (containing insertions from the unit and odd cohomology classes of the target curve) in terms of the stationary ones. In the case of an elliptic curve, I will show that these Virasoro constraints can be explicitly solved leading to a very explicit formula for the full GW potential in terms of the stationary invariants. In particular, this implies that the Dubrovin-Zhang hierarchy for the elliptic curve is Miura equivalent to its dispersionless limit.

 

Bio: Alexander Buryak is an associate professor at HSE University. His research interests are mathematical physics, algebraic geometry, topology and combinatorics.