Quantum differential equations and helices

TL;DR

This paper introduces the isomonodromic approach to quantum cohomology and Dubrovin's conjecture, summarizing recent joint research results that connect quantum differential equations with geometric and algebraic structures.

Contribution

It provides a concise, self-contained overview of the isomonodromic approach to quantum cohomology and discusses recent advances related to Dubrovin's conjecture.

Findings

Recent results linking quantum differential equations to geometric structures

Progress on Dubrovin's conjecture in joint works

Connections between monodromy data and quantum cohomology

Abstract

These notes partly touch the topic of the talk given by the author at the XXXVIII Workshop on Geometric Methods in Physics, hold in June-July 2019 in Bia\l{}owie\.{z}a, Poland. They consist of a short and self-contained introduction to the isomonodromic approach to quantum cohomology, and Dubrovin's conjecture. An overview of recent results obtained in joint works with B. Dubrovin and D. Guzzetti (arXiv:1811.09235), and A. Varchenko (arXiv:1909.06582) is given.