We prove mirror symmetry for supersymmetric sigma models on Kahler manifolds in 1+ 1
dimensions. The proof involves establishing the equivalence of the gauged linear sigma …

We compute the elliptic genera of general two-dimensional N=(2, 2) N=(2, 2) and N=(0, 2)
N=(0, 2) gauge theories. We find that the elliptic genus is given by the sum of Jeffrey–Kirwan …

This is an introduction to a very active field of research, on the boundary between
mathematics and physics. It is aimed at graduate students and researchers in geometry and …

We define relative Gromov-Witten invariants and establish a general gluing theory of pseudo-
holomorphic curves for symplectic cutting and contact surgery. Then, we use our general …

In even space-time dimensions, the multi-loop Feynman integrals are integrals of rational
function in projective space. By using an algorithm that extends the Griffiths–Dwork …

Abstract Many N=(2, 2) N=(2, 2) two-dimensional nonlinear sigma models with Calabi–Yau
target spaces admit ultraviolet descriptions as N=(2, 2) N=(2, 2) gauge theories (gauged …

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Can artificial intelligence learn mathematics? The question is at the heart of this original
monograph bringing together theoretical physics, modern geometry, and data science. The …

The concept of a Frobenius manifold was introduced by B. Dubrovin [9] to capture in an
axiomatic form the properties of correlators found by physicists (see [8]) in two-dimensional …

We study various aspects of Script N=(2, 2) supersymmetric non-Abelian gauge theories in
two dimensions, with applications to string vacua. We compute the Witten index of SU (k) …