This is a review article on the quantum toroidal algebras, focusing on their roles in various
solvable structures of 2d conformal field theory, supersymmetric gauge theory, and string …

We demonstrate that twisted equivariant differential K-theory of transverse complex curves
accommodates exotic charges of the form expected of codimension= 2 defect branes, such …

We explore the relationship between four-dimensional N=2 quantum field theories and their
associated BPS quivers. For a wide class of theories including super-Yang-Mills theories …

We propose machine learning inspired methods for computing numerical Calabi-Yau (Ricci
flat Ka ̈hler) metrics, and implement them using Tensorflow/Keras. We compare them with …

A bstract We construct supersymmetric AdS 3 solutions in F-theory, that is Type IIB
supergravity with varying axio-dilaton, which are holographically dual to 2d\(\mathcal …

A bstract We study the Gauge/Bethe correspondence for two-dimensional\(\mathcal {N}\)=(2,
2) supersymmetric quiver gauge theories associated with toric Calabi-Yau three-folds …

A bstract We study half-BPS line operators in 3d\(\mathcal {N}\)= 4 gauge theories, focusing
in particular on the algebras of local operators at their junctions. It is known that there are …

Tropical geometry provides an explanation for the remarkable power of mirror symmetry to
connect complex and symplectic geometry. The main theme of this book is the interplay …

A bstract We apply supersymmetric localization to\(\mathcal {N}=\left (2, 2\right)\) gauged
linear sigma models on a hemisphere, with boundary conditions, ie, D-branes, preserving B …

A bstract The quiver Yangian, an infinite-dimensional algebra introduced recently in [1], is
the algebra underlying BPS state counting problems for toric Calabi-Yau three-folds. We …