462 problems

Atiyah–Floer conjecture. Under appropriate hypotheses, there should be an isomorphism

The paper considers partition functions arising from framed quiver moduli and their relationship with gauge-theoretic generating functions. Nekrasov's conjecture. These partition f…

Let $\mathcal{M}$ be the complex symplectic manifold arising from the three-dimensional moduli space of a four-dimensional $\mathcal{N}=2$ supersymmetric gauge theory of class $S$…

Isomorphism conjecture. The map $\varphi$ is an isomorphism of Poisson vertex algebras.

Let $G$ be a gauge group and let ${}^LG$ denote its Langlands dual group. The associated Yang–Mills theories are compared at the quantum level. Montonen–Olive conjecture. The Yang–…

Let the $u$-plane be the modular curve parametrizing the vacua of the low-energy effective theory, and let the regularized $u$-plane integral have boundary contributions from the c…

Let $h$ denote the helicity of a massless particle and let $C$ denote the Chern number characterizing the topology of its particle bundle. Chern number–helicity conjecture. The rel…

Moyal-product and wall-crossing conjecture. The Witten indices can be read off from the Moyal products of the expectation values of the minimal 't Hooft operators, and wall-crossin…

The claim concerns a particular class of integrable systems, including closed Toda chains, elliptic Calogero–Moser systems, and their relativistic versions, together with observabl…

Mariño–Moore's conjecture. There should be a generalisation of Witten's conjecture to these higher-rank invariants, implying in particular that they do not contain new differential…

Let $K$ be the compact gauge quotient group, let $\rho_s$ be the heat-kernel measure on $K$ at time $s$, and let $P_s$ be the regularized measure on the space of connections…

In an ${\mathcal N}=1$ supersymmetric quiver gauge theory, suppose that different gauge theories have the same infrared moduli space, and that this moduli space is toric. Toric dua…

The physical configuration space of a gauge theory may be compact in certain directions, as indicated by the possibility that the averaging integral has infinitely many stationary…

Let a solution have $n$ units of magnetic charge and belong to a $(4n-1)$-parameter family of solutions. The parameters describe the moduli of multi-monopole configurations. Weinbe…

Let $(A_i,$Phii$)$ be Calabi–Yau monopoles with increasingly large mass parameters on a Calabi–Yau 3-fold, and let $L$ be a special Lagrangian 3-fold near which their curvature con…

Sivek–Zentner conjecture. The only $\mathrm{SU}(2)$-averse knots are the nontrivial torus knots.

Let $N$ be a smooth manifold such that its tangent bundle admits a CYMH GT, and let $K\to S$ be a Lie algebroid bundle over a smooth manifold $S$ which also admits a CYMH GT. Set ……

The Yang–Mills functional is defined on the infinite-dimensional space of connections over a compact Riemann surface, with the gauge group acting on this space. An equivariantly pe…

Let an elliptic fibration geometrically engineer a gauge group, and let its Mordell–Weil group be the group of rational sections of the fibration. The center of the gauge group is…

Gaiotto–Witten bijectivity conjecture. The maps $I_{\mathrm{NP}}$ and $I_{\mathrm{GNP}}$ are both bijective. This is the proposed Kobayashi–Hitchin-type correspondence for the exte…

Let $M$ be a $3$-manifold presented by a Heegaard splitting with Heegaard surface a Riemann surface, and let the associated Lagrangians lie in the moduli space of flat connections…

In a two-dimensional conformal field theory with Virasoro symmetry, consider its conformal blocks, and in four-dimensional gauge theory consider the instanton partition functions c…

Alday–Tachikawa conjecture. The “fully-ramified” Nekrasov instanton partition function should be related to Hitchin's integrable system.

Let the parameter space of hyperbolic monopoles contain a compact subset and a disjoint subset, and let the monopoles have sufficiently small mass. Small-mass asymptotic separation…

A hyperbolic monopole is a solution of the Bogomolny equation on hyperbolic space ${\mathbb H}^3$, with an asymptotic value given by its limiting data on the sphere at infinity…