129 problems

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 $X$ be a smooth four-manifold, let $\xi$ be a class defining a wall, and let $\Delta_{\xi,d}^X$ denote the corresponding wall-crossing term for Donaldson invariants. The multip…

Let $\Omega_{\gamma,\theta}(y)$ denote the refined, or motivic, Donaldson–Thomas invariant associated with charge $\gamma$ and stability parameter $\theta$. In a quantum torus, def…

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…

Let $n$ be a positive integer, let $\frac{r}{s}$ be a term of the $n$-th Farey sequence, and let $\tilde{M}_{r/s}$ and $\tilde{M}^{\prime}_{r/s}$ be the compositions of generalized…

Let $S$ be a smooth projective surface, let $X=\operatorname{Tot}_S(\omega_S)$ be its associated local surface, and let $v=(\beta,n)\in N_{\leq 1}(S)$ be primitive with $\beta>0$.…

Let $n$ be a prime number, let $\operatorname{sgn}_n$ be the partition of $n$ corresponding to the sign representation of $S_n$, and let $r$ be a term in the $n$-th Farey sequence.…

Genus-zero wall-crossing conjecture. There exists $\mathbf{t}\in\mathcal{H}[[z]]$ such that

Let $W/2/{\bf G}$ be a GIT quotient corresponding to a semi-positive triple $(W,{\bf G},\theta)$. Let $F_g^{\varepsilon }$ and $F_g^\infty$ denote the genus-$g$ quasimap and Gromov…

Let $Q$ be a finite quiver, let $W$ be a polynomial potential on $Q$, and let $\operatorname{\mathsf{nil}}(\mathcal P(Q,W))$ be the category of finite-dimensional right modules ove…

Fix $\mathbb K=\mathbb C$. Let $P$ be a Calabi–Yau $3$-fold, set $\mathcal A=\operatorname{coh}(P)$, and let $\mathfrak F_{\mathcal A}$ and $K(\mathcal A)$ be as in the source. Let…

Let $(M,J,\omega,\Omega)$ be a generic almost Calabi--Yau $3$-fold. For $\delta\in H_3(M,\mathbb Z)$, let $S(\delta)$ be the set of compact immersed, possibly singular special Lagr…

Let $X$ be an oriented compact four-manifold with $b^+=1$ and even $b_1=2q$. Let $w\in H^2(X;\mathbb{Z})$. Choose $\Sigma\in H^2(X)$ generating the image of…

Let $S$ be a rational surface, let $N,d,r$ be the parameters in the wall-crossing formula, let $K^2$ denote $K_S^2$, and let $Q_i(N,d,r,K^2)$ and $P_i(N,d,r,K^2)$ be the polynomial…

Global Stokes transformation–BPS spectrum-generator conjecture. The global Stokes transformation can be identified with the spectrum generator of BPS invariants.

Let $X$ be a smooth threefold, and consider a step of its minimal model program. Moduli spaces of stable objects are understood with respect to an appropriate stability condition,…

Stokes-constant conjecture. The Stokes constant associated with the singularity … gammainGamma$.

Let $M_{Q_4}(\vec{r},n)$ be the moduli space defined using the stable condition, and let $M_{Q_4}^c(\vec{r},n)$ be the moduli space defined using co-stability, namely the condition…

Let $\varepsilon_\alpha^\mu$ denote the generalized $K$-theoretic invariant associated with a class $\alpha$ and stability condition $\mu$, and let a homological lift mean a homolo…

Let $\mathcal A$ be the category under consideration, let $\alpha$ be a class and let $\mu$ be a stability condition, with $\varepsilon_\alpha^\mu$ the associated generalized $K$-t…

Let $Y$ be a symplectic resolution of a conical symplectic singularity with an action of the torus $T$. The small quantum $T$-equivariant cohomology gives a family of commutative a…

Let a 4d $\mathcal{N}=2$ class $\mathcal{S}$ theory have a BPS spectrum encoded in a Kontsevich–Soibelman motivic wall-crossing formula, and let … can be generalized to all such 4d…

Let $M$ be the monodromy operator of a four-dimensional ${\mathcal N}=2$ superconformal field theory, and let $N>1$ be an integer. Denote by $\operatorname{Tr}M^N$ the trace of its…

In the $X_{6,6}$ model, let $gamma_1=(-1,-1,2,1)$ and $gamma_2=(0,0,-1,0)$ be the charges appearing in the decay … At $z=-10\mu$, the associated Stokes constants are…

Let $J(X,\omega)$ be the space of compatible almost-complex structures on a symplectic manifold $(X,\omega)$, and let $W_\infty$ denote the wall associated with the full, unbounded…