Related papers: Wall-crossing between stable and co-stable ADHM da…
For each positive rational number epsilon, the theory of epsilon-stable quasimaps to certain GIT quotients W//G developed in arXiv:1106.3724[math.AG] gives rise to a Cohomological Field Theory. Furthermore, there is an asymptotic theory…
We consider Hyers-Ulam stability of a functional equation for continuous functions on a space on which a topological group acts, analogous to the additive functional equation on a group. We show, among other things, that our generalized…
A factorization formula for certain automorphisms of a Poisson algebra associated to a quiver is proved, which involves framed versions of moduli spaces of quiver representations. This factorization formula is related to wall-crossing…
We prove an unstable version of Morel's $\mathbb{A}^1$-connectivity theorem over arbitrary base schemes. In the stable setting, this recovers (and simplifies the proof of) the known connectivity bounds due to Morel, Schmidt--Strunk,…
We consider a stochastically perturbed reaction diffusion equation in a bounded interval, with boundary conditions imposing the two stable phases at the endpoints. We investigate the asymptotic behavior of the front separating the two…
Following up on the construction of Bridgeland stability condition on $\mathbb{P}^3$ by Macr\`i, we develop techniques to study concrete wall crossing behavior for the first time on a threefold. In some cases, such as complete intersections…
Once famous and a little mysterious, AGT relations between Nekrasov functions and conformal blocks are now understood as the Hubbard-Stratanovich duality in the Dijkgraaf-Vafa (DV) phase of a peculiar Dotsenko-Fateev multi-logarithmic…
We present a general counting result for the unstable eigenvalues of linear operators of the form $JL$ in which $J$ and $L$ are skew- and self-adjoint operators, respectively. Assuming that there exists a self-adjoint operator $K$ such that…
In this work, we study the dynamics of piecewise smooth systems on a codimension-2 transverse intersection of two codimension-1 discontinuity sets. The Filippov convention can be extended to such intersections, but this approach does not…
Recent work of Borwein, Choi, and the second author examined a collection of polynomials closely related to the Goldbach conjecture: the polynomial $F_N$ is divisible by the $N$th cyclotomic polynomial if and only if there is no…
Spatial segregation in the wall normal direction is investigated in suspensions containing a binary mixture of Neo-Hookean capsules subjected to pressure driven flow in a planar slit. The two components of the binary mixture have unequal…
Monte Carlo simulation, experiment and continuum theory are used to examine the anchoring exhibited by a nematic liquid crystal at a patterned substrate comprising a periodic array of rectangles that, respectively, promote vertical and…
We study various models of random non-crossing configurations consisting of diagonals of convex polygons, and focus in particular on uniform dissections and non-crossing trees. For both these models, we prove convergence in distribution…
For a Fermat quasi-homogeneous polynomial, we study the associated weighted Fan-Jarvis-Ruan-Witten theory with narrow insertions. We prove a wall-crossing formula in all genera via localization on a master space, which is constructed by…
We study the dynamical evolution toward steady state of the stochastic non-equilibrium model known as totally asymmetric simple exclusion process, in both uniform and non-uniform (staggered) one-dimensional systems with open boundaries.…
The $J$-equation proposed by Donaldson is a complex Hessian quotient equation on K\"ahler manifolds. The solvability of the $J$-equation is proved by Song-Weinkove to be equivalent to the existence of a subsolution. It is also conjectured…
We give a visual construction of stable maps from the $3$-sphere into the real plane enjoying the following properties; the set of definite fold points coincides with a given two-bridge link and the map only admits certain types of fibers…
We establish a formula which decomposes the cohomologies of various sheaves on a simple normal crossings divisor (SNC) $D$ in terms of the simplicial cohomologies of the dual complex $\Delta(D)$ with coefficients in a presheaf of vector…
We shift the perspective on the interval fragmentation problem from division points to division spacings. This leads to a proof that is both simpler and stronger, establishing limiting distributions for partition points and spacings and,…
In this article, we introduce the logarithmic de Rham stack of a pair (X, D), for a smooth variety X over a field k of positive characteristic p, and D a strict normal crossings divisor on X. Using this stack, we prove a new version of…