Related papers: Wall-crossing for vortex partition function and ha…

We investigate functionals defined on manifolds through parameterizations. If they are to be meaningful, from a geometrical viewpoint, they ought to be invariant under reparameterizations. Standard, local, integral functionals with this…

An extension of the method and results of A. Schwarz for evaluating the partition function of a quadratic functional is presented. This enables the partition functions to be evaluated for a wide class of quadratic functionals of interest in…

The partition functions of Pasquier models on the cylinder, and the associated intertwiners, are considered. It is shown that earlier results due to Saleur and Bauer can be rephrased in a geometrical way, reminiscent of formulae found in…

We study the semiclassical partition function in the frame work of the Morse theory, to clarify the phase factor of the partition function and to relate it to the eta invariant of Atiyah. Converting physical system with potential into a…

We develop the technique of weight truncation in the context of wall-crossings in birational cobordisms, parallel to that in [HL15, BFK19]. More precisely, for each such wall-crossing, we embed the bounded above derived category of coherent…

The notion of limit stability on Calabi-Yau 3-folds is introduced by the author to construct an approximation of Bridgeland-Douglas stability conditions at the large volume limit. It has also turned out that the wall-crossing phenomena of…

We study Translation functors and Wall-Crossing functors on infinite dimensional representations of a complex semisimple Lie algebra using D-modules. This functorial machinery is then used to prove the Endomorphism-theorem and the…

We study thermal Casimir and quantum non-retarded Lifshitz interactions between dielectrics in general geometries. We map the calculation of the classical partition function onto a determinant which we discretize and evaluate with the help…

There have been major developments in the theory of moduli of varieties in the past decade, essentially settling the construction of moduli spaces of log canonically polarized slc pairs and moduli spaces of K-polystable log Fano pairs.…

When the symmetries of homogenous isotropic turbulent flows are broken, different sets of modes with different physical roles emerge. In particular, choosing a forcing which puts more weight on one or the other of these sets may result in…

We provide a general framework for wall-crossing of equivariant K-theoretic enumerative invariants of appropriate moduli stacks $\mathfrak{M}$, by lifting Joyce's homological universal wall-crossing arXiv:2111.04694 to K-theory and to…

When formulated in twistor space, the D-instanton corrected hypermultiplet moduli space in N=2 string vacua and the Coulomb branch of rigid N=2 gauge theories on $R^3 \times S^1$ are strikingly similar and, to a large extent, dictated by…

We analyze the tunneling of a particle through a repulsive potential resulting from an inverted harmonic oscillator in the quantum mechanical phase space described by the Wigner function. In particular, we solve the partial differential…

Partition functions of N=2 theories on the squashed 3-sphere have been recently shown to localise to matrix integrals. By explicitly evaluating the matrix integral we show that abelian partition functions can be expressed as a sum of…

Exact analytic solutions of the time dependent Schrodinger equation are produced that exhibit a variety of vortex structures. The qualitative analysis of the motion of vortex lines is presented and various types of vortex behavior are…

We state a wall-crossing formula for the virtual classes of epsilon-stable quasimaps to GIT quotients and prove it for complete intersections in projective space, with no positivity restrictions on their first Chern class. As a consequence,…

We study motivic Donaldson-Thomas invariants in the sense of Behrend-Bryan-Szendroi. A wall-crossing formula under a mutation is proved for a certain class of quivers with potentials.

We study random plane partitions with respect to volume measures with periodic weights of arbitrarily high period. We show that near the vertical boundary the system develops up to as many turning points as the period of the weights, and…

Partitions of unity in ${\mathbf R}^d$ formed by (matrix) scales of a fixed function appear in many parts of harmonic analysis, e.g., wavelet analysis and the analysis of Triebel-Lizorkin spaces. We give a simple characterization of the…

We analyze N = 1 theories on S5 and S4 x S1, showing how their partition functions can be written in terms of a set of fundamental 5d holomorphic blocks. We demonstrate that, when the 5d mass parameters are analytically continued to…