Related papers: Higher Poles and Crossing Phenomena from Twisted G…
For a balanced wall crossing in geometric invariant theory, there exist derived equivalences between the corresponding GIT quotients if certain numerical conditions are satisfied. Given such a wall crossing, I construct a perverse sheaf of…
In this paper, we introduce a novel approach for bounding the cumulant generating function (CGF) of a Dirichlet process (DP) $X \sim \text{DP}(\alpha \nu_0)$, using superadditivity. In particular, our key technical contribution is the…
The setting is the representation theory of a simply connected, semisimple algebraic group over a field of positive characteristic. There is a natural transformation from the wall-crossing functor to the identity functor. The kernel of this…
The large $N$ asymptotic expansion of the partition function for the normal matrix model is predicted to have special features inherited from its interpretation as a two-dimensional Coulomb gas. However for the latter, it is most natural to…
Recently, Dial et al. presented measurements of the tunneling density of states into the bulk of a two dimensional electron gas under strong magnetic fields. Several high energy features appear in the measured spectrum showing a distinct…
Suppose $E$ is an elliptic curve over $\mathbb{Q}$ and $\chi$ is a Dirichlet character. We use statistical properties of modular symbols to estimate heuristically the probability that $L(E,\chi,1) = 0$. Via the Birch and Swinnerton-Dyer…
The precise calculations are carried out on the flavor changing neutral current couplings in the process $pp \to gg \to t\bar{c}(\bar{t}c)$ at the large hadron collider(LHC) and very large hadron collider(VLHC) in both frameworks of the…
In this paper, we study relations between positivity of the curvature and the asymptotic behavior of the higher cohomology group for tensor powers of a holomorphic line bundle. The Andreotti-Grauert vanishing theorem asserts that partial…
We study a special class of topological phase transitions in two dimensions described by the inversion of bands with relative angular momentum higher than 1. A band inversion of this kind, which is protected by rotation symmetry, separates…
The fractional quantum Hall (FQH) effect arises from strong electron correlations in a quantising magnetic field, and features exotic emergent phenomena such as electron fractionalisation. Using the diagrammatic Monte Carlo approach with…
In this paper, we provide an alternative proof of Donaldson's almost-holomorphic section theorem and symplectic Lefschetz pencil theorem, through constructions of certain special kind of Donaldson-type sections of the line bundle based on…
In recent work, we demonstrated that a spectral variety for the Berry connection of a 2d $\mathcal{N}=(2,2)$ GLSM with K\"ahler vacuum moduli space $X$ and abelian flavour symmetry is the support of a sheaf induced by a certain action on…
We develop a theory of abstract arithmetic Chow rings where the role of the fibers at infinity is played by a complex of abelian groups that computes a suitable cohomology theory. This theory allows the construction of many variants of the…
Consider a random real tree whose leaf set, or boundary, is endowed with a finite mass measure. Each element of the tree is further given a type, or allele, inherited from the most recent atom of a random point measure…
The possibility of observing large signatures of new CP-violating and flavor-changing Higgs-Top couplings in a future e^+e^- collider experiments such as e^+e^- -> t bar-t h, t bar-t Z and e^+e^- -> t bar-c \nu_e bar-\nu_e, t bar-c e^+ e^-…
We study abelian gauge-Higgs models on the lattice and consider gauge groups Z(3) and U(1). For both cases the partition sums are mapped exactly to a dual representation where the degrees of freedom are surfaces for the gauge fields and…
We derive a sum rule which establishes a linear relation between a particle's anomalous magnetic moment and a quantity connected to the photoabsorption cross-section. This quantity cannot be measured directly. However, it can be computed…
Given a prime, alternating link diagram, we build a special cover of the link complement whose degree is bounded by a factorial function of the crossing number. It follows that a subgroup of the link group of that index embeds into…
We study a one-dimensional particles system, in the overdamped limit, where nearest particles attract with a force inversely proportional to a power of their distance and coalesce upon encounter. The detailed shape of the distribution…
We present a paradoxical finding that, in the vicinity of a topological phase transition in a quantum anomalous Hall system (Chern insulator), topology nearly always (except when the system obeys charge-conjugation symmetry) results in a…