Related papers: Elliptic Blowup Equations for 6d SCFTs. III: E-str…
In this paper, we study existence of boundary blow-up solutions for elliptic equations involving regional fractional Laplacian. We also discuss the optimality of our results.
The perturbative $\alpha^{\prime}$ corrections to Type-IIA String Theory compactified on a Calabi-Yau three-fold allow the construction of regular three-charge supersymmetric black holes in four dimensions, whose entropy scales with the…
Heterotic orbifolds provide promising constructions of MSSM-like models in string theory. We investigate the connection of such orbifold models with smooth Calabi-Yau compactifications by examining resolutions of the T^6/Z6-II orbifold…
Microscopic black hole entropy calculations in string theory usually proceeds through identifying them as wrapped strings in one higher dimension. For M-theory on elliptic Calabi-Yau threefolds this proceeds via its relation to F-theory in…
The present paper concerns with the existence of blow-up solution for a class of elliptic system with convection term. Here, we prove a result involving sub and supersolution for a class of elliptic system whose nonlinearity can depend of…
We use mirror symmetry, the refined holomorphic anomaly equation and modularity properties of elliptic singularities to calculate the refined BPS invariants of stable pairs on non-compact Calabi-Yau manifolds, based on del Pezzo surfaces…
We study the quantum geometry of the class of Calabi-Yau threefolds, which are elliptic fibrations over a two-dimensional toric base. A holomorphic anomaly equation for the topological string free energy is proposed, which is iterative in…
We consider the 8-supercharge 5d su(N) gauge theories from M-theory compactified on elliptic Calabi-Yau threefolds. By matching the triple intersection numbers in the elliptic Calabi-Yau with the 5d Chern-Simons levels, we determine the…
In this short paper, we are concerned with the blowup phenomenon of stochastic parabolic equations. By using comparison principle and the results of deterministic parabolic equations, we obtain blowup results of solutions for stochastic…
In this paper we study black hole and black string solutions in five dimensional N=2 supergravity theories arising from the compactification of M-theory on Calabi-Yau manifolds. In particular, we consider explicit examples of three…
We study a class of D=11 BPS spacetimes that describe M-branes wrapping supersymmetric 2 and 4-cycles of Calabi-Yau 3-folds. We analyze the geometrical significance of the supersymmetry constraints and gauge field equations of motion for…
For a class of semi-linear elliptic equations with critical Sobolev exponents and boundary conditions, we prove point-wise estimates for blowup solutions and energy estimates. A special case of this class of equations is a locally defined…
We construct a solution for a class of strongly perturbed semilinear heat equations which blows up in finite time with a prescribed blow-up profile. The construction relies on the reduction of the problem to a finite dimensional one and the…
We consider M-theory compactification on Calabi-Yau threefolds. The recently discovered connection between the BPS states of wrapped M2 branes and the topological string amplitudes on the threefold is used both as a tool to compute…
We give an introductory review of topological strings and their application to various aspects of superstrings and supersymmetric gauge theories. This review includes developing the necessary mathematical background for topological strings,…
Heterotic orbifold models are promising candidates for models with MSSM like spectra. But orbifolds only correspond to a special place in moduli space, the bigger picture is described by the moduli space of Calabi-Yau spaces. In this talk…
Boundedness and blow-up of solutions for a nonlinear elliptic system arising in probability and stochastic processes
We explore Seshadri constants associated to weighted blow-ups of complex projective varieties and demonstrate how to use this notion to construct symplectic embeddings of ellipsoids. We illustrate the utility of this point of view by…
We construct families of blowing-up solutions to elliptic systems on smooth bounded domains in the Euclidean space, which are variants of the critical Lane-Emden system and analogous to the Brezis-Nirenberg problem. We find a function which…
The dynamics of a stack of M5 branes probing a transverse multi-centered Taub-NUT space are described by a class of 6d $\mathcal{N}=(1,0)$ superconformal field theories known as the M-string orbifold SCFTs. We determine the equivariant…