In recent years, many Type IIn supernovae have been found to share striking similarities with the peculiar SN 2009ip, whose true nature is still under debate. Here, we present 10 yr of observations of SN 2011fh, an interacting transient with spectroscopic and photometric similarities to SN 2009ip. SN 2011fh had an M ( r ) similar to -16 mag brightening event, followed by a brighter M ( r ) similar to -18 mag luminous outburst in 2011 August. The spectra of SN 2011fh are dominated by narrow to intermediate Balmer emission lines throughout its evolution, with P Cygni profiles indicating fast-moving material at similar to 6400 km s(-1). HST/WFC3 observations from 2016 October revealed a bright source with M (F814W) approximate to -13.3 mag, indicating that we are seeing the ongoing interaction of the ejecta with the circumstellar material or that the star might be going through an eruptive phase five years after the luminous outburst of 2011. Using HST photometry of the stellar cluster around SN 2011fh, we estimated an age of similar to 4.5 Myr for the progenitor, which implies a stellar mass of similar to 60 M (circle dot), using single-star evolution models, or a mass range of 35-80 M (circle dot), considering a binary system. We also show that the progenitor of SN 2011fh exceeded the classical Eddington limit by a large factor in the months preceding the luminous outburst of 2011, suggesting strong super-Eddington winds as a possible mechanism for the observed mass loss. These findings favor an energetic outburst in a young and massive star, possibly a luminous blue variable.

Let $(M,I,J,K,g)$ be a hyperkähler manifold. Then the complex manifold $(M,I)$ is holomorphic symplectic. We prove that for all real $x,y$ , with $x^{2}+y^{2}=1$ except countably many, any finite-energy $(xJ+yK)$ -holomorphic curve with boundary in a collection of $I$ -holomorphic Lagrangians must be constant. By an argument based on the Łojasiewicz inequality, this result holds no matter how the Lagrangians intersect each other. It follows that one can choose perturbations such that the holomorphic polygons of the associated Fukaya category lie in an arbitrarily small neighborhood of the Lagrangians. That is, the Fukaya category is local. We show that holomorphic Lagrangians are tautologically unobstructed. Moreover, the Fukaya $A_{\infty }$ algebra of a holomorphic Lagrangian is formal. Our result also explains why the special Lagrangian condition holds without instanton corrections for holomorphic Lagrangians.

We present X-ray, UV/optical, and radio observations of the stripped-envelope, core-collapse supernova (SN) 2011ei, one of the least luminous SNe IIb or Ib observed to date. Our observations begin with a discovery within 1 day of explosion and span several months afterward. Early optical spectra exhibit broad, Type II-like hydrogen Balmer profiles that subside rapidly and are replaced by Type Ib-like He-rich features on the timescale of one week. High-cadence monitoring of this transition suggests that absorption attributable to a high velocity (> 12,000 km/s) H-rich shell is not rare in Type Ib events. Radio observations imply a shock velocity of v = 0.13c and a progenitor star mass-loss rate of 1.4 x 10^-5 Msun yr^-1 (assuming wind velocity v_w=10^3 km/s). This is consistent with independent constraints from deep X-ray observations with Swift-XRT and Chandra. Overall, the multi-wavelength properties of SN 2011ei are consistent with the explosion of a lower-mass (3-4 Msun), compact (R* <= 1x10^11 cm), He core star. The star retained a thin hydrogen envelope at the time of explosion, and was embedded in an inhomogeneous circumstellar wind suggestive of modest episodic mass-loss. We conclude that SN 2011ei's rapid spectral metamorphosis is indicative of time-dependent classifications that bias estimates of explosion rates for Type IIb and Ib objects, and that important information about a progenitor star's evolutionary state and mass-loss immediately prior to SN explosion can be inferred from timely multi-wavelength observations.