Luminous Supernovae

Supernovae (SNe), the luminous explosions of stars, were observed since antiquity, with typical peak luminosity not exceeding 1.2x10^{43} erg/s (absolute magnitude >-19.5 mag). It is only in the last dozen years that numerous examples of SNe that are substantially super-luminous (>7x10^{43} erg/s; <-21 mag absolute) were well-documented. Reviewing the accumulated evidence, we define three broad classes of super-luminous SN events (SLSNe). Hydrogen-rich events (SLSN-II) radiate photons diffusing out from thick hydrogen layers where they have been deposited by strong shocks, and often show signs of interaction with circumstellar material. SLSN-R, a rare class of hydrogen-poor events, are powered by very large amounts of radioactive 56Ni and arguably result from explosions of very massive stars due to the pair instability. A third, distinct group of hydrogen-poor events emits photons from rapidly-expanding hydrogen-poor material distributed over large radii, and are not powered by radioactivity (SLSN-I). These may be the hydrogen-poor analogs of SLSN-II.Comment: This manuscript has been accepted for publication in Science (to appear August 24). This version has not undergone final editing. Please refer to the complete version of record at http://www.sciencemag.org/. The manuscript may not be reproduced or used in any manner that does not fall within the fair use provisions of the Copyright Act without the prior, written permission of AAA

Multiplicity estimates, analytic cycles and Newton polytopes

We consider the problem of estimating the multiplicity of a polynomial when restricted to the smooth analytic trajectory of a (possibly singular) polynomial vector field at a given point or points, under an assumption known as the D-property. Nesterenko has developed an elimination theoretic approach to this problem which has been widely used in transcendental number theory. We propose an alternative approach to this problem based on more local analytic considerations. In particular we obtain simpler proofs to many of the best known estimates, and give more general formulations in terms of Newton polytopes, analogous to the Bernstein-Kushnirenko theorem. We also improve the estimate's dependence on the ambient dimension from doubly-exponential to an essentially optimal single-exponential.Comment: Some editorial modifications to improve readability; No essential mathematical change

MESON2016 -- Concluding Remarks

Several topics presented and discussed at MESON2016 are highlighted, including pentaquarks, dibaryons and meson-nuclear bound states.Comment: concluding plenary talk given at MESON2016 -- the 14th International Workshop on Meson Production, Properties and Interaction, 2nd-7th June 2016, Krak\'ow, Poland, to appear in the EPJ Web of Conferences, v2 -- references update

Semantics, Modelling, and the Problem of Representation of Meaning -- a Brief Survey of Recent Literature

Over the past 50 years many have debated what representation should be used to capture the meaning of natural language utterances. Recently new needs of such representations have been raised in research. Here I survey some of the interesting representations suggested to answer for these new needs.Comment: 15 pages, no figure

Multiplicity Estimates: a Morse-theoretic approach

The problem of estimating the multiplicity of the zero of a polynomial when restricted to the trajectory of a non-singular polynomial vector field, at one or several points, has been considered by authors in several different fields. The two best (incomparable) estimates are due to Gabrielov and Nesterenko. In this paper we present a refinement of Gabrielov's method which simultaneously improves these two estimates. Moreover, we give a geometric description of the multiplicity function in terms certain naturally associated polar varieties, giving a topological explanation for an asymptotic phenomenon that was previously obtained by elimination theoretic methods in the works of Brownawell, Masser and Nesterenko. We also give estimates in terms of Newton polytopes, strongly generalizing the classical estimates.Comment: Minor revision; To appear in Duke Math. Journa