Most Accessed Articles: Research in the Mathematical Scienceshttp://resmathsci.springeropen.comMost Accessed Articles: Research in the Mathematical SciencesVariants of the Selberg sieve, and bounded intervals containing many primeshttp://resmathsci.springeropen.com/articles/10.1186/s40687-014-0012-7Fri, 17 Oct 2014 00:00:00 GMThttp://resmathsci.springeropen.com/articles/10.1186/s40687-014-0012-7DHJ Polymath2014-10-17T00:00:00ZBogomolov’s proof of the geometric version of the Szpiro Conjecture from the point of view of inter-universal Teichmüller theoryhttp://resmathsci.springeropen.com/articles/10.1186/s40687-016-0057-xThe purpose of the present paper is to expose, in substantial detail, certain remarkable similarities between inter-universal Teichmüller theory and the theory surrounding Bogomolov’s proof of the geometric versi...Sun, 05 Jun 2016 00:00:00 GMThttp://resmathsci.springeropen.com/articles/10.1186/s40687-016-0057-xShinichi Mochizuki2016-06-05T00:00:00ZProof of the umbral moonshine conjecturehttp://resmathsci.springeropen.com/articles/10.1186/s40687-015-0044-7The Umbral Moonshine Conjectures assert that there are infinite-dimensional graded modules, for prescribed finite groups, whose McKay–Thompson series are certain distinguished mock modular forms. Gannon has pr...Thu, 10 Dec 2015 00:00:00 GMThttp://resmathsci.springeropen.com/articles/10.1186/s40687-015-0044-7John F. R. Duncan, Michael J. Griffin and Ken Ono2015-12-10T00:00:00ZAlgebraic boundaries of convex semi-algebraic setshttp://resmathsci.springeropen.com/articles/10.1186/s40687-015-0022-0We study the algebraic boundary of a convex semi-algebraic set via duality in convex and algebraic geometry. We generalise the correspondence of facets of a polytope with the vertices of the dual polytope to g...Fri, 20 Mar 2015 00:00:00 GMThttp://resmathsci.springeropen.com/articles/10.1186/s40687-015-0022-0Rainer Sinn2015-03-20T00:00:00ZS n -equivariant sheaves and Koszul cohomologyhttp://resmathsci.springeropen.com/articles/10.1186/s40687-014-0010-9We give a new interpretation of Koszul cohomology, which is equivalent under the Bridgeland-King-Reid equivalence to Voisin’s Hilbert scheme interpretation in dimensions 1 and 2 but is different in higher dime...Thu, 20 Nov 2014 00:00:00 GMThttp://resmathsci.springeropen.com/articles/10.1186/s40687-014-0010-9David H Yang2014-11-20T00:00:00Z