Recent zbMATH articles in MSC 20C15https://www.zbmath.org/atom/cc/20C152021-05-28T16:06:00+00:00WerkzeugTowards the classification of finite simple groups with exactly three or four supercharacter theories.https://www.zbmath.org/1459.200012021-05-28T16:06:00+00:00"Ashrafi, A. R."https://www.zbmath.org/authors/?q=ai:ashrafi.ali-reza"Koorepazan-Moftakhar, F."https://www.zbmath.org/authors/?q=ai:koorepazan-moftakhar.fatemehThe uncertainty principle: variations on a theme.https://www.zbmath.org/1459.810642021-05-28T16:06:00+00:00"Wigderson, Avi"https://www.zbmath.org/authors/?q=ai:wigderson.avi"Wigderson, Yuval"https://www.zbmath.org/authors/?q=ai:wigderson.yuvalSummary: We show how a number of well-known uncertainty principles for the Fourier transform, such as the Heisenberg uncertainty principle, the Donoho-Stark uncertainty principle, and Meshulam's nonabelian uncertainty principle, have little to do with the structure of the Fourier transform itself. Rather, all of these results follow from very weak properties of the Fourier transform (shared by numerous linear operators), namely that it is bounded as an operator \(L^1\to L^\infty\), and that it is unitary. Using a single, simple proof template, and only these (or weaker) properties, we obtain some new proofs and many generalizations of these basic uncertainty principles, to new operators and to new settings, in a completely unified way. Together with our general overview, this paper can also serve as a survey of the many facets of the phenomena known as uncertainty principles.Representation varieties of finite index subgroups of Baumslag-Solitar groups.https://www.zbmath.org/1459.200022021-05-28T16:06:00+00:00"Benyash-Krivets, V. V."https://www.zbmath.org/authors/?q=ai:benyash-krivets.valerii-vatslavovich"Govorushko, I. O."https://www.zbmath.org/authors/?q=ai:govorushko.i-oSummary: Representation varieties of finite index subgroups of Baumslag-Solitar groups are investigated. It is proved that all irreducible components of the representation variety of a finite index subgroup of a Baumslag-Solitar group are birational isomorphic to irreducible components of the representation variety of some another Baumslag-Solitar group.Cutoff for the warp-transpose top with random shuffle.https://www.zbmath.org/1459.600092021-05-28T16:06:00+00:00"Ghosh, Subhajit"https://www.zbmath.org/authors/?q=ai:ghosh.subhajitSummary: We consider a random walk on the complete monomial group \(G_n \wr S_n\) generated by the elements of the forms \((\mathrm{e},\cdots,e,g;\mathrm{id})\) and \((\mathrm{e},\cdots,\mathrm{e},g^{-1},\mathrm{e},\ldots,\mathrm{e},g;(i,n))\) for \(g\) in \(G_n\), \(1\le i < n\). We call this the warp-transpose top with random shuffle on \(G_n \wr S_n\). We find the spectrum of the transition probability matrix for this shuffle. We prove that the mixing time for this shuffle is of order \(n \log(n)+(1/2)n \log(|G_n|-1)\) and under some condition on \(|G_n|\), this shuffle exhibits the cutoff phenomenon.