If a black box simple group is known to be isomorphic to a classical group over a field of known characteristic, a Las Vegas algorithm is used to produce an explicit isomorphism. The proof relies on the geometry of the classical groups rather than on difficult group-theoretic background. This algorithm has applications to matrix group questions and to nearly linear time algorithms for permutation groups. In particular, we upgrade all known nearly linear time Monte Carlo permutation group algorithms to nearly linear Las Vegas algorithms when the input group has no composition factor isomorphic...
If a black box simple group is known to be isomorphic to a classical group over a field of known characteristic, a Las Vegas algorithm is used to prod...
Studies various subsets of the tracial state space of a unital $C^*$-algebra. This book considers II$_1$-factor representations of a class of $C^*$-algebras by Sorin Popa.
Studies various subsets of the tracial state space of a unital $C^*$-algebra. This book considers II$_1$-factor representations of a class of $C^*$-al...
The 'recognition theorem' for graded Lie algebras is an essential ingredient in the classification of finite-dimensional simple Lie algebras over an algebraically closed field of characteristic p.3. This monograph presents the first complete proof of this fundamental result.
The 'recognition theorem' for graded Lie algebras is an essential ingredient in the classification of finite-dimensional simple Lie algebras over an a...
The author considers the fundamental lemma for twisted endoscopy, for the units of Hecke algebras only. He proves that it is true if two other lemmas are true - the fundamental lemma for Lie algebras (and non-twisted endoscopy) and another lemma called 'non-standard fundamental lemma'.
The author considers the fundamental lemma for twisted endoscopy, for the units of Hecke algebras only. He proves that it is true if two other lemmas ...
The authors study Forman's discrete Morse theory from an algebraic viewpoint. Analogous to independent work of Emil Skoldberg, this book shows that this theory can be applied to chain complexes of free modules over a ring and provides four applications of this theory.
The authors study Forman's discrete Morse theory from an algebraic viewpoint. Analogous to independent work of Emil Skoldberg, this book shows that th...
Brings together two unrelated theories dealing with weighted inequalities for the Hardy-Littlewood maximal operator $M$. This work considers the boundedness of $M$ in the weighted Lorentz space $Lambda^p_u(w)$. It gives a unified version of these two theor
Brings together two unrelated theories dealing with weighted inequalities for the Hardy-Littlewood maximal operator $M$. This work considers the bound...
The author obtains some classification result for the mapping class groups of compact orientable surfaces in terms of measure equivalence. In particular, the mapping class groups of different closed surfaces cannot be measure equivalent.
The author obtains some classification result for the mapping class groups of compact orientable surfaces in terms of measure equivalence. In particul...
An important theorem by Beilinson describes the bounded derived category of coherent sheaves on $mathbb^n$, yielding in particular a resolution of every coherent sheaf on $mathbb^n$ in terms of the vector bundles $Omega_{mathbb^n}^j(j)$ for $0le j
An important theorem by Beilinson describes the bounded derived category of coherent sheaves on $mathbb^n$, yielding in particular a resolution of ...
A memoir dealing with the hypoelliptic calculus on Heisenberg manifolds, including CR and contact manifolds. In this context the main differential operators at stake include the Hormander's sum of squares, the Kohn Laplacian, the horizontal sublaplacian, t
A memoir dealing with the hypoelliptic calculus on Heisenberg manifolds, including CR and contact manifolds. In this context the main differential ope...
