2008, Benson, Dave, Iyengar, Srikanth B., Krause, Henning

We classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple (or, equivalently all) modules. One application is a proof of the telescope conjecture in this context. Others include new proofs of the tensor product theorem and of the classification of thick subcategories of the finitely generated modules which avoid the use of cyclic shifted subgroups. Along the way we establish similar classifications for differential graded modules over graded polynomial rings, and over graded exterior algebras.

2009, Morier-Genoud, Sophie, Ovsienko, Valentin

We study the notion of Γ-graded commutative algebra for an arbitrary abelian group Γ. The main examples are the Clifford algebras already treated in [2]. We prove that the Clifford algebras are the only simple finite-dimensional associative graded commutative algebras over R or C. Our approach also leads to non-associative graded commutative algebras extending the Clifford algebras.

2007, Berstein, Yael, Lee, Jon, Maruri-Aguilar, Hugo, Onn, Shmueel, Riccomagno, Eva, Weismantel, Robert, Wynn, Henry

We study the problem of optimizing nonlinear objective functions over matroids presented by oracles or explicitly. Such functions can be interpreted as the balancing of multi-criteria optimization. We provide a combinatorial polynomial time algorithm for arbitrary oracle-presented matroids, that makes repeated use of matroid intersection, and an algebraic algorithm for vectorial matroids. Our work is partly motivated by applications to minimum-aberration model-fitting in experimental design in statistics, which we discuss and demonstrate in detail.

2009, Blagojevi´c, Pavle V.M., Matschke, Benjamin, Ziegler, Günter M.

We prove a "Tverberg type" multiple intersection theorem. It strengthens the prime case of the original Tverberg theorem from 1966, as well as the topological Tverberg theorem of B´ar´any et al. (1980), by adding color constraints. It also provides an improved bound for the (topological) colored Tverberg problem of B´ar´any & Larman (1992) that is tight in the prime case and asymptotically optimal in the general case. The proof is based on relative equivariant obstruction theory.

2008, Chen, Xia, Mörters, Peter

We determine the precise asymptotics of the logarithmic upper tail probability of the total intersection local time of p independent random walks in Zd under the assumption p(d−2)>d. Our approach allows a direct treatment of the infinite time horizon.

2009, Anderson, J.M., Hinkkanen, Aimo

Let f1, . . . , fp be entire functions that do not all vanish at any point, so that (f1, . . . , fp) is a holomorphic curve in CPp−1. We introduce a new and more careful notion of counting the order of the zero of a linear combination of the functions f1, . . . , fp at any point where such a linear combination vanishes, and, if all the f1, . . . , fp are polynomials, also at infinity. This enables us to formulate an inequality, which sometimes holds as an identity, that sharpens the classical results of Cartan and others.

2009, Haak, Bernhard H., Jacob, Birgit

Volterra observations systems with scalar kernels are studied. New sufficient conditions for admissibility of observation operators are developed and some examples are discussed.

2008, Badea, Catalin, Grivaux, Sophie, Müller, Vladimir

For each fixed number " in (0, 1) we construct a bounded linear operator on the Banach space `1 having a certain orbit which intersects every cone of aperture ", but with every orbit avoiding a certain ball of radius d, for every d > 0. This answers a question from [8]. On the other hand, if T is an operator on the Banach space X such that for every " > 0 there is a point in X whose orbit under the action of T meets every cone of aperture ", then T has a dense orbit.

2008, Axelsson, Owe, Karátson, János

Preconditioning methods via approximate block factorization for block tridiagonal matrices are studied. Bounds for the resulting condition numbers are given, and two methods for the recursive construction of the approximate Schur complements are presented. Illustrations for elliptic problems are also given, including a study of sensitivity to jumps in the coefficients and of a suitably motidied Poincaré-Steklov operator on the continuous level.

2008, Lee, Jon, Onn, Shmuel, Weismantel, Robert

We consider the problem of optimizing a nonlinear objective function over a weighted independence system presented by a linear-optimization oracle. We provide a polynomial-time algorithm that determines an r-best solution for nonlinear functions of the total weight of an independent set, where r is a constant that depends on certain Frobenius numbers of the individual weights and is independent of the size of the ground set. In contrast, we show that finding an optimal (0-best) solution requires exponential time even in a very special case of the problem.