Two adapted stochastic processes can have similar laws but give different results in applications such as optimal stopping, queuing theory, or programming. The reason is that the topology of weak convergence does not account for growth information over time captured filtration an process. To address discontinuities, Aldous introduced extended topology, and subsequently, Hoover Keisler showed bo...

It is shown that the result of Tso-Wu on the elliptical shape of the numerical range of quadratic operators holds also for the C*-algebra numerical range.

We study modular polynomials classifying cyclic isogenies between Drinfeld modules of arbitrary rank over the ring Fq[T ].

Building on recent work of Robertson and Steger, we associate a C∗–algebra to a combinatorial object which may be thought of as a higher rank graph. This C∗–algebra is shown to be isomorphic to that of the associated path groupoid. Various results in this paper give sufficient conditions on the higher rank graph for the associated C∗–algebra to be: simple, purely infinite and AF. Results concer...

We give an upper bound for the rank r of homogeneous (even) Clifford structures on compact manifolds of non-vanishing Euler characteristic. More precisely, we show that if r = 2a · b with b odd, then r ≤ 9 for a = 0, r ≤ 10 for a = 1, r ≤ 12 for a = 2 and r ≤ 16 for a ≥ 3. Moreover, we describe the four limiting cases and show that there is exactly one solution in each case. 2010 Mathematics Su...

The classical Mersenne problem has been a stimulating challenge to number theorists and computer scientists for many years. After briefly reviewing some of the natural settings in which this problem appears as a special case, we introduce an analogue of the Mersenne problem in higher rank, in both a classical and an elliptic setting. Numerical evidence is presented for both cases, and some of t...