Hala Masri: Singer

Hala! Position Paper

PROLOGUE In the last years our knowledge has rapidly increased allowing us to focus our research resources to very specific areas. As a consequence we know far more about specifics and less about everything. Good examples of this trend are the Navigation and Airspace Management domains. Future ATM tools and technology may provide the users with all the required information about any flight at a...

Wolf Singer

Nilpotent Singer Groups

Let N be a nilpotent group normal in a group G. Suppose that G acts transitively upon the points of a finite non-Desarguesian projective plane P. We prove that, if P has square order, then N must act semi-regularly on P. In addition we prove that if a finite non-Desarguesian projective plane P admits more than one nilpotent group which is regular on the points of P then P has non-square order a...

The Kadison-Singer Conjecture

We are given a large integer N , and a fixed basis {ei : 1 ≤ i ≤ N} for the space H = C . We are also given an N -by-N matrix H that has all its diagonal entries zero, and has norm one. If σ ⊆ {1, 2, . . . , N}, let Pσ be the projection onto the space Hσ := ∨{ei : i ∈ σ}. Call such a projection basic, and the range of a basic projection a basic subspace. For each constant 0 < γ < 1, we want to ...

- Patodi - Singer Index Theorem ∗

In [Wu], the noncommutative Atiyah-Patodi-Singer index theorem was proved. In this paper, we extend this theorem to the equivariant case.