Probability and Statistics Seminar at Northeastern University 2005-2006

Details

• Time: Tuesdays, 2:00 pm
• Place: 509 Lake Hall

Schedule

• September 20.
  • Speaker: Koenraad Audenaert (Imperial College London)
  • Title: Norm Compression Inequalities for Block Matrices
  • Abstract. I consider inequalities for the Schatten q-norms, which are non-commutative generalistions of the l_q norms. Given a block partitioned matrix, one can try and bound the q-norm of the matrix itself in terms of the q-norms of the blocks. The inequalities that arise can be called norm compression inequalities, because the bound is stated in terms of the elements of the norm compression of the matrix, which is what you get when replacing every block of the matrix by its norm. In this talk I give an overview of previously known bounds of this kind. I then present some norm compression bounds for positive semidefinite 2X2 block matrices, complementing earlier work by Chris King. Finally, I give an overview of various conjectured norm compression inequalities, and discuss some of the implications their validity would have in quantum information theory. Ê See also math.FA/0505680
• November 1.
  • Speaker: Rajmohan Rajaraman (Northeastern University)
  • Title: On the Capacity of Internet-Like Graphs
  • Abstract. There have been several recent research efforts aimed at understanding the scaling properties of Internet-like networks. Two popular models for studying large-scale internetworks are the power law random graph model and the preferential connectivity model. In this seminar, I will first define these models. We will then discuss recent theoretical results on the capacity of networks generated under these models -- in terms of the congestion incurred for a certain traffic pattern. We will also consider the impact of basic Internet routing schemes on the capacity of such networks, and end with some open problems in this area. Mathematical techniques used: probability theory, graph theory.
  
  Last updated October 25, 2005.