Date  Speaker  Topic 

M Sep 12  –  Organizational Meeting 
M Sep 19  Chris Dock (Tufts)  Lipschitz stability of U(r) Phase Retrieval
Abstract: The classical phase retrieval problem arises in contexts ranging from speech recognition to xray crystallography and quantum state tomography. The generalization to matrix frames that are U(r) phase retrievable is natural in the sense that it corresponds to quantum tomography of impure states. The U(r) phase retrieval problem is also essentially equivalent to low rank matrix recovery, and in particular to the Euclidean Distance Geometry problem. We provide computable global stability bounds for the quasilinear analysis map β and a path forward for understanding related problems in terms of the differential geometry of the semialgebraic variety of positive semidefinite matrices. In particular, we manifest a Whitney stratification of the PSD matrices of low rank, which allows us to “stratify” the computation of the global stability bound. We show that in contrast to the rank 1 case, for the impure state case no such global stability bounds can be obtained for the nonlinear analysis map α with respect to certain natural distance metrics. Finally, our computation of the global lower Lipschitz constant for the β analysis map provides novel conditions for a matrix frame to be U(r) phase retrievable. 
M Sep 26  Clare Wickman Lau (JHU APL)  Wasserstein Gradient Flows for Potentials in Frame Theory
Abstract: In this talk, I will discuss some key ideas and methods of two disparate fields of mathematical research, frame theory and optimal transport, using the methods of the second to answer questions posed in the first. In particular, I will discuss construction of gradient flows in the Wasserstein space for a new potential, the tightness potential, which is a modification of the probabilistic frame potential. The potential is suited for the application of a gradient descent scheme from optimal transport that can be used as the basis of an algorithm to evolve a given frame toward a tight probabilistic frame. 
M Oct 3 
Noel Walkington (CMU)  Numerical Approximation of Multiphase Flows in Porous Media Abstract: This talk will review models and structural properties of the 
M Oct 10  No seminar  University Holiday 
M Oct 17  Yekaterina Epshteyn (University of Utah)  Grain Structure, Grain Growth and Evolution of the Grain Boundary Network
Abstract: Cellular networks are ubiquitous in nature. Most technologically useful The evolution of grain boundaries and associated grain growth is a very 
M Oct 24  Karamatou Yacoubou Djima (Wellesley) 

M Oct 31 11am12pm  Hung M. Phan (UMass Lowell) 

M Nov 7  Patrick Farrell (Oxford) 

M Nov 14  Arkadz Kirshtein (Tufts) 

M Nov 21  No Seminar  Thanksgiving week. Let’s rest 
M Nov 28  Tal Shnitzer (MIT) 

M Dec 5  Paola Sebastiani (Tufts Med) 
