This award supports a Research Network in Mathematical Sciences:?Kinetic description of emerging challenges in multiscale problems of natural sciences (KI-net). Kinetic descriptions have traditionally played a central role in many areas of mathematical physics. In the last two decades, however, kinetic descriptions have emerged as an indispensable tool for a quantitative description of diverse phenomena, ranging from semi-conductors, polymers and plasma, to cell migrations, swarming, and neuron networks, as well as traffic, social and economic networking. It is in this context that the KI-net will foster cross-fertilization between mathematics and other scientific disciplines, with particular focus on the following three areas:* Quantum dynamics with applications to chemistry;*  Network dynamics with applications to social sciences; and*  Kinetic models of biological processes.The principal objectives are to foster new kinetic-based national and international collaborations; to train a future generation of researchers to address new challenges, and to sustain the United-States? leading role on the international stage in this field. The proposed KI-net will bring the full range of mathematical techniques to bear on important scientific challenges in kinetic descriptions of new phenomena in physical, biological and social sciences. The ultimate goal is the development, analysis and computation of novel kinetic descriptions with various applications in these disciplines. KI-net will offer a unique platform to carry out these objectives. It will be centered around three hubs: the Center for Scientific Computation & Math Modeling (CSCAMM) in the University of Maryland, the Institute for Computational and Engineering Science (ICES) at UT Austin, and the Department of Mathematics at the University of Wisconsin-Madison. At the initial stage, they will inter-connect 12 nodes through a series of edges, involving 25 core participants. KI-net Research Network home page: http://www2.cscamm.umd.edu/ki-net/.