Simon Levin

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  Collective motion and collective decision-making
  Simon Levin
  There is a long history of research on the mathematical modeling of animal populations, largely built on diffusion models. The classical literature, however, is inadequate to explain observed spatial patterning, or foraging and anti-predator behavior, because animals actively aggregate. This lecture will discuss models of animal aggregation, and the role of leadership in collective motion. It will also explore models of the evolution of collective behavior, and implications for the optimal design of robotic networks of interacting sensors, with particular application to marine systems.
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  Challenges In Mathematical Ecology: Scaling And Collective Phenomena
  Simon Levin
  The subject of mathematical ecology is one of the oldest in mathematical biology, having its formal roots a century ago in the work of the great mathematician Vito Volterra, with links, some long before, to demography, epidemiology and genetics. Classical challenges remain in understanding the dynamics of populations and connections to the structure of ecological communities. However, the scales of integration and scope for interdisciplinary work have increased dramatically in recent years. Metagenomic studies have provided vast stores of information on the microscopic level, which cry out for methods to allow scaling to the macroscopic level of ecosystems, and for understanding biogeochemical cycles and broad ecosystem patterns as emergent phenomena; indeed, global change has pushed that mandate well beyond the ecosystem to the level of the biosphere. Secondly, the recognition of the importance of collective phenomena, from the formation of biofilms to the dynamics of vertebrate flocks and schools to collective decision-making in human populations poses important and exciting opportunities for mathematicians and physicists to shed light. Finally, from behavioral and evolutionary perspectives, these collectives display conflict of purpose or fitness across levels, leading to game-theoretic problems in understanding how cooperation emerges in Nature, and how it might be realized in dealing with problems of the Global Commons. This lecture will attempt to weave these topics together and both survey recent work, and offer challenges for how mathematics can contribute to open problems.
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  Mathematical Ecology: A Century of Progress, and Challenges for the Next Century
  Simon Levin

  Mathematical ecology is one of the oldest and most successful branches of mathematical biology, and one that has profited both ecology and mathematics. The great mathematician Volterra was a pioneer a century ago, and the subject has built on the dynamical systems approaches he introduced. As attention has turned to the ecological challenges of the present- climate change, biodiversity loss, critical transitions and the management of the global commons, new methods have entered from stochastic processes to game theory, from statistical physics to topological data analysis, and with a heavy emphasis on high-speed computation.  In this talk, I will trace out some of the historic successes, and introduce modern challenges.