Professor Peszynska has been chosen as one of the plenary speakers at SIAM Conference on Mathematical and Computational Issues in the Geosciences to be held Sept 11--14 in Erlangen, Germany. The title of her talk is "Methane hydrate modeling, analysis and simulation: coupled systems and scales". http://www.siam-gs17.de/program/invited-talks-prize-presentations/ Methane hydrate is an ice-like substance abundantly present in deep ocean sediments and in the Arctic. Geoscientists recognize the tremendous importance of gas hydrate as a crucial element of the global carbon cycle, a contributor to climate change studied in various deep ocean observatories, as well as a possible energy source evaluated in recent pilot engineering projects in the US and Japan. Hydrate evolution however is curiously not very well studied by computational mathematics community. In the talk Peszynska will present the challenges of hydrate modeling, which start with the need to respond to the interests of geophysicists to enable lasting collaborations that deliver meaningful results. Next we present a cascade of complex to simplified models. For the latter, some analysis of the underlying well-posedness in a very weak setting can be achieved. For the former, interesting scenarios involving multiple scales, and coupled phenomena of flow, transport, phase transitions, and geomechanics, can be formulated. She will report on most recent results obtained jointly with the geophysicists Marta Torres (Oregon State), Wei-Li Hong (Arctic University of Norway), mathematicians Ralph Showalter (Oregon State) and F. Patricia Medina (WPI), computational scientist Anna Trykozko (University of Warsaw), as well as many current and former students to be named in the talk.