SM: Graph Models in Nanotechnology, Photonics, Chemistry, and Other Areas

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KuchmentDMS-0648786 The series of a tutorial and three workshops is a part of asemester-long program at the Isaac Newton Institute forMathematical Sciences in Cambridge, UK. The program assembles alarge international group of mathematicians and physicistsinterested in graph models arising in widely disparate areas ofhigh practical and theoretical importance. Analysis on graphshas been developing very quickly in the last decades, due toneeds of number theory, algebra, probability theory, and spectralgeometry. This area has experienced recently a surge of newimportant applications, new methods, and new models. Newobjects, such as quantum graphs (quantum networks) ordifferential operators on fractals, have emerged, which providesimplified models of complex systems and help with studyingdifficult issues such as, for instance, Anderson localization andquantum chaos. All these developments have sparked the interestof experts in other areas of sciences and mathematics in analysison graphs and in the diversity of methods employed. The programstarts with a tutorial workshop where young researchers andstudents are introduced to the basics of analysis on graphs,quantum graphs, and fractals. Then two workshops follow devotedto spectral analysis and quantum chaos on quantum graphs andgraph models for nanotechnology, chemistry, optics,microelectronics, and other areas. The third workshop addressesalgebraic aspects of analysis on graphs and fractals. Besidesworkshop participation, longer term visits of both establishedand young researchers are arranged. Analysis on graphs has experienced sharp growth in recentyears, due to many new applications that sweep throughout a widescientific landscape: computer graphics, information technology,Internet studies, nanotechnology, microelectronics,superconductivity, optics, chemistry, and material science. Researchers in these areas meet problems that are similar tothose faced by mathematicians in areas like number theory,combinatorics, differential equations, and spectral theory. Theprogram facilitates the urgently needed communication andcooperation among researchers in different areas of mathematicsand sciences. It thus accelerates progress in this new area thathas extensive applications in crucial scientific and technologyfields, such as nanotechnology, photonics, and material science. It alsos help to increase participation and visibility of USresearchers in these fields. Significant training for juniorresearchers and graduate students is provided, includingspecially designed tutorials, seminars, and open problemssessions. A proceedings volume is planned to be published. Thegrant supports US-based participants in the program, mostly USstudents, postdocs, junior faculty, women, and otherunderrepresented groups.