Solitons, Spectral Theory Graphs Educational Tools

主要研究者的研究计划的主要目标是拓扑和几何与分析的统一。他对描述现实世界物理中拓扑特征起关键作用的一些现象的具体结果特别感兴趣。特别是，这些现象是由主要研究小组在强磁场存在下的单晶金属的导电性，非线性波理论（孤子）和量子线理论（图上的量子力学）中发现的。该奖项将支持主要研究拓扑和几何与分析的统一的数学学院的访问者和研究生。通过这种方式，年轻的数学家可以与各种杰出的科学家互动。这些互动包括在研讨会上与参观者举行科学会议，以及出席特邀杰出科学家的简短系列讲座。这些互动将有助于吸引研究生学习这门学科，并提高他们在职业生涯开始时的培训质量。

DMS-0072700Sergey NovikovThe main objective of the principal investigator's research program is the unification of topology and geometry with analysis. He is especially interesing in specific results describing some phenomena in real world physics where topological features play akey role. In particular, such phenomena were found by the principal investigators's group in the conductivity of single crystal metals in the presence of strong magnetic field, in the theory of nonlinear waves (solitons), and in the theory of quantum wires (quantum mechanics on graphs). This award will support visitors and graduate students inthe principal investigator's school of mathematics which isprimarily concerned with the unification of topology andgeometry with analysis. In this way young mathematicians caninteract with a variety of outstanding scientists. These interactions include scientific meetings with visitors in miniseminars and attendance at short series of lectures by specially invited outstanding scientists. These interactions will help attract graduate students to the subject and improve the quality of their training at the beginning of their careers.