The proposed project is to support eight graduate students in Berkeley to travel to the Center for Quantum Geometry of Moduli Spaces in Aarhus, Denmark. Graduate students will participate in research workshops, attend master-classes and other research activities as well as to work together with their peers in Europe.
The research topics lie at the interface of representation theory and mathematical physics. More specifically, it aims at problems in the representation theory of quantum groups at roots of 1, on invariants of 3-manifolds, certain problems in local quantum field theory (such as the construction of perturbative Chern-Simons theory), and on problems in integrable systems and solvable models of statistical mechanics. One of the central questions in modern theoretical physics is the construction of the model of fundamental interaction which is consistent with experiment and mathematically adequate. The framework of local quantum field theory is the main concept behind the standard model. However the framework of quantum field theory still largely remains a mathematical puzzle. Part of the research will focus on understanding this puzzle in the context of semi-classical quantization. The goal of other parts of the proposal is the construction of topological and integrable quantum field theories combinatorially and the study of emerging algebraic and analytical problems.
This was a travel supplement grant which allowed graduate students from Berkeley to participate in workshops and schools at the Center for Quantum Geometry of Moduli Spaces at Aarhus, Denmark. The trips were highly successful. They were instrumental for student's research, resulted in publications. Eight students participated, some came more then once. The program was co-funded by the Center. While visiting the Center students developed international collaborations and participated in European workshops. One student graduated in 2013, and received NSF postdoctoral Fellowship. Three other students graduated in 2014. All found good academic jobs. Four remaining students are very successful in their research. One of them will go back to the Center in the summer 2014, supported by the Center to continue joint research with a graduate student from Aarhus. Students learned a lot of mathematics and mathematical physics. The focal scientific theme was the geometry of moduli spaces of flat connections with applications to topology and related problems in mathematical physics. This is a rapidly developing field closely related to recent advances in quantum field theory. In physics terms moduli spaces can be thought as spaces of physical vacua in gauge theories (such as the Standard Model is partical physics). Students developed networks with fellow students from Oxfrod and Aarhus and other places. Now they understand better the research landscape in Europe and in Asia (since some of the participants were from China and India).
