A new understanding of the infrared dynamics of QCD theories has emerged in recent years, leading to nonperturbative renormalization group flows of QCD theories. We will discuss some of these developments, including QCD theories that develop a mass gap, the endpoint of renormalization group flows, and the (conjectural) emergence of nonperturbative condensates.
One of the most wonderful gifts from string theory to pure mathematics comes from Mike Douglas' ideas on the decay of D-branes and walls of marginal stability. Tom Bridgeland formalized structures discovered by Mike as stability conditions in abstract triangulated categories. This notion became central in modern homological algebra and is also pivotal in the theory of Donaldson-Thomas...
