Title: Waring's problem with shifts
Speaker: Sam Chow (Bristol)
Abstract: Since its formulation in 1770, Waring's problem has been the benchmark for research on diophantine equations in many variables. Following a broad discussion of diophantine equations, we provide a survey on Waring's problem. The Hardy-Littlewood circle method plays a crucial r\^ole in this saga. Next we enter the world of diophantine inequalities, where the corresponding tool is the Davenport-Heilbronn circle method. We present two analogues to Waring's problem: one has been studied extensively, and the other is new.