Abstract: Fundamental operators arising in Euclidean harmonic analysis are often associated with sets of directions. What are these operators? Why are they important? How do direction sets enter the picture and influence their behaviour? The central issues underpinning these questions are rooted in analysis and geometry, but recently tools from extremal combinatorics and algebraic geometry have also played an important role in their study. This talk will provide a brief history of these problems, compare and contrast a few such operators and discuss some modern 

approaches for their treatment.

 

Since the talk will be online, the plan is to present the material in short 5-10 minute modules, with breaks in between for questions and answers. A large portion of the talk is intended to be accessible to graduate students. Please bring lots of questions - curiosity is a plus!