American Institute of Mathematics, San Jose, California
Theresa Anderson, Frank Thorne, and Trevor Wooley
Number theory and analysis share many interactions, and there are several emerging areas where input from both fields will likely be quite fruitful. Arithmetic statistics is a subject focused on counting of objects of algebraic interest, has been extensively investigated by Bhargava and collaborators, and seems ripe for Fourier analytic input. Discrete restriction, as pioneered by Bourgain, is rooted in analysis but is sometimes amenable to number theoretic exponential sum estimates inaccessible to such tools as decoupling methods. Discrete analogues in harmonic analysis have been classified in many ways, but are frequently impeded by limited progress on deep number theoretic problems. By bringing together researchers from both analysis and number theory and having them interact on a variety of problems of emerging interest, we hope to make progress on several areas including:
The workshop schedule.
A report on the workshop activities.
Papers arising from the workshop: