## Low Algebraic Dimension Matrix Completion

Laura Balzano

September 11, 2020

Laura Balzano

September 11, 2020

Rafael Irizarry

September 10, 2020

Nancy Zhang

September 10, 2020

Sarah Peluse

Institute for Advanced Study and Princeton University; Veblen Research Instructor, School of Mathematics

September 10, 2020

A subset D of a finite cyclic group Z/mZ is called a "perfect difference set" if every nonzero element of Z/mZ can be written uniquely as the difference of two elements of D. If such a set exists, then a simple counting argument shows that m=n2+n+1 for some nonnegative integer n. Singer constructed examples of perfect difference sets in Z/(n2+n+1)Z whenever n is a prime power, and it is an old conjecture that these are the only such n for which a perfect difference set exists.

Anru Zhang

September 10, 2020

David Dunson

September 9, 2020

Jay Taylor

University of Southern California; Member, School of Mathematics

September 9, 2020

This talk will form part of a series of three talks focusing on Broué’s Abelian Defect Group Conjecture, which concerns the modular representation theory of finite groups. We will pay particular attention here to the ‘geometric’ form of the conjecture which concerns finite reductive groups such as GLn(q) and SLn(q). Broué’s conjecture gives a strong structural reason for many numerical coincidences one sees amongst characters and is part of a general ‘local/global phenomena’ that is abundant in the theory.

Grace Yi

September 9, 2020

Rod Little

September 8, 2020

Julie Josse

September 8, 2020