Mathematical Conversations

Gaussian elimination is one of the oldest and most popular techniques for factoring a matrix. The growth of entries in Gaussian elimination is an important practical problem. Modern results as well as practice show that entry growth is not a practical concern, yet this still remains a fascinating theoretical question. Cryer's conjecture regarding pivot growth was disproved decades ago, yet the gap between constructions and upper bounds remains surprisingly large. Please come, bring your mathematical ideas, and help me solve this problem!