George Lusztig is a prominent mathematician known for his contributions to the fields of representation theory and algebraic geometry. He has made significant advancements in understanding the structures of Lie groups and algebraic groups, which are essential in various areas of mathematics and theoretical physics. Lusztig is also recognized for his work on character sheaves and quantum groups, which have important applications in both pure and applied mathematics. His research has influenced many areas, including combinatorics and number theory, making him a respected figure in the mathematical community.