His main research interests are convex geometry and its connections with analysis and information theory.
He spent the earliest years of his childhood in the Soviet Union, Romania, Israel, Italy, and Venezuela before he settled in Brooklyn when he was ten.
He graduated from the Polytechnic Institute of Brooklyn, now New York University Tandon School of Engineering with a B.S.
[5] Erwin Lutwak is known for his Dual Brunn Minkowski Theory,[6] his notion of intersection body and his contribution to the solution of the Busemann–Petty problem,[7] for proving the long-conjectured upper-semicontinuity of affine surface area,[8] his contributions to the Lp Brunn Minkowski Theory and, in particular, his Lp Minkowski problem[9] and its solution in important cases.
They have one daughter, Hope Lutwak, who graduated with a Bachelor of Science in 2018 from the Massachusetts Institute of Technology.