Applications of noncommutative analysis

Abstract:

The talk will discuss recent powerful results in noncommutative analysis, obtained jointly with D. Potapov and F. Sukochev, and the role of those results in the resolution of Koplienko's Conjecture (1984) in mathematical physics. This line of research was initiated by studies in theoretical physics in the 1940s and later became guided by research on discrete and continuous Schrödinger operators. The mentioned results are formulated in simple terms (which makes them accessible to a broad audience), yet the proofs are very sophisticated and rely on various techniques of modern and classical analysis.