Ivo Dell'Ambrogio

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My research gravitates around triangulated categories, their models, and their applications. The highly interdisciplinary nature of this subject allows me to work on problems ranging from K-theory, algebraic geometry, algebraic topology, to operator algebras, representation theory, and category theory.

Let me try to be a little more precise. Much of my research is related to Paul Balmer's tensor triangular geometry, a geometric theory of tensor triangulated categories that allows one to extend ideas and methods of algebraic geometry to such diverse areas as the modular representation theory of finite groups, (motivic) stable homotopy, and noncommutative geometry. Other mathematicians working in tensor triangular geometry are Paul Balmer, Giordano Favi, Greg Stevenson, Beren Sanders, Sebastian Klein and Bregje Pauwels.

I am also interested in the following topics:

  • Quillen model categories, homotopical algebra
  • equivariant K-theory and KK-theory of C*-algebras
  • representation theory of finite groups and finite dimensional algebras
  • Mackey functors and biset functors
  • quadratic forms, Witt groups, Brauer groups
  • Gorenstein homological algebra, relative homological algebra
  • Hilbert modules over C*-algebras and C*-categories
  • (noncommutative) motives
  • categorification and higher categories