Ivo Dell'Ambrogio

My research mostly concerns homological algebra and its applications, as it tends to gravitate around triangulated categories and their models. The highly interdisciplinary nature of this subject allows me to work on a wide range of problems throughout K-theory, algebraic geometry, algebraic topology, operator algebras, representation theory, and category theory. The work I have done in this area between 2008-2016 is surveyed in my Habilitation memoir.

In particular, since my thesis I have been especially interested in tensor triangular geometry, a geometric theory of tensor triangulated categories which allows the extension of many 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 include its initiator Paul Balmer, Giordano Favi, Greg Stevenson, Beren Sanders, Sebastian Klein, Bregje Pauwels, Tobias Barthel, Drew Heard…

In more recent years, in joint work with Paul Balmer and starting with this monograph, I have been developing the theory of Mackey 2-functors as a broad framework for studying equivariant questions in all corners of mathematics where finite groups and linear categories are involved. I am also growing interested in certain applied topics such as machine learning.