Takeshi Saito studied at the University of Tokyo under Kazuya Kato and received his doctorate in 1989. He began his career at the University of Tokyo as an assistant in 1987, was promoted to lecturer in 1990, assistant professor in 1992, and full professor in 1999.

Among his most influential works are a series of articles with Kazuya Kato on the Bloch conductor formula and ramification theory of varieties over perfect or local fields and a series of articles with Ahmed Abbes on ramification groups of local fields. His research on ramification theory culminated in 2017 with a milestone article establishing an algebraic theory of characteristic cycles in positive characteristic.

Personnal webpage

Videos:

• Upper Ramification Groups of Local Fields with Imperfect Residue Fields : lecture 1 – lecture 2 – lecture 3
• Micro Support of a Constructible Sheaf in Mixed Characteristic
• Characteristic Cycle of an \ell-adic Sheaf

Dennis Gaitsgory studied at Tel Aviv University under Joseph Bernstein (1990-1996) and received his doctorate in 1997. Prior to his 2021 appointment at Max-Planck-Institute for Mathematics, Bonn, he was an associate professor at the University of Chicago from 2001–2005 and a professor at Harvard University from 2005-2021.

His work in geometric Langlands culminated in a joint 2002 paper with Edward Frenkel and Kari Vilonen, which established the conjecture for finite fields. In 2004, Dennis Gaitsgory published a separate paper, generalizing the proof to include the field of complex numbers as well.

Personal webpage.