This list (URL: https://81018.com/geometers-living/ ) was initiated in March 2025 and has not been rigorously edited. An alphabetical listing of just a few leading thinkers. Those who have died will remain listed, but their name will be in gray with their birth-and-death year). Eventually there will be a total over lap with our mathematicians list. Most of these names were recommended by…

• Yve André (Wiki) (direct summand conjecture with the help of perfectoid spaces, etc.)
• Michael Artin (Artin approximation theorem, etc.)
• Alexander Beilinson (perverse sheaves, etc.)
• Joseph Bernstein (perverse sheaves, etc.)
• Bhargav Bhatt (Tannaka duality theorems for maps of algebraic spaces, perfectoid spaces applied to the direct summand conjecture, etc.)
• Pierre Deligne (Weil conjectures, etc.)
• David Eisenbud (great overall person for the community: MSRI, etc.)
• Gerd Faltings (Faltings’ theorem)
• William Fulton (great writing)
• Joe Harris (great writing)
• Robin Hartshorne (famous textbook)
• Luc Illusie (cotangent complex, etc.)
• Aise Johan de Jong (singularity theory, Stacks Project)
• Nick Katz (p-adic methods, etc.)
• Sheldon Katz (mathematical string theory)
• Kiran Kedlaya (lots of exciting arithmetic geometry: p-adic Hodge theory, perfectoid spaces, etc.)
• Maxim Kontsevich (physical connections)
• Yuri Manin (Diophantine geometry, etc.)
• Shinichi Mochizuki (anabelian geometry, esp. abc conjecture)
• David Mumford (moduli spaces, etc.)
• Bjorn Poonen (number theory, decidability)
• Michael Rapoport (Shimura varieties, etc.*)
• Miles Reid (great writing)
• Peter Scholze (perfectoid spaces, etc.)
• Jean-Pierre Serre (FCA, GAGA, etc.)
• John Tate (Tate conjectures, etc.)
• Ravi Vakil (Gromov-Witten theory, famous lecture notes)
• Claire Voisin (Hodge theory)
• Xijia Wang
• Charles Weibel (motivic Bloch-Kato, famous textbook)
• Shing-Tung Yau
• Shou-Wu Zhang (Bogomolov conjecture, partial BSD conjecture)