Tame Geometry for Hodge Theory

Explore a comprehensive lecture on tame geometry and its applications to Hodge Theory presented by Thomas Warren Scanlon from the University of California, Berkeley, at the 2022 Virtual Joint Mathematics Meetings. Delve into advanced mathematical concepts, including the Accounting Theorem, major advances in the field, and the intricacies of Hodge Theory. Examine topics such as topology, definable structures, restricted analytic functions, and cell decomposition theorems. Gain insights into geometric variation, the beautiful theorem, and functional transcendence. This 52-minute AMS Current Events Bulletin lecture offers a deep dive into cutting-edge mathematical research, providing a valuable resource for mathematicians and advanced students in the field.

Introduction
Welcome
Accounting Theorem
Proofs
First major advance
Second major advance
Hodge Theory
Other Papers
All Minimality
topology moderate
topology and ominous structures
definable structures
restricted analytic functions
piecewise continuous
cell decomposition theorem
definable child theorem
suggestive connections
comparison theorem
Hodge decomposition
Hodge classes
Geometric variation
The beautiful theorem
The functional transcendence theorem
Conclusion
Discussion