Motives, mapping class groups, and monodromy
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916380802023424 |
|---|---|
| author | Litt, Daniel |
| author_facet | Litt, Daniel |
| contents | We survey some recent developments at the interface of algebraic geometry, surface topology, and the theory of ordinary differential equations. Motivated by "non-abelian" analogues of standard conjectures on the cohomology of algebraic varieties, we study mapping class group actions on character varieties and their algebro-geometric avatar -- isomonodromy differential equations -- from the point of view of both complex and arithmetic geometry. We then collect some open questions and conjectures on these topics. These notes are an extended version of my talk at the April 2024 Current Developments in Mathematics conference at Harvard. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_02234 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Motives, mapping class groups, and monodromy Litt, Daniel Algebraic Geometry Geometric Topology Number Theory 32S40, 14C30, 57K20 We survey some recent developments at the interface of algebraic geometry, surface topology, and the theory of ordinary differential equations. Motivated by "non-abelian" analogues of standard conjectures on the cohomology of algebraic varieties, we study mapping class group actions on character varieties and their algebro-geometric avatar -- isomonodromy differential equations -- from the point of view of both complex and arithmetic geometry. We then collect some open questions and conjectures on these topics. These notes are an extended version of my talk at the April 2024 Current Developments in Mathematics conference at Harvard. |
| title | Motives, mapping class groups, and monodromy |
| topic | Algebraic Geometry Geometric Topology Number Theory 32S40, 14C30, 57K20 |
| url | https://arxiv.org/abs/2409.02234 |