REU 2025: algorithmic and machine learning methods in algebraic geometry

In the summer of 2025 I directed a Research Experience for Undergraduates. Our topic was algorithmic methods in algebraic geometry, and applications of machine learning in pure mathematics.

Here is the reading list we followed:  

•  Chapters 1 through 5 from Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra

• three classic papers arXiv:1406.1078, arXiv:1409.0473 and arXiv:1706.03762 about recursive neural networks, and transformers

• and a paper about Gröbner basis and transformers

Here are some of my lecture notes:

• gradient descent more details are in these notes 

• interpolation and regression

• neural networks and RNNs

• word embeddings and transformers