In this course we will discuss the progression of ideas in the history of algebraic geometry, with a focus on the period from Riemann through Grothendieck (roughly 1850 - 1970). Please see the ...

This graduate textbook offers a self-contained introduction to the concepts and techniques of logarithmic geometry, a key tool for analyzing compactification and degeneration in algebraic geometry and ...

In the Fall of 2018 the seminar was on Topologies and Descent. Please see the webpage with information. In the Spring of 2018 the seminar was on local cohomology in algebraic geometry (following SGA2 ...

Thanks Martin for making such nice notes and also making them available. If you just want to browse at some of the code, here is what we talked about in Lecture 1. If you want to go further, and learn ...

The following lecture notes are taken during my year in Part III of the MASt Pure Mathematics course in the University of Cambridge. You can download them via the ...

Arising from the 2022 Japan-US Mathematics Institute, this book covers a range of topics in modern algebraic geometry, including birational geometry, classification of varieties in positive and zero ...

Both algebraic and arithmetic geometry are concerned with the study of solution sets of systems of polynomial equations. Algebraic geometry deals primarily with solutions lying in an algebraically ...

I am also interested in theoretical computer science, problems and tools in scientific computing, algorithms for algebraic geometry, and teaching cryptography. I am perhaps best known for my ...