Noah Olander NSF Postdoctoral Scholar UC Berkeley Department of Mathematics Email: nolander[at]berkeley[dot]edu

About

I'm a mathematician studying algebraic geometry, especially derived categories of algebraic varieties, positive characteristic geometry, and algebraic stacks. I am currently an NSF Postdoc at UC Berkeley supervised by Martin Olsson. From September 2022 until September 2024 I was a postdoc of Lenny Taelman at the University of Amsterdam, although in Fall 2023 I was working at the Hausdorff Research Institute for Mathematics in Bonn as part of the Junior Trimester Program Algebraic geometry: derived categories, Hodge theory, and Chow groups. Before that I was a PhD student of Johan de Jong at Columbia University.

Curriculum Vitae

Papers and preprints

• When is Frobenius epic? (with Javier Carvajal-Rojas, Rankeya Datta, and Axel Stäbler).
• Derived categories of quadric bundles and moduli stacks of spinor sheaves (with Raymond Cheng).
• On automorphisms of p-torsion G_m-gerbes.
• A characteristic p analog of formal lifting properties (with Rankeya Datta), International Mathematics Research Notices (IMRN).
• Gerbes for trigonalizable group schemes (with Martin Olsson).
• A derived category analogue of the Nakai--Moishezon criterion (with Daigo Ito).
• Approximation by perfect complexes detects Rouquier dimension (with Pat Lank), Moscow Math Journal .
• On weakly étale morphisms (with Johan de Jong), JPAA .
• Ample line bundles and generation time, Journal für die reine und angewandte Mathematik (Crelle's Journal).
• The Diagonal Dimension of Curves, International Mathematics Research Notices (IMRN).
• Orlov's Theorem in the Smooth Proper Case, Journal of Algebra .

Other writing

• My PhD thesis Resolutions, bounds, and dimensions for derived categories of varieties.
• The chapter "Theorem of the Base" (with Raymond Cheng, Lena Ji, and Matt Larson) of the book Stacks Project Expository Collection, London Mathematical Society Lecture Note Series.
• A section of the Stacks Project I wrote proving that a perfect generator of a quasi-compact and quasi-separated scheme can detect when complexes are bounded. Here is a neat application which gives a characterization of relatively perfect complexes on a proper, flat, finitely presented morphism.
• An example of a line bundle on an algebraic space which is not Zariski locally trivial: example.pdf. This is not the first known example. I constructed this one during the BIRS workshop The Geometry of Algebraic Stacks after discussions with Andres Fernandez-Herrero, Siddharth Mathur, David Rydh, and other participants.
• Some handouts I made when I taught advanced middle and high school students during my time in the LA Math Circle (now the Olga Radko Endowed Math Circle).