Beren Sanders
Associate Professor
Mathematics Department
University of California, Santa Cruz
1156 High Street
Santa Cruz, CA 95064
Office: McHenry 4184
E-mail: My first name @ ucsc.edu
Phone: (831) 459-4550
About Me
I'm an associate professor in the Mathematics Department at UC Santa Cruz. Previously, I was a postdoc at EPFL and at the University of Copenhagen. I completed my PhD at UCLA under the supervision of Paul Balmer.
Research Interests
Triangulated categories and their applications, especially tensor triangular geometry and examples arising in stable homotopy theory, modular representation theory, and algebraic geometry. Other interests include equivariant homotopy theory, motivic homotopy theory, higher category theory, and the representation theory of groups and associative algebras.
Publications
- The spectrum of excisive functors. Preprint, 89 pages, 2024. Joint with
Gregory Arone,
Tobias Barthel and Drew Heard. [arxiv] [pdf]
- On surjectivity in tensor triangular geometry. Preprint, 6 pages, 2023. Joint with Tobias Barthel, Nàtalia Castellana and Drew Heard. [arxiv] [pdf]
- Descent in tensor triangular geometry. Preprint, 46 pages, 2023. Joint with Tobias Barthel, Nàtalia Castellana, Drew Heard, Niko Naumann and Luca Pol. [arxiv] [pdf]
- Cosupport in tensor triangular geometry. Preprint, 87 pages, 2023. Joint with Tobias Barthel, Nàtalia Castellana and Drew Heard. [arxiv] [pdf]
- Stratification and the comparison between homological and tensor triangular support. The Quarterly Journal of Mathematics 74(2):747-766, 2023. Joint with Tobias Barthel and Drew Heard. [arxiv] [journal [pdf]
- Stratification in tensor triangular geometry with applications to spectral Mackey functors. Cambridge Journal of Mathematics 11(4):829-915, 2023. Joint with Tobias Barthel and Drew Heard. [arxiv] [journal] [pdf]
- A characterization of finite étale morphisms in tensor triangular geometry. Épijournal de Géométrie Algébrique, 6:18, 2022. [arxiv] [journal] [pdf]
- The spectrum of derived Mackey functors. Transactions of the American Mathematical Society, 375(6):4057-4105, 2022. Joint with Irakli Patchkoria and Christian Wimmer. [arxiv] [journal] [pdf]
- The compactness locus of a geometric functor and the formal construction of the Adams isomorphism. Journal of Topology, 12(2):287-327, 2019. [arxiv] [journal] [pdf]
- A note on triangulated monads and categories of module spectra. Comptes Rendus Mathématique, 356(8):839-842, 2018. Joint with Ivo Dell’Ambrogio. [arxiv] [journal] [pdf]
- The spectrum of the equivariant stable homotopy category of a finite group. Inventiones Mathematicae, 208(1):283-326, 2017. Joint with Paul Balmer. [arxiv] [journal] [pdf]
- Grothendieck-Neeman duality and the Wirthmüller isomorphism. Compositio Mathematica, 152(8):1740-1776, 2016. Joint with Paul Balmer and Ivo Dell’Ambrogio. [arXiv] [journal] [pdf]
- Restriction to finite-index subgroups as étale extensions in topology, KK-theory and geometry. Algebraic & Geometric Topology, 15(5):3025-3047, 2015. Joint with Paul Balmer and Ivo Dell’Ambrogio. [arXiv] [journal] [pdf]
- Higher comparison maps for the spectrum of a tensor triangulated category. Advances in Mathematics, 247:71-102, 2013. [arXiv] [journal] [pdf]
Teaching
MATH202 - Algebra III (Spring 2024)
MATH111B - Algebra (Spring 2024)
MATH111A - Algebra (Fall 2023)
MATH281 - Topics in Algebra (Spring 2023)
MATH111B - Algebra (Spring 2023)
MATH111A - Algebra (Winter 2023)
MATH201 - Algebra II (Winter 2023)
MATH194 - Senior Seminar (Spring 2022)
MATH117 - Advanced Linear Algebra (Spring 2022)
MATH281 - Topics in Algebra (Fall 2021)
MATH239 - Homological Algebra (Fall 2021)
MATH234 - Riemann Surfaces (Spring 2021)
MATH210 - Manifolds III (Spring 2021)
MATH111A - Algebra (Winter 2021)
MATH211 - Algebraic Topology (Winter 2021)
MATH210 - Manifolds III (Spring 2020)
MATH19A - Calculus For Science, Engineering, And Mathematics (Fall 2019)
MATH203 - Algebra IV (Fall 2019)
MATH117 - Advanced Linear Algebra (Spring 2019)
MATH23B - Vector Calculus (Winter 2019)
MATH200 - Algebra I (Fall 2018)
Videos
Those with an excess amount of time on their hands can watch my
talk at Triangulated Categories and Applications (recorded for the ages on 23 June 2016 in beautiful Banff).
Thrilling stuff.
More recently, here is my (virtual)
talk at the
Workshop on Homotopy Theory and Group Theory (recorded on 8 July 2021). Here are the [slides].
Even more recently, here is my
talk at the
Workshop on Spectra, Triangles and Higher Structures
(recorded on 5 December 2022 at the Hausdorff Research Institute for Mathematics).