Student Algebra Seminar
The Student Algebra Seminar (SAS) is an initiative for postgraduate and honours students. We learn and share knowledge of algebra and related areas, primarily through presentations on individual research or themes of study. The environment is intended to be low pressure, since everyone in the audience is a student too.
The SAS is currently co-organised by Joshua Ciappara and Bregje Pauwels. It is run online via Zoom. If you are interested in participating or attending, please e-mail ciappara@maths.usyd.edu.au.
Previous iterations of the seminar were organised by Joel Gibson:
Semester 1, 2021
This semester, the seminar's theme will be perverse sheaves. We will be using the paper of BBD as a roadmap, but will refer to various other sources for talk preparation and content, such as:
- M. A. A. de Cataldo and L. Migliorini. The Decomposition Theorem, Perverse Sheaves, and the Topology of Algebraic Maps. Bulletin of the American Mathematical Society 46(4):535–633, 2009.
- P. Achar. Introduction to Perverse Sheaves. Lecture notes, 2007.
- A. Chambert-Loir. An introduction to Perverse Sheaves. Lecture notes, 2018.
- G. Williamson. An Illustrated Guide to Perverse Sheaves. Lecture notes, 2015.
- B. Bhatt. Perverse Sheaves. Lecture notes, 2015.
Schedule
| Time | Speaker | Topic |
|---|---|---|
| Week 3 | Bregje Pauwels | Triangulated categories (abstract) |
| Week 4 | Joshua Ciappara | Derived categories and functors (abstract) |
| Week 5 | Linyuan Liu | t-structures and hearts (abstract) |
| Week 6 | Joseph Baine | Categories of sheaves (abstract) |
| Week 7 | Will Hardesty | The recollement situation (abstract) |
| Week 8 | Chris Hone | Constructibility and the perverse t-structure (abstract) |
| Week 9 | Giulian Wiggins | The intermediate-extension functor (notes by G. Burrull; abstract) |
| Week 10 | Giulian Wiggins | Perverse sheaf examples (notes by G. Burrull; abstract) |
| Week 11 | Michael Zhao | Representations of affine Hecke algebras via perverse sheaves (abstract) |
| Week 12 | Joshua Ciappara | Introduction to Kazhdan–Lusztig theory (abstract) |
| Week 14 | Bregje Pauwels | Springer theory (abstract) |
| Week 16 | Gaston Burrull | Classical motivation (abstract) |
Semester 2, 2020
At least to begin with in Semester 2, the seminar's theme will be topological K-theory. We will mostly follow the text by A. Hatcher, supplementing gaps and adding topics at various points.
Schedule
| Time | Speaker | Topic |
|---|---|---|
| Week 0 | Joshua Ciappara | Introduction to vector bundles (abstract) |
| Week 1 | Joshua Ciappara | Constructions with vector bundles (abstract) |
| Week 2 | Joseph Baine | The K-theory functor (abstract) |
| Week 3 | Giulian Wiggins | Bott periodicity (abstract) |
| Week 4 | Bregje Pauwels | Division algebras and parallelizable spheres (abstract) |
| Week 5 | Giulian Wiggins | Grassmannians and the universal bundle (abstract) |
| Week 6 | Vishnu Mangalath | Stiefel-Whitney and Chern classes (abstract) |
| Week 7 | Joseph Baine | The Thom isomorphism (abstract) |
| Week 8 | Joshua Ciappara | Euler and Pontryagin classes (abstract) |
| Week 9 | Christopher Hone | Characteristic classes as obstructions (abstract) |
| Week 10 | Vishnu Mangalath | The Chern character (abstract) |
| Week 11 | Bregje Pauwels | K-theory of complex projective spaces (abstract) |
Additional references
A useful set of course notes:
- O. Randal-Williams. Characteristic classes and K-theory, 2018.
- K-theory: An elementary introduction. Conference notes at the Clay Mathematics Research Academy, 2006.
- K-theory: An introduction. Springer-Verlag, 1978.
- J. F. Adams. Vector fields on spheres. Annals of Mathematics 75(3):603–632, 1962.