Computational Algebraic Topology


The third problem sheet is now available! It will be due on Monday the 4th of March.

Want more Persistent Homology in your life? Here are the papers I mentioned recently which describe the existence and computation of barcodes as well as a readable account of the stability theorem for persistence modules.

The second problem set was collected on Monday of Week 5. The first problem set, which was not collected, is still available here.


You may (and should!) use the following lecture notes as an outline for reviewing the material. See also Prof Tillmann's webpage for some useful resources.

Lec 01: Complexes (Prof Tillmann's slides)
Lec 02: Homology (minor fixes on 30/1)
Lec 03: Functoriality (major fixes on 30/1)
Lec 04: Cohomology
Lec 05: Persistence (Stability Theorem added on 7/2)
Lec 06: Cellular Sheaves
Lec 07: Discrete Morse Theory (HUGE update 14/2. Happy Valentine's Day.)

Lec 08: Quantum computation
Lec 09: The topology of paradox

The following research papers serve as references for the material covered in the second half of this course:


Location: Lectures meet every Monday and Thursday from 4 PM to 5 PM in Room L2 of the Andrew Wiles Building. In addition, you must attend four hour and a half long Problem Sessions across the term:

  • Wed of Week 2 at 11 AM in C4,
  • Wed of Week 4 at 12 PM in C4,
  • Tue of Week 6 at 03 PM in C4, and
  • Wed of Week 8 at 10 AM in C4.

Your Marks will be available on Minerva.