Geometry of numbers and lattices

Tel Aviv University, Fall 2024

Monday 9:10-12:00, Shenkar building room 105


Grading For those taking the course for a grade, and for those seeking a particular form of pleasure, here is the EXERCISE SHEET (final version). The exercise sheet is due on April 21. Please send me your work by email.



Notes

  • In the lecture of November 11, I stated a criterion for a k-tuples of vectors in a lattice to be a primitive k-tuple, but did not have time to complete the proof. Here is the proof.

  • In the lecture of December 2, I didn't have time to prove a claim, which was needed in the proof that when G acts transitively on X, and a regular G-invariant Radon Borel measure on X exists, then this measure is unique up to scaling. Here is the statement of the claim and its proof.

  • In the lecture of January 13, I didn't give the details of proof of the stability lemma. For the proof, please see this paper of Alam, Ghosh and Yu (Lemma 3.1).



  • References
  • Similar course I gave over zoom in fall 2020. Note: The courses are not identical, the overlap is approximately 70%. Here is the link to that that course's webpage.
  • J. W. S. Cassels, Introduction to the geometry of numbers
  • P. M. Gruber and C. G. Lekkerkerker, Geometry of numbers
  • C. L. Siegel, Lectures on the geometry of numbers
  • Course notes of Oded Regev (Tel Aviv University and NYU).