Geometry of Numbers

Tel Aviv University, Fall 2020

Sunday 10:10-13:00, remotely by zoom. Here is the link to the meeting room.


Grading For those taking the course for a grade, or for those looking for a meaningful way to spend their time on planet earth, here is the exercise sheet. Please submit your work by email, no later than April 18, 2021.




Notes
  • Video recording and notes of lecture 1, October 18.
    Here is a link to a paper of McMullen answering a question that was asked in the lecture: every convex set that tiles by translations admits a lattice tiling.
  • Video recording and notes of lecture 2, October 25.
  • Video recording and notes of lecture 3, November 1.
  • Video recording and notes of lecture 4, November 8. Please note: There was a mistake in the lecture which is corrected in the notes, and is relevant for the exercise sheet.
  • Video recording and notes of lecture 5, November 15.
  • Video recording and notes of lecture 6, November 22.
  • Video recording and notes of lecture 7, November 29.
  • Video recording and notes of lecture 8, December 6.
  • No lecture on December 13 (Hannukah)
  • Video recording and notes of lecture 9, December 20.
  • Video recording and notes of lecture 10, December 27.
  • Video recording and notes of lecture 11, January 3. Please note: there are several mistakes in the lecture (can you can find them?). They are corrected in the notes.
  • Video recording and notes of lecture 12, January 10.
    Here is a link to a Lecture of Silverman giving a historical overview and some basic ideas of lattice based cryptography.
  • Video recording and notes of lecture 13, January 17.






  • References
  • J. W. S. Cassels, An introduction to the geometry of numbers
  • C. L. Siegel, Lectures on the geometry of numbers
  • P. M. Gruber and C. G. Lekkerkerker, Geometry of numbers
  • J. H. Conway and N. J. A. Sloane, Sphere packings, lattices and groups
  • Link to the webpage of a course given in 2004 by Oded Regev