Date:

Thu, 04/11/202116:00-17:15

live link:

https://huji.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=a9302362-5419...

abstract:

In my talks I will try to give some examples of how homogeneous dynamics can bu used to establish (and count) the number of solutions to Diophantine inequalities as well as to study the distribution of rational points on varieties.

For the former I plan to discuss Margulis proof of the Oppenheim conjecture, as well as some more quantitative subsequent results.

The latter - study of integer points - is somewhat more surprising, and requires an Adelic (or at least S-arithmetic) point of view. I will explain what this means and as an example discuss work of Ellenberg and Venkatesh regarding representing a positive definite integer quadratic form in k variables by an integer quadratic form in l>k variables.

https://huji.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=a9302362-5419...

abstract:

In my talks I will try to give some examples of how homogeneous dynamics can bu used to establish (and count) the number of solutions to Diophantine inequalities as well as to study the distribution of rational points on varieties.

For the former I plan to discuss Margulis proof of the Oppenheim conjecture, as well as some more quantitative subsequent results.

The latter - study of integer points - is somewhat more surprising, and requires an Adelic (or at least S-arithmetic) point of view. I will explain what this means and as an example discuss work of Ellenberg and Venkatesh regarding representing a positive definite integer quadratic form in k variables by an integer quadratic form in l>k variables.