Group, Lie and Number Theory Seminar
Optimal lifting, optimal Diophantine exponent, and automorphic forms (Special room and time)
We start by talking about two arithmetic problems with similar flavors. The first one is about quantifying the density of SL(n, Z[1/p]) in SL(n, R). A conjecture of Ghosh--Gorodnik--Nevo predicts that the elements of SL(n, R) can be "optimally approximated" by the elements in SL(n, Z[1/p]). The second problem is about quantifying the surjectivity of the mod q map from SL(n, Z) to SL(n, Z/qZ). A conjecture of Sarnak predicts that almost all elements in SL(n, Z/qZ) can be "optimally lifted" to SL(n, Z).
In a recent joint work with Amitay Kamber, we prove the optimal lifting conjecture for square-free q. In another work with Amitay Kamber, we also prove the optimal approximation conjecture but conditionally on the "Density hypothesis". We will describe how the spectral theory of automorphic forms crucially plays a central role in our proofs. These are based on the following two recent preprints.
https://arxiv.org/abs/2210.16291
https://arxiv.org/abs/2211.05106
Speaker(s): Subhajit Jana (Queen Mary University, London)
In a recent joint work with Amitay Kamber, we prove the optimal lifting conjecture for square-free q. In another work with Amitay Kamber, we also prove the optimal approximation conjecture but conditionally on the "Density hypothesis". We will describe how the spectral theory of automorphic forms crucially plays a central role in our proofs. These are based on the following two recent preprints.
https://arxiv.org/abs/2210.16291
https://arxiv.org/abs/2211.05106
Speaker(s): Subhajit Jana (Queen Mary University, London)
| Building: | East Hall |
|---|---|
| Event Type: | Workshop / Seminar |
| Tags: | Mathematics |
| Source: | Happening @ Michigan from Department of Mathematics, Group, Lie and Number Theory Seminar - Department of Mathematics |
