Title: Well-posedness of magnetic evolution equations on adapted modulation spaces

 

Abstract:
In this talk, we study wave and Schrödinger equations for magnetic Schrödinger operators with unbounded background fields. Based on a magnetic phase space transform, we construct a parametrix for such operators, and establish well-posedness in modulation spaces adapted to the magnetic potential.
This talk is based on joint work with Siliang Weng.

 

 

Title: A fractal local smoothing problem

 

 

Title: The Nevo-Thangavelu spherical maximal function on two step nilpotent Lie groups.

 

Abstract:
Consider $\mathbb R^d\times \mathbb R^m$ with the group structure of a $2$-step Carnot  group and natural parabolic dilations. The maximal operator originally introduced by Nevo and Thangavelu  in the setting of the Heisenberg groups is generated by   (noncommutative)  convolution  associated with measures on  spheres  in $\mathbb R^d$.  We review some previous work about $L^p$ boundedness  and then talk about joint  work with Jaehyeon Ryu in which  the nondegeneracy condition in the known results on M\'etivier groups is dropped. The new results have the sharp $L^p$ boundedness range for all  two step Carnot  groups with $d\ge 3$. We also discuss  recent results regarding  stability of the results under small perturbations.

 

 

Title: Off‐diagonal estimates for the helical maximal function