Rearrangement of series: The Riemann rearrangement theorem tells us that you can rearrange the terms of a conditionally convergent series to converge to any real number you want. But can you do it without disturbing any of the already convergent series? Can you make more series to converge? In this project, we will investigate how permutations change conditionally convergent series. Do you think everything is known in this area? You will be surprised by many open problems.

https://www.jstor.org/stable/4145013?seq=1#metadata_info_tab_contents

 

Bergman projection, Toeplitz operators, and Geometry: The Bergman projection and Toeplitz operators are defined on specific function spaces, and their action depends heavily on the geometry of the underlying domain or manifold. In this project, we will investigate how geometry and the mapping properties of these operators relate. We will study problems on specific domains and pursue explicit calculations.

https://arxiv.org/abs/2005.08311