SMS scnews item created by Daniel Hauer at Wed 19 Feb 2020 1107
Type: Seminar
Modified: Mon 7 Sep 2020 1242
Distribution: World
Expiry: 24 Feb 2020
Calendar1: 21 Sep 2020 1400-1500
CalLoc1: https://uni-sydney.zoom.us/j/92382270144
CalTitle1: The Calderon Problem with Unbounded Potential in Two Dimensions
Auth: dhauer@p635m2.pc (assumed)

# The Calderon Problem with Unbounded Potential in Two Dimensions

### Yilin Ma

Yilin Ma
University of Sydney
Mon 21th Sept 2020, 2-3pm, Zoom (AGR)

## Abstract

In this talk we will investigate the inverse problem of recovering an unbounded potential for the Schrödinger equation in two dimensions. In contrary with its analogy in higher dimensions, we need to construct semiclassical Carleman estimates for the operator $\Delta +V$ with holomorphic weight and a better order of decay. This will be done by exploiting the factorisation $\Delta =2{\stackrel{̄}{\partial }}^{\star }\stackrel{̄}{\partial }$ and we explain how a classical result of Gunning-Narasimhan that every Riemann surface admits a holomorphic function with non-vanishing gradient provides the natural weight. Finally, we will discuss some limitations of the existing method.

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