for reference onlymost material is beyond the scope the course MR3136492

For reference onlymost material is beyond the scope

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Mathematical Society, Providence, RI, 2013. (for reference only—most material is beyond the scope of the course). MR 3136492 Inverse Problems for Boundary Value Problems Lecturer: L. Tzou This course forms part of the mathematical foundation behind Gunther Uhlmann’s Sydney Ideas Lecture "Inverse Problems and Harry Potter’s Cloak" on March 26th 2018. Students interested in this course are encouraged to attend and enjoy the public lecture. Can we recover the conductivity of an object by making only voltage-to-current mea- surements on the boundary? Also, can there be portions which are invisible from these measurements? In order to answer this question posed by Calderón one needs to have a deep understanding of analysis and geometry. This course will use these questions as motivation to introduce some of the important tools in modern PDE - microlocal analysis, Carleman estimates, and semiclassical analysis. We will see how these tools can be put together to answer Calderón’s question. At the end of this course the student will have the tools to read recently published research papers on this subject (e.g. see some of the references) with the help of the instructor. Assessment: 80% Assignments, 20% Final Exam Prerequisite: We will use some ideas (e.g. Hahn-Banach, Riesz Representation, and B.L.T. Thm) from Functional Analysis in Semester I. Some basic knowledge of Fourier transform will also be helpful. Resources: [1] John Sylvester and Gunther Uhlmann, A global uniqueness theorem for an inverse boundary value problem , Ann. of Math. (2) 125 (1987), no. 1, 153–169. MR 873380 [2] Leo Tzou, The reflection principle and Calderón problems with partial data , Math. Ann. 369 (2017), no. 1-2, 913–956. MR 3694665 [3] Colin Guillarmou and Leo Tzou, Calderón inverse problem with partial data on Riemann surfaces , Duke Math. J. 158 (2011), no. 1, 83–120. MR 2794369
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18 CHAPTER . COURSE DESCRIPTIONS
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Samuel Johnson Chapter 4 The Essay 4.1 Introduction q The essay project has several objectives. First and foremost, it is intended to provide an essentially open-ended framework whereby you may pursue, develop and discover your interests in mathematics unencumbered by syllabus and the prospect of eventual written examination. Basic to this process is the use of the library and communication with others, most especially your supervisor. The writing of the essay is a most valuable part of the project. The very act of writing is an invaluable aid to comprehension. A good essay should be carefully organised, clear, readable by others, laid out well, properly referenced and convey the essential ideas. Attainment of such writing skills is of great benefit whether or not you elect to stay in mathematics. One point should, perhaps, be emphasized: the essay project is not generally intended to be a contribution to original research; however, the essay must clearly demonstrate that you understand and have mastered the material. Originality in presentation or view in the essay is required. 4.2 Choosing a Supervisor and topic
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