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MATH 857: Topics in Analysis: Fourier Analysis and Convexity (Spring 2023)

Course Information:

Syllabus

References:

[Ba] Barvinok, A. A course in convexity, Graduate Studies in Mathematics, no 54, Amer. Math. Soc. (Library call no. QA639.5 .B37 2002)
[DC] Do Carmo, M. Differential Geometry of Curves and Surfaces, Prentice Hall (1976) (Library call no. QA641 .C33)
[Ga] Gardner, R. Geometric Tomography (Encyclopedia of Mathematics and its Applications, no 58) Cambridge U. Press. (Library call no. QA639.5 G37 2006)
[Gr] Groemer, H. Geometric Applications of Fourier Series and Spherical Harmonics (Encyclopedia of Mathematics and its Applications, no 61) Cambridge U. Press. (QA403.5 .G76 2009)
[Po] Pogorelov, A.V. Differential Geometry (Library Call no. QA641 .P613 1967)
[Sc] Schneider, R: The use of spherical harmonics in convex geometry.



Week of Jan 16: Introductory Material About Convexity, based on Barvinok Chapter 1 and Gardner Chapter 0. (Presented by Morgan, Michael, Gulnar and Chase)
                                 These notes may be useful

Week of Jan 23: Gardner's illustration of transformations in R^n
      Please register for this conference

Weeks of Jan 30 and February 6: Characterizations of Ellipsoids: Brunn and Blaschke's Theorem, the False Center Theorem

Week of Feb 13: Differential geometry of curves and surfaces (following [Po])

Week of Feb 20: Presentations by Stephanie, Gulnar and Michael. Differential geometry of curves and surfaces (following [Po])

Presentation papers: Rogers central symmetry characterization; A lemma of Nakajima and Suss

Weeks of Feb 27 and March 6: Differential geometry of curves and surfaces (following [Po])

Week of March 20: On Monday we finished Differential geometry of surfaces. On Wednesday and Friday, and on Monday March 27 you will work on HW 3 as a group in class.

Week of March 27: Monday: Group HW during class time. Wednesday: Uniqueness results about projections (following [Ga, chapter 3])

Weeks of April 3 and 10: Uniqueness results about projections (following [Ga, chapter 3])

April 17: Presentation by Morgan and Chase
No class on April 19, 21, 24 due to conference

April 26: Presentation by Stephanie

Homework: