source material for the seminar:
https://mat.uab.cat/~xtolsa/mesuraharmonica.pdf
office hours: Wed. 2-4 Β (or by appointment) in HG F27.1.
List of topics, dates and suggested reading:
21.02.24: overview of harmonic functions and greens functions (Chapter 2, 3.1-3.3)
28.02.24: Perron's method of subharmonic lifting and harmonic measure (5.1-5.3)
06.03.24: Wiener regularity and barriers (5.4), and potentials (6.1, 6.2 until remark 6.6). π
13.03.24: Wiener's criterion (rest of 6.2-6.4. Read the statements of 6.5-6.6)
20.03.24: Harmonic measure and greens functions (7.1, 7.3)π
27.03.24: Harmonic measure and greens functions (7.5-7.6) π
03.04.24: (NO CLASS)
10.04.24: Harmonic measure in NTA domains (8.1-8.3)π
17.04.24: Harmonic measure in NTA domains (8.4-8.5)π
24.04.24: Dahlberg's Theorem (10.1) π
01.05.24: (NO CLASS)
08.05.24: L^p solvability of the Dirichlet problem (10.2-10.3) π
15.05.24: (NO CLASS)
22.05.24:
29.05.24
Topics to choose from for the last month:
harmonic measure and brownian motion: https://galton.uchicago.edu/~lalley/Courses/385/HarmonicFunctions2015.pdf
planar harmonic measure (dimension, conformal maps, etc.) : https://www.math.stonybrook.edu/~bishop/classes/math627.S22/papers/Jones-Wolff.pdf
rectifiability of harmonic measure
harmonic measure in higher codimension : https://arxiv.org/pdf/1807.07035