Seminar in Harmonic measure

source material for the seminar:

https://mat.uab.cat/~xtolsa/mesuraharmonica.pdf

office hours: Wed. 2-4  (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). 👍

• 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)👍

• 27.03.24: Harmonic measure and greens functions (7.5-7.6) 👍

• 03.04.24: (NO CLASS)

• 10.04.24: Harmonic measure in NTA domains (8.1-8.3)👍

• 17.04.24: Harmonic measure in NTA domains (8.4-8.5)👍

• 24.04.24: Dahlberg's Theorem (10.1) 👍

• 01.05.24: (NO CLASS)

• 08.05.24: L^p solvability of the Dirichlet problem (10.2-10.3) 👍

• 15.05.24: (NO CLASS)

• 22.05.24:

• 29.05.24

Topics to choose from for the last month:

• harmonic measure and brownian motion

• planar harmonic measure (dimension, conformal maps, etc.)

• rectifiability of harmonic measure

• harmonic measure in higher codimension