Summer 2012
Analysis Seminar

Thursday 24 May.

• Speaker: Michael Jury.
• Title: The maximum modulus of a random polynomial.
• Abstract: Flip a fair coin N times, and let e_k be +1 if the kth flip was heads, and -1 if it was tails. Form the random polynomial
  sum e_k z^k
  The maximum modulus of such a random polynomial on the unit circle is then a random variable M. Simple estimates show that
  sqrt{N} leq M leq N
  surely. A theorem of Salem and Zygmund shows that there is a constant C so that with high probability,
  M \leq C \sqrt{N \log N}.
  for all N sufficiently large. I will discuss this theorem and its extension to several variables (due to Kahane).

Tuesday 22 May.

• Speaker: Joel Rosenfeld.
• Title: Extensions of Reproducing Kernel Presentations

Thursday 17 May.

• Speaker: Michael Dritschel, Newcastle University, UK.
• Title: Test Functions, kernels, realizations and interpolation II.

Tuesday 15 May.

• Speaker: Michael Dritschel, Newcastle University, UK.
• Title: Test Functions, kernels, realizations and interpolation I.