Summer Mini-Courses 2018

​Summer 2018 will feature two mini-courses:

Mini-Course #1
Math 8910 - Analysis and Number Theory
Instructor: Neil Lyall
Ten Lectures on June 18-22 (MTWRF) and 25-29 (MTWRF), 10:00-11:00 AM, Boyd 410

Lecture 1:   Basic Prime Number Estimates
Lecture 2:   The Riemann-Zeta Function
Lecture 3:   Newman's Short Proof of the Prime Number Theorem
Lecture 4:   Dirichlet Convolution, Dirichlet's Hyperbola Method, and Landau's Theorem on the Mean Value of the Mobius Function 
Lecture 5:   Borel's Law of Large Numbers and Hausdorff's improvement, Random Series, and a second proof of Hausdorff's improvement 
Lecture 6:   Maximal Functions and the Lebesgue Differentiation Theorem
Lecture 7:   Ergodic Theory I - Examples, Weyl's equidistribution theorem and V.I. Arnold’s "first digits of the powers of 2" problem
Lecture 8:   Ergodic Theory II - Poincare Recurrence, Ergodicity, and von-Neumann's Mean Ergodic Theorem
Lecture 9:   Ergodic Theory III - Birkhoff's Pointwise Ergodic Theorem
Lecture 10: Ergodic Theory IV - Applications to Normal Numbers and Continued Fractions (Khintchine’s constant)

Mini-Course #2
Math 8920 - A crash course on homotopy theory
Instructor: Weiwei Wu
Seven Lectures on June 11-14 (MTWR) and 20-22 (WRF), 1:30-3:00 PM, Boyd 410

Course Description: The course is to cover basic notions of homotopy groups, homotopy fibrations and cofibrations, Puppe sequences, Hurewicz and Whitehead theorems. Time allowing I will explain how this fits into the framework of model categories, or in a different direction, I could go towards generalized homology and spectra, depending on student interests. The main reference will be Chapters 6 and 8 of "Lecture Notes in Algebraic Topology" by Davis and Kirk.