# Summer Mini-Courses 2018

Summer 2018 will feature two mini-courses:

**Mini-Course #1****Math 8910 - Topics in Analysis**

CRN#62067

Instructor: Neil Lyall

Ten Lectures on June 18-22 (MTWRF) and 25-29 (MTWRF), 10:00-11:00 AM, Boyd 410

Course Description: I would plan to cover some large subset (depending on the interest of students) of the following self-contained topics. I have a slight preference for the first three topics as I believe they will be of broader appeal.

1. __Prime Number Theorem (PNT)__ [2-3 lectures]

Quick review of complex analysis

Newman's short proof of the PNT

What is a Tauberian Theorem? Overview of other proofs of the PNT?

2. __What is Ergodic Theory?__ [2-3 lectures]

Quick review of measure theory

Mean and pointwise theorems

Normal numbers, Continued fractions and Khinchine’s constant

3. __The Isoperimetric Inequality__ [2-3 lectures]

Basics about Fourier Series and a first proof

The Brunn-Minkowski Theorem and a second proof

Other proofs? More about Fourier Series?

4. __The Gauss Circle Problem__ [2-3 lectures]

Fourier transform of arc-length measure

Poisson Summations and the Gauss Circle problem

More on oscillatory integrals. Other lattice point problems?

5. __Differentiation__ [2-3 lectures]

Cricket averages, Covering Lemmas and Maximal functions (beautiful topic no longer covered in Math 8100)

Differentiation Theorems

Thin sets and Besicovitch sets (sets of measure zero that contain line segments that point in all possible directions)

**Mini-Course #2**__Math 8920 - A crash course on homotopy theory__

CRN#61994

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.