| Name: | Elliot Glazer |
|---|---|
| Email: | eglazer (at) reu (dot) dimacs (dot) rutgers (dot) edu |
| Office: | Hill 323 |
| School: | Rutgers University |
| Project: | Complex manifolds and several complex variables |
| Advisor: | Xiaojun Huang, Department of Mathematics, Rutgers University |
This is a project in complex analysis, complex manifolds, and several complex variables.
I gave a presentation introducing my project. I studied model theory, forcing, and descriptive set theory to prepare for my project. I learned a proof of analytic determinacy from a measurable cardinal.
I studied more descriptive set theory and have begun making my way through the course notes for Professor Sargsyan's course Invitation to Inner Model Theory. Realizing that the initial project wasn't enough, the project has evolved to me writing an improved presentation of the Inner Model Theory course, which I have begun doing.
I went to a conference in Copenhagen this week.
I have begun studying direct models and iterated ultrapowers, and have continued studying the large cardinal hierarchy. I met with my professor and discussed a variety of topics, including Kurepa trees and Shoenfield absoluteness.
I learned some more background material for the project, including forcing and infinitary combinatorics. I studied descriptive set theory in more detail.
I wrote the first 3 lectures of the lecture note, and have begun work on the fourth. I placed more emphasis on the descriptive set theory notes, going well beyond what was taught into the course, and I am considering writing an extra lecture on that subject.
I finished the fourth lecture, on measurable cardinals, and began working on the fifth lecture, which will deal with critical sequences and iterated ultrapowers, as well as an extra lecture on descriptive set theory. I applied to enter a conference on set theory in October. I will no longer be meeting with my professor since he is in Poland.
Presentation 2 2015 July 17