| 5/24/26 - 5/31/26 |
On Monday I met with Dr. Calderoni to discuss the aim of our project and some background reading from Eklof and Mekler's Almost Free Modules. On Tuesday I arrived, moved into my apartment, and met the other program participants. On Wednesday we had orientation. I had lunch with Dr. Cecelia Higgins and the Sofias (Sofia A. and Sofia T.) on Thursday Throughout the week I worked on background reading and drafting my presentation. I enjoyed meeting my fellow participants, learning new card games (Cabo), throwing a Frisbee around, and exploring New Brunswick.
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| 6/1/26 - 6/7/26 |
On Monday, I met with Dr. Calderoni to discuss my reading and worked om proving a statement on clubs, stationary sets, and Fodor’s lemma. I gave a short presentation on my project to other participants. I enjoyed hearing about other students’ work. I continued my reading focusing on chapter four from Almost Free Modules and doing some exercises. On Thursday I met with the Sofias and Dr. Higgins for lunch, and then with Dr. Higgins to discuss my reading. That weekend, I read about some compactness results for almost
free modules and attempted to bake gluten free bread. |
| 6/8/26-6/14/26 |
On Monday I met with Dr. Calderoni. He lectured on compactness results in Almost free modules. I read about projective modules and met with Dr. Calderoni again on Thursday to discuss the reading. I worked on generalizing a compactness result on free modules to projective modules. On Thursday (6/11/26) Dr. Neil Sloane gave a talk on integer sequences and the OEIS. We celebrated a REU participant’s birthday, watched part of the World Cup, and went to the Rutger’s Gardens and farmers’ market. Dr. Calderoni, very kindly, toured the Sofias and I around the Princeton campus and art museum (which had both a great show on de Kooning featuring Black Friday and elsewhere in the European gallery Dürer's Holy Family with Three Hares paired with the original printing block!) and graveyard (where we found the graves of Von Neumann and Kurt Gödel). Dr. Calderoni and Dr. Sinapova hosted us for dinner (thank you!).
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| 6/15/26-6/28/36 | I met with Dr. Calderoni on Monday to discuss my proof for the a result and next steps in the project. Over the course of the week I worked on writing up our progress and reading a couple papers looking at different directions for the next part of the project. I read a bit about lattice theory. On Tuesday, there was a seminar on game theory given by Thotsaporn Thanatipanoda. On Thursday we had a workshop on scientific writing and I met with Dr. Calderoni to revise the write up and discuss the next paper we would look at, specifically on a reflection result which might be useful in our context. That evening Dr. Calderoni very kindly took some of the REU students to see live jazz (a local celebrity was in attendance).
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| 6/22/26-6/28/26 |
Under Construction
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