Herbert Huachaca

DIMACS REU 2026

General Project Information

Your Photo

Name: Herbert Huachaca

Project Mentor: Paul Feehan

Email: hkh29@scarletmail.rutgers.edu

Office Location: CoRE, Room 415

University: Rutgers University

Acknowledgements

I would like to thank professor Feehan for his guidance and support throughout this project. I'd also like to thank the Rutgers Math Department and the NSF for funding my participation in DIMACS.

About Me

I am an undergraduate at Rutgers University studying mathematics. I like topology and differential geometry. If I had to bring one book to a desert island it would be Lee Smooth Manifolds. Aside from math I like reading the other works of mathematicians who are better known for other work. Shoutout Costin Alamariu and Ted K. My favorite tarot card is The Fool (0).

Project Description

We attempt to find some simple solutions to the Yang-Mills equations on 4-manifolds.

In particular I will be looking at a paper by Donaldson and expound on a certain gluing lemma used in the construction.

...

Weekly Log

Week 1: 5/27-5/30

Got situated with the program. Met my roommates Arnav, John, and Ryan, went over Lee smooth manifolds chapters 1 & 2 as review.

Week 2: 6/2-6/6

Met my officemate Nathan and we got to know each other a bit. I finally achieved my lifelong dream of becoming a Discord mod!!! Am now owner of the 2026 DIMACS Discord server.

Week 3: 6/9-6/13

Learned about vector bundles and riemannian metrics from the relevant chapters in Lee. Met with professor to discuss some sources he wanted me to read through.

Week 4: 6/16-6/20

...

Week 5: 6/23-6/27

...

Week 6: 6/30-7/4

...

Week 7: 7/7-7/11

...

Week 8: 7/14-7/18

...

Week 9: 7/21-7/25

...