---
# System prepended metadata

title: SURF Progress Journal

---

# SURF Progress Journal
June 4th: In the group meeting with Nadler, we discussed the definition of polytope ring, its relation with Chow ring, and equivariant cohomology.

June 5th:

June 7th:

June 10th:

June 12th: In the group meeting with Nadler, we sketched the proof of the isomorphism between polytope ring and Chow ring.

June 14th: 

June 17th: We found out a way to do smooth resolution for any given Gelfand-Zeitlin polytope.

June 19th:

June 24th:

June 26th: STEM Career Tracks Workshop

June 27th: Sheafification, sheaf cohomology, injective resolution, acyclic resolution, double complex, Godement resolution, Morse theory.

June 28th: Quasi-isomorphism, derived category, representation theory for $\text{sl}_n(\mathbb{C})$, $\text{gl}_n(\mathbb{C})$, and $\text{GL}_n(\mathbb{C})$.

July 1st: Intersection cohomology, stratification, f-vectors, h-vectors

July 3rd: Intersection theory, parameter space, Chow ring, vector bundles and Chern classes.

July 5th: Differential geometry, intersection theory (continued)

## SURF Notes
[Click here to edit](https://www.overleaf.com/1142423742whxfrbrjfghs)

## Reference Books
***Introduction to Toric Varieties*** - Jean-Paul Brasselet
***Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra*** - David A. Cox, John Little, and Donal O'Shea
***Toric Varieties*** - David A. Cox, John Little, and Henry K. Schenck
***Combinatorial Convexity and Algebraic Geometry*** - Günter Ewald
***Introduction to Toric Varieties*** - William Fulton
***An Introduction to Homological Algebra*** - Charles Weibel
***Complex Semisimple Lie Algebras*** - Jean-Pierre Serre
