# Sage/Oscar Days for Combinatorial Algebraic Geometry Feb 15 - 19, 2021
Main page: https://icerm.brown.edu/programs/sp-s21/w2/.
Add your projects here
* Finish review of [#31391](https://trac.sagemath.org/ticket/31391) (Dan Bump, Anne Schilling)
* SageMath/Julia Interop [#27762](https://trac.sagemath.org/ticket/27762)
* Polynomials and multilinear algebra in Sage:
- [Meta-ticket: Use new features from FLINT 2.x](https://trac.sagemath.org/ticket/31408) - including the very fast multi-variate polynomials.
- https://trac.sagemath.org/ticket/30096 (sage.tensor.modules: Add backends using TensorFlow Core and PyTorch)
* Fix subfield bugs [#23801](https://trac.sagemath.org/ticket/23801)
* Symbolic computation for polynomials with variable exponents: e.g. the polynomial
p = a(1)+a(2)xy+a(3)xy^2 +a(4)x^2y+a(5)xyz +a(6)xy^a z^2, a some Integer, a(i) Paramters, x,y,z variables.
How to compute the derivative of p w.r.t x,y,z? Is it possible to use saturation, elimination or computation
of radical and degrees of ideals containing such symbolic polynomials?
--> best shot in Sage would be using the "toy Buchberger" https://doc.sagemath.org/html/en/reference/polynomial_rings/polynomial_rings_toy_implementations.html + parameter space analysis
* Real and semialgebraic geometry in Sage
* Update LR Calculator to version 2.0. [#31355](https://trac.sagemath.org/ticket/31355)
* Sage support for Varieties, orbifolds, DM Stacks, Artin stacks, including:
Resolutions of singularities. Morphisms of schemes, tests for isomorphism and
birational isomorphism. Coherent sheaves and cohomology.
* Exterior algebras. Modules over exterior algebras. Compute cohomology of projective
space using resolutions of modules over exterior algebras.
* Spectral sequences. Derived computations. Derived pullback, pushforward, tensor, etc.
* [completed] Review the beginner ticket used in the tutorial: [#30826] (https://trac.sagemath.org/ticket/30826)
* Singular upgrade in Sage ... https://trac.sagemath.org/ticket/25993
* Oda's strong conjecture (in dim 3): Take existing (see https://arxiv.org/pdf/0911.4693.pdf) /new implementation of a proposal algorithm for Oda's Strong Conjecture. Parallelize/Optimize? Run over all examples of a given depth + collect data. From experimental data, find a way to prove it. Extend algorithm to >3 and prove general conj. (see also Dan's slides in Slack: https://icermspring2021.slack.com/files/U01LRGFH727/F01NLP2V2CS/oda___s_strong_conjecture_2.pdf)
* Anders Buch (Rutgers University)
* Wolfram Decker (Technische Universität Kaiserslautern)
* Benjamin Hutz (Saint Louis University)
* Michael Joswig (TU Berlin & MPI Leipzig)
* Julian Rüth
* Anne Schilling (UC Davis)