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Sage Days 116

Kakao Talk Open Chat

https://open.kakao.com/o/gqcunDVe

Dates

• Dec 27-30, 2022

Venue

• Sol Beach, Yangyang, South Korea

• Lecture Hall: Hotel building (Tower A), first floor, Sapphire II

Organizing Committee

• Meesue Yoo, Chair (Chungbuk National University)

• JiSun Huh (Ajou University)

• Jang Soo Kim (Sungkyunkwan University)

Plenary Speakers

• Yasuhide Numata (Hokkaido University)
• Travis Scrimshaw (Hokkaido University)
• Heesung Shin (Inha University)

Invited Speakers

• Meesue Yoo (Chungbuk National University)
• Eunjeong Lee (Chungbuk National University)
• Taehyeok Heo (Seoul National University)
• Seung Jin Lee (Seoul National University)

Software demo

• Jang Soo Kim (Sungkyunkwan University)

Schedule

Abstracts

Plenary Talks

• Yasuhide Numata (Hokkaido University)
  • Talk 1
    • Title: On data structures of Python/Sage.
    • Abstract: First, I will introduce fundamental data structures of Python. Roughly speaking, Sage is Python with additional structures. The original data structures of Python can be used in Sage, too. Some of them are, however, overwritten. We see the difference between Python and Sage.
  • Talk 2
    • Title: How to use classes as user of Sage.
    • Abstract: First, we see basic syntax to define a new class in Python. Then I will introduce how to extend some class as a user of Sage.
  • Project(s)

    • Make Korean quick references (Level: For newbie): We have quick references [1], i.e., cheatsheets. Almost of them are distributed with GFDL, and some of them are translated into some languages. We, however, have no Korean version. So translate them into Korean, or make a new reference for your research topics. [1] https://wiki.sagemath.org/quickref

• Travis Scrimshaw (Hokkaido University)
  • Talk 1

    • Title: The details of contributing to SageMath

    • Abstract: In this talk, we will discuss how to prepare your code for inclusion into SageMath. These include things such as: (1) how to find the right place to put your code; (2) formatting your code, e.g., PEP8; (3) writing (good) documentation and doctests. Additionally, we will look at the current development model for SageMath and go through the contribution process. Lastly, we see what will change with the upcoming transition to GitHub's model.

  • Talk 2

    • Title: Getting the full potential from SageMath

    • Abstract: SageMath is built from numerous open source packages, but there are additional packages that are not installed by default (optional/experimental packages) and those further built on top of Sage (downstream packages). We will discuss some of these packages and how to install them from a source build, and highlight some of them and how they expand the computational abilities of SageMath (with the speaker's bias). Furthermore, not every feature of these packages (such as GAP) are immediately accessible in SageMath. We discuss how to access some of these packages within SageMath and leverage some of their more advanced capabilities (which make for good things to contribute to SageMath).

  • Projects

    • Implement representations of simple Lie algebras. lie_algebra_reprs.sage

    • Implement q-characters by the Frenkel-Muhkin algorithm. q_characters.sage

    • Implement q,t-characters for simply-laced types using Nakajima's or Hernandez's algorithm.
    • Implement (dual) Grothendieck polynomials.

    • Implement Specht modules for the symmetric group. specht_modules.sage

    • Implement type C Fock space and the corresponding global crystal basis.

    • Implement the cactus group by using https://arxiv.org/abs/2202.00860.

    • Implement G(r,p,n) as a subgroup of the colored permutation group.
    • Implement the type q crystal structure on shifted tableaux (see, e.g., Assaf and Oguz) and reduced factorizations (see Marberg).

    • Implement the q-commuting Laurent polynomials https://trac.sagemath.org/ticket/34472

    • Implement the Coxeter complex for finite Coxeter groups. (Bonus: the Milnor fiber complex of finite reflection groups; defined in the same way by cosets.)
• Heesung Shin (Inha University)
  • Sage Tutorial 1
    • Title: Sage as a Calculator

    • Abstract: In the first tutorial, we will look at some simple SageMath commands that can be used like a calculator.

  • Sage Tutorial 2
    • Title: Analysis and Algebra

    • Abstract: In the second tutorial, we will practice SageMath commands that are often used in analysis and algebra.

  • Sage Tutorial 3
    • Title: Graphics and Programming

    • Abstract: In the third tutorial, you will run some commands used in SageMath for 2D or 3D visualization. If possible, we will cover programming that includes loops and conditional statements in SageMath.

  • See also: https://ensual.github.io

Invited Talks

• Meesue Yoo (Chungbuk National University)
  • Title: Enumeration of standard barely set-valued tableaux of shifted shapes
  • Abstract: In this work, we prove the CDE property of the trapezoidal shifted shapes by counting standard barely set-valued tableaux via q-integral method. A standard barely set-valued tableau of shape λ is a filling of the Young diagram λ with integers 1,2,...,|λ|+1 such that the integers are increasing in each row and column, and every cell contains one integer except one cell that contains two integers. Counting standard barely set-valued tableaux is closely related to proving Young's lattice has the coincidental down-degree expectations (CDE) property. Using q-integral techniques we give a formula for the number of standard barely set-valued tableaux of arbitrary shifted shapes. We then prove a conjecture of Reiner, Tenner and Yong on the CDE property of trapezoidal shifted shape (n,n-2,...,n-2k). This work was initiated in Sage Days held in Slovenia, generalizing Sam Hopkins' work presented in Fpsac held a week before. This workshop might be the right place to present the result. This is joint work with Jang Soo Kim and Michael Schlosser.
• Eunjeong Lee (Chungbuk National University)
  • Title: On toric varieties in the flag variety
  • Abstract: Let G be a simple Lie group and let B be a Borel subgroup. The homogeneous space G/B becomes a smooth projective variety called the flag variety. The flag variety provides an interesting connection between geometry, topology, representation theory, and combinatorics as is exhibited in the Borel-Weil-Bott theorem, Schubert calculus, and so on. A maximal (complex) torus T acts on the flag variety and there are lots of toric varieties with respect to this torus action. Indeed, the T-orbit closure of a point in the flag variety is always a toric variety. One can produce toric Schubert varieties and toric Richardson varieties in this way. In this talk, we study toric varieties in the flag variety, especially certain smooth toric Richardson varieties containing toric varieties of Catalan type and toric Schubert varieties. This talk is based on joint work with Mikiya Masuda and Seonjeong Park.
• Taehyeok Heo (Seoul National University)
  • Title: The crystal structure of King tableaux
  • Abstract: The King tableau is a symplectic generalization of semistandard tableaux, which describes irreducible modules over symplectic Lie algebras. Whereas it is a very well-known object in combinatorics, its crystal structure is not, but Lee recently explains its crystal structure via oscillating tableaux. In this talk, I will briefly explain the crystal structure of King tableaux. This talk is a review of Lee's article (arXiv:1910.04459).
• Seung Jin Lee (Seoul National University)
  • Title: Rook placements and chromatic quasisymmetric functions
  • Abstract: In this talk, we describe two types of rook placements, arising from the Hall-Littlewood expansion and e-expansion of chromatic quasisymmetric functions. I will describe the relationship between these rook placements and discuss how Sage can help us to understand the relationship.

Software demo

• Jang Soo Kim (Sungkyunkwan University)
  • Title: Introduction to Newbiemacs
  • Abstract: Newbiemacs is a pre-configured GNU Emacs distribution inspired by Spacemacs. Newbiemacs is desiged for mathematician who are new to Emacs. In this talk we will see basic features of Newbiemacs, for example, how to manage pdf and tex files, and how to organize notes using org-mode.

  • Newbiemacs Home: https://jangsookim.github.io/newbiemacs/newbiemacs-home.html