Faculty mentor
Directed Study · Spring 2026
Lorentzian Polynomials Directed Study Project
A directed study project exploring Lorentzian polynomials and related problems, including bounded ratios, convex geometry, and algebraic combinatorics, through weekly talks,shared notes, and examples.
Latest update
The paper has been submitted to arXiv and is available for public viewing now! See the links in the Resources section.
01 · About
A shared place for the work
This site keeps the project’s purpose, meetings, notes, and responsibilities visible in one place.
Our goal is to explore the properties and applications of Lorentzian polynomials. An important aspect of this project is to understand the bounded ratios for Lorentzian polynomials and their implications in various mathematical contexts.
Lorentzian polynomials
Bounded ratios
Convex geometry
Algebraic combinatorics
02 · People
Project team
Faculty mentor, project lead, and group members.
Project Lead
Marcus Chen
Personal page
dchen426 at math.wisc.eduGroup member
Bowen Gan
Personal page
bgan5 at math.wisc.eduGroup member
Ivy Liu
Personal page
ivy.liu at math.wisc.eduGroup member
Jackmon Wang
zwang3694 at math.wisc.eduGroup member
Chengzhi Wu
Personal page
cwu493 at math.wisc.edu03 · Schedule
Weekly plan
Thursdays 4:00-5:30 PM or Sundays · 9:00-10:30 AM · In person or via Zoom
| Date | Presenter | Topic | Notes | Status |
|---|---|---|---|---|
| Feb 5 | Botong | Orientation and project plan | Project plan | Complete |
| Feb 19 | Marcus | Foundational material | Week 2 notes | Complete |
| Feb 26 | Marcus | The logical chain from Lemma 2.8 and 2.9 to Theorem 2.13 | Week 3 notes | Complete |
| Mar 5 | Marcus and Ivy | Finish presenting Chapter 2.1 and proof of Theorem 2.23 (beginning) | Week 4 notes | Complete |
| Mar 12 | Ivy | Proof of Theorem 2.23 (continued) | Week 5 notes | Complete |
| Mar 19 | Ivy | Proof of Theorem 2.23 (final) | Week 6 notes | Complete |
| Mar 26 | Jackmon | Basics of Matroid Theory | Week 7 notes | Complete |
| Apr 2 | None | Spring Break | None | Complete |
| Apr 9 | Jackmon | Different ways to define a matroid | Week 9 notes | Complete |
| Apr 16 | Chengzhi | The Strongest Mason's Conjecture | Week 10 notes | Complete |
| Apr 23 | Bowen | Several foundational notions from Algebraic Geometry | Week 11 notes | Complete |
| Until May 8 | None | Prepare for final exam | None | Complete |
| May 17 | Bowen | Algebraic Geometry notions and the volume polynomial | Week 14 notes | Complete |
| May 24 | Bowen | Section 4.2: Projective varieties and Lorentzian polynomials | Week 15 notes | Complete |
| May 31 | Bowen | Section 4.2: Projective varieties and Lorentzian polynomials (continued) | Week 16 notes | Complete |
| June 2 | Botong | Next stage: bounded ratios and optimal bounding constants for ternary Lorentzian polynomials | Next stage | Complete |
| Aug 30 | Whole group | Discuss initial version of the paper | Initial paper | Complete |
04 · Resources
Working materials
Keep the latest version of each resource easy to find.
Questions or corrections?