# Tropical Geometry: Graphs and Curve Degenerations

### Welcome to the homepage for the Tropical Geometry Seminar.

This seminar is co-organized by Andrew Tawfeek and Dhruv Bhatia.

We meet twice weekly on Mondays and Wednesdays in

Padelford Hall (PDL) C-38 from 11:30am - 12:30pm.

We will alternate between lectures days and discussion/coding days.

Note: The coding project now has it's own webpage.

The seminar maintains a Zulip chat for continued discussion and has a shared Google Drive.*

* Both of these require your @uw.edu email to access.

### Sources:

Our main resource will be Melody Chan's lecture notes on Tropical Curves and their Moduli Spaces. Here are videos from these lectures given at CIMPA-CIMAT-ICTP School of Moduli of Curves.

For a primer on these notions, see this AMS Notice on Moduli Spaces of Curves: Classical and Tropical.

Other helpful and frequently discussed sources include:

The Geometry of Matroids by Federico Ardila

Tropical Geometry: Forward and Backwards by Dhruv Ranganathan

What is a Toric Variety? by David Cox

Introduction to Tropical Geometry through Curves (Part 1 and Part 2) by Madeline Brandt

Geometry of Algebraic Curves. Volume II. by E. Arbarello, M. Cornalba, and P. A. Griffiths

Degeneration of Linear Series From the Tropical Point of View by M. Baker and D. Jensen

Stacks and Moduli by Jarod Alper

## Summer 2024 Schedule:

### Week 1:

Wednesday, June 26th, 2024

Dhruv Bhatia lectures on Embedded Tropicalizations of Finite-Type Schemes.

### Week 2:

Monday, July 1st, 2024

Andrew Tawfeek lectures on Stable Curves and Dual Graphs.

Wednesday, July 3rd, 2024

Discussion Day

### Week 3:

Monday, July 8th, 2024

Dhruv Bhatia lectures on Moduli Space of Tropical Curves.

Wednesday, July 10th, 2024

Briant Nugent lectures on Existence and Uniqueness of Stable Models.

Discussion Day

### Week 4:

Monday, July 15th, 2024

Andrew Tawfeek lectures on Toric Varieties.

Wednesday, July 17th, 2024

Coding Day: Computing the cells of the moduli space of tropical curves in SageMath/Python

### Week 5:

Monday, July 22nd, 2024

Dhruv Bhatia lectures on Tropical Perspective of Analytification.

Wednesday, July 24th, 2024

Carlos Rivera lectures on Berkovich Analytification.

Coding Day (continued): Computing the cells of the moduli space of tropical curves in SageMath/Python

### Week 6:

Monday, July 29th, 2024

Leopold Mayer lectures on Deligne-Mumford Stacks.

Wednesday, July 31st, 2024

Coding Day (continued): Computing the cells of the moduli space of tropical curves in SageMath/Python

### Week 7:

Monday, August 5th, 2024

Lorenzo Bottiglione lectures on Toroidal Embeddings.

Wednesday, August 7th, 2024

Coding Day (continued): Computing the cells of the moduli space of tropical curves in SageMath/Python

### Week 8:

Monday, August 12th, 2024

Wednesday, August 14th, 2024

Patrick O'Melveny lectures on Matroids and Adiprasito-Huh-Katz's proof of the Heron-Rota-Welsh conjecture.

## Autumn 2024 Schedule:

### Upcoming Talks:

Giovanni Inchiostro will present on Wall Crossings and Parameter Spaces.