Monday, June 24 |
07:00 - 08:45 |
Breakfast ↓ Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building. (Vistas Dining Room) |
09:00 - 10:00 |
Yue Ren: Tropical homotopies served two ways in OSCAR ↓ Polyhedral homotopies were originally introduced by Huber and
Sturmfels nearly 30 years ago, and have since become a staple strategy
for solving polynomial systems. Main topic of the talk is a
generalisation thereof.
Building on ideas of Jensen, Leykin, and Yu, we will discuss two
distinct types of tropical homotopies: First, we will discuss how to
use tropical points to construct homotopies for solving systems of
polynomial equations. Second, we will discuss how to compute tropical
points using homotopies for intersecting systems of balanced
polyhedral complexes.
Centerpiece of the talk are systems of parametrized polynomial
equations, and we will focus two main cases:
Vertically parametrized polynomial systems are systems in which
parameters are shared between equations but always bound to the same
monomial. These are for example the steady state equations of chemical
reaction networks or they arise in the computation of ED or ML
degrees.
Horizontally parametrized polynomial systems are systems in which
parameters are shared between monomials but always bound to the same
equation. These are prominently studied using the theory of Khovanskii
bases and Newton Okounkov bodies.
We conclude the talk with an OSCAR demo on tropical geometry. (TCPL 201) |
10:00 - 10:30 |
Coffee Break (TCPL Foyer) |
10:30 - 11:30 |
Sara Veneziale: Machine learning detects terminal singularities ↓ In this talk, I will describe recent work in the application of machine learning to explore questions in algebraic geometry, specifically in the context of the study of Q-Fano varieties. These are Q-factorial terminal Fano varieties, and they are the key players in the Minimal Model Program. In this work, we ask and answer if machine learning can determine if a toric Fano variety has terminal singularities. We build a high-accuracy neural network that detects this, which has two consequences. Firstly, it inspires the formulation and proof of a new global, combinatorial criterion to determine if a toric variety of Picard rank two has terminal singularities. Secondly, the machine learning model is used directly to give the first sketch of the landscape of Q-Fano varieties in dimension eight. This is joint work with Tom Coates and Al Kasprzyk. (TCPL 201) |
11:30 - 13:00 |
Lunch ↓ Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building. (Vistas Dining Room) |
13:00 - 14:00 |
Guided Tour of The Banff Centre ↓ Meet in the PDC front desk for a guided tour of The Banff Centre campus. (PDC Front Desk) |
14:00 - 14:20 |
Group Photo ↓ Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo! (TCPL Foyer) |
14:20 - 15:10 |
Tim Dokchitser: Reduction types of algebraic curves ↓ The primary invariant for a family of curves is the combinatorial description of `bad' fibers. When the curves are elliptic, the classification of possible geometric configurations (`reduction types') is due to Kodaira and Neron, in genus 2 to Namikawa-Ueno, and in genus 3 to Ashikaga-Ishizaka. In this talk, I would like to describe a possible classification for curves of arbitrary genus, and give an overview of what are the classes of curves for which we can currently compute their reductions. (Online) |
15:00 - 15:30 |
Coffee Break (TCPL Foyer) |
15:40 - 16:40 |
Discussion: Resources for computational geometry ↓ Discussion lead by Frank Sottile.
Description: Ambitious computational exploration of phenomena in geometry requires serious resources: computing, software development and maintenance, data storage, and of course people and their time. During this week at BIRS devoted to building a community of computational mathematicians working in geometry, I'd like to engage the participants in a formal discussion about procuring the resources we need for our work. This includes sharing ideas and stories about how we obtained resources as well as looking ahead about how we may induce grant agencies to respond to these research needs. With such a diverse, influential, and international group of attendees there is much that we can learn from one another and accomplish. (TCPL 201) |
17:30 - 19:30 |
Dinner ↓ A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building. (Vistas Dining Room) |