**July 1-5, 2019 - ICTP, Trieste**

## TAGSS III - algebraic Geometry towards applications

Nowadays the number of researchers who use algebraic geometry in industrial and applied mathematics is bigger than ever, and it keeps growing. The methods they use have already seen applications in: biology, coding theory, cryptography, combustion, computational geometry, computer graphics, quantum computing, control theory, geometric design, complexity theory, machine learning, nonlinear partial differential equations, optimization, robotics, and statistics.

The school featured courses by:

Alicia
Dickenstein - `Universidad
de Buenos Aires`,

**Biochemical reaction networks modeled by mass-action
kinetics**

- basics on reaction networks with mass-action kinetics: biochemical
notions, algebraic notions, dynamical notions

- steady state invariants and computational algebraic geometry

- networks with toric steady states

- counting the number of positive steady states and real solutions
to polynomial systems

and

Sandra Di Rocco - `KTH
Royal Institute of Technology Stockholm`,

**Algebraic Geometry of data clouds**

- Algebraic modelling (Kinematics) (slides)

- Sampling algebraic varieties: the reach (slides)

- Classical theory: projective embeddings and polar classes

- Euclidean Distance Degree (slides)

- the Bottleneck degree of varieties (slides)