# Seminar - Applied CATS

Applied Combinatorics, Algebra, Topology & Statistics

The seminar will take place in** F11** for the first 18 people to arrive. Overflow audience and those who are working from home can participate via Zoom with meeting ID
62586628413
.

## Next Talk

Tuesday, 22 September, 11:15

**Liam Solus**

*Combinatorics, Algebra, and Intervention*

The modern theory of causality is founded in our ability to encode both probabilistic and causal information about a data-generating distribution within the structure of a graph. Doing so in the proper way allows us to derive theorems which can be applied when developing data-driven causal structure learning algorithms, as well as probabilistic and causal inference. Such algorithms work best in the cases where the corresponding theorems point to nice combinatorial structure in the graph. Going deeper, if we also consider a parameterization of the joint distribution, we find that nice properties of the model can be attributed to nice properties of its defining algebraic variety in the ambient parameter space. Classic results of this nature are known for probabilistic graphical models. In this talk, we will see how such results generalize to interventional graphical models, which are now being used to learn causal structure from a mixture of observational and interventional data. Time permitting, we will explore how the proofs of these algebraic results give rise to new methods for modeling causation in context-specific settings.

- Tuesday, 22 September, 11:15

**Liam Solus** - Tuesday, 29 September, 11:15
- Tuesday, 6 October, 11:15

**Maria Dostert** - Tuesday, 13 October, 11:15

**Orlando Marigliano**

- Tuesday, 15 September, 11:15

**Angélica Torres**

*Dynamics of chemical reaction networks and positivity of polynomials*

In biochemical processes, different molecules are consumed and produced as they interact with each other. The evolution of their concentration through time can be modelled with a system of differential equations that, under certain assumptions, is polynomial. In this case, the equilibrium points form an algebraic variety. In this talk I will present how these systems arise, and how deciding whether a polynomial can attain positive or negative values is used for detecting multistationarity and stability in the biochemical system. slides (pdf 307 kB) - Tuesday, 8 September, 11:15

**Rene Corbet**

*An overview of the pipeline of multiparameter persistence*

In the last two decades, persistent homology and its generalizations have grown to a substantial branch of mathematical research. It gives rise to various research problems in algebra, category theory, geometry, topology, and other areas. Moreover, having immediate applications in data science, efficient algorithms, computational and probabilistic methods, and concrete implementations deserve the same amount of attention. Multiparameter persistence is the generalization of persistence to multiple independent parameters taken into account at once. While the theory of multiparameter persistence is provably much more complicated than the theory of ordinary persistence, new computational challenges arise as well. In this talk, I give a rough overview of the computational pipeline of multiparameter persistence, mention some important challenges, and outline the projects of my PhD thesis along these lines. slides (pdf 9.8 MB)