Introduction: Topics of these seminars include differential equations (ODEs, PDEs, DDEs, FDEs, etc.), dynamical systems theory, and their applications (often in mathematical biology). To get the brain gears turning, each session will kick off with a fun trivia!

Stabilizer codes offer a robust and efficient framework for encoding quantum information and detecting errors. This family includes a large class of codes such as CSS codes, surface codes and Toric codes. In this talk, we will focus on the fundamental mathematical principles of stabilizer codes. Using the aspects of subgroups of Pauli groups, this family of the codes offers a unified scheme for detecting and correcting errors in quantum world. This unification simplifies both error detection and error correction for these family of codes.

Given a reduced crystallographic root system $R$ with the associated Weyl group $W$, the Weyl chambers from a fan and then give out a complex toric variety and its real part $X_{\mathbb{R}}$. We will see that the underlying topological space $X_{\mathbb{R}}/W$ is contractible.

This is a continuation of last week's talk.

We will present the fastest known algorithm for computing discrete cubical homology, a valuable graph invariant with a wide range of applications, including matroid theory, hyperplane arrangements, and topological data analysis. This invariant is capable of detecting certain types of "holes" within a graph, providing insight into its structure.

We will begin by defining discrete cubical homology and outlining the standard approach to its computation. We will then present an algorithm designed to improve efficiency by using techniques such as faster generation of singular cubes, reducing chain complex dimensions through quotients over automorphisms, and preprocessing graphs using results from discrete homotopy theory. These advancements aim to make the invariant more accessible computationally for applications. We are now able to compute examples that were previously considered out of reach by experts.

This talk is based on the paper: Kapulkin, Kershaw, Efficient computations of discrete cubical homology, arXiv:2410.09939.