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.

The basic notion of this talk is the interplay between mathematics done by computer algebra systems and mathematics done by humans. It will be partly based on first-hand experiences with Maple. One of the unlikely successes of Maple software is the current popularity of the Lambert W special function. The role of Western in this success will be described.

This is part of our "Basic Notions" series.

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 $X_R$. We will see that the underlying topological space $X_R/W$ is contractible.

Elementary toposes are categories that share many properties of the category of sets. Every elementary topos has an internal language which is a version of typed intuitionistic higher-order logic obtained from the lattices of subobjects. It thus makes sense to speak of an elementary topos as a local set theory. The notion of elementary infinity-topos generalises this concept to infinity-categories. It is conjectured that the internal language of an elementary infinity-topos is a version of Homotopy Type Theory. Thus, it makes sense to speak of elementary infinity toposes as univalent dependent type theories, where instead of the lattice of subobjects we have a universal infinity-groupoid of all (small) objects. In the talk, I will introduce and motivate the notion of elementary infinity-topos, focussing on the concept of object classifiers and I will sketch the progress that has been made so far towards proving the conjecture. I will not assume any prior knowledge about toposes, logic or type theory.