Fall 2026
EP2602: An Introduction to LS Category#
- Speaker: Aditya De Saha (Ben Gurion University)
- Abstract: “How many critical points must a smooth function on a surface have?” In 1934, Lusternik and Schnirelmann answered this with a simple idea: cover your space with pieces that can be deformed to points, and count how many you need. This was their ‘category’, which was a numerical invariant. With the advent of category theory shortly after, this ended up being called LS-Category going forward. In general it is a hard invariant to compute, but techniques exist to create upper and lower bounds for it using a variety of different machinery. In this talk, we will give a very broad overview of the history and some surprising properties of this invariant, and see some examples.
- Video: [TBU]
- Date and Time: Wednesday, 5th August 2026, 6:00 - 7:00 PM
- Venue: 2nd Floor Auditorium, Academic Building
EP2601: An Introduction to Computational Topology#
- Speaker: Shubhankar Varshney (Purdue University)
- Abstract: It is a fundamental tenet of modern data science that data has shape, and that shape has meaning. Computational topology provides the mathematical machinery to rigorously quantify these structures. Starting from a point cloud \(X \subset \mathbb{R}^d\), we construct a sequence of simplicial complexes \({X_i}_{i \in \mathbb{I}}\), known as a filtration. These complexes are linked by inclusion maps. In this talk, I will introduce the 1-parameter filtration which is a specific case when \(I=\mathbb{N}\), and demonstrate how the homology groups of \(X_i\) evolve through induced maps. Finally, we will arrive at the persistence barcode—a complete, discrete topological invariant that serves as a powerful “fingerprint” for complex datasets. Then I will go on with multiparameter persistence.
- Video: [TBU]
- Date and Time: Sunday, 2nd August 2026, 3:45 - 5:30 PM
- Venue: 2nd Floor Auditorium, Academic Building