25 people sitting in a seminar room

The Applied Topology Day 2025 was a success. Next year, we are planning to extend it to a two days event! Stay tuned.

In the filtered setting, new ideas are required, and a key [partially open] problem is: given a graph G on n vertices, and precisely e edges, what is the tight upper bound on betti_k(Flag(G))? The problem of maximizing total persistence feels much more difficult (see also discussion).

Kozlov, Björner, and others have fully understood how to maximize any Z-linear function on either the dimension vector (f-vector) or the vector of Betti numbers (b-vector). It is a linear optimization problem, and the maxima will appear on vertices of the convex hull of all possible graphs.

We provide a filtered complex which is extremal in multiple ways, and we conjecture that it is the unique maximizer of total persistence for H_1. The construction is rather counter-intuitive and our [technical, combinatorial] proof was based on a conjecture formed from computer experiments.

Questions we consider include: How many (off-diagonal) points can you maximally have in the persistence diagram of a data set on n vertices? What is the longest possible bar? What is the maximal total persistence?

Extremal Betti Numbers and Persistence in Flag Complexes We investigate several problems concerning extremal Betti numbers and persistence in filtrations of flag complexes. For graphs on $n$ vertices, we show that $β_k(X(G))$ is maximal when $G=\mathcal{T}_...

In a recent paper with L. Beers (accepted to SoCG '25) we consider simple questions related to Rips complexes and persistent homology. arxiv.org/abs/2502.21294

I'm hiring a PhD student to work on multiparameter persistence. Deadline: March 15. Please feel free to reach out with any questions. workingat.vu.nl/vacancies/ph...

Ok, thanks for the clarification. I must've missed something.

I heard that the acceptance rate for TDA papers at SoCG this year was a fair bit lower than the general acceptance rate. Wouldn't surprise me if it's always like that.

Kongen er tilbake i statsråd.