Magnus B. Botnan

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.

12.04.2025 12:43 — 👍 2    🔁 1    💬 0    📌 0

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).

06.03.2025 09:34 — 👍 0    🔁 0    💬 0    📌 0

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.

06.03.2025 09:33 — 👍 0    🔁 0    💬 1    📌 0

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.

06.03.2025 09:33 — 👍 0    🔁 0    💬 1    📌 0

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?

06.03.2025 09:33 — 👍 0    🔁 0    💬 1    📌 0

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

06.03.2025 09:33 — 👍 1    🔁 1    💬 1    📌 0

Vacancy — PhD position in area of topological data analysis Do you have an inquisitive mind and a passion for mathematics? Please apply for a PhD position at Vrije Universiteit Amsterdam.

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...

24.02.2025 12:42 — 👍 1    🔁 2    💬 0    📌 0

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

20.02.2025 15:09 — 👍 0    🔁 0    💬 1    📌 0

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.

20.02.2025 07:54 — 👍 0    🔁 0    💬 1    📌 0

Kongen er tilbake i statsråd.

06.02.2025 09:30 — 👍 0    🔁 0    💬 0    📌 0