BIMSA-HSE Joint Seminar on Data Analytics and Topology: Сергей Усанов

Аннотация:
The search for powerful invariants to distinguish knots is a central problem in the knot theory. A key tool in this area is the sl2 weight system, which transforms knot diagrams into polynomials. While the structure of these polynomials is well-studied, finding explicit combinatorial formulas for their coefficients remains a significant challenge.

In this talk, we address this problem for the next unknown coefficient, a3. We demonstrate how techniques from data science and machine learning can be successfully applied to this pure mathematical question. By framing the problem as a regression task on a space of graphs, we use computational data to derive a precise candidate formula for a3 as a linear combination of subgraph-counting functionals.

We will discuss the theoretical foundation that justifies this data-driven approach, relying on reconstruction theorem from finite restrictions. In addition, I will outline an independent verification on small graphs using the known relationship between the sl₂ weight system and the chromatic polynomial.

Страница семинара  https://bimsa.net/activity/BIMJoiSemonDatAnaandTop/

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