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BIMSA-HSE Joint Seminar on Data Analytics and Topology
On coefficients of the sl_2 weight system
On coefficients of the sl_2 weight system
Organizers
Speaker
Sergei Usanov
Time
Monday, November 24, 2025 8:00 PM - 9:00 PM
Venue
Online
Online
Zoom 468 248 1222
(BIMSA)
Abstract
$\large\{\{\{\text{The seminar is scheduled online for Monday from 20:00 to 21:00(Beijing Time)/15:00 to 16:00(Moscow Time).}\}\}\}$
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 of this polynomial, 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.
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 of this polynomial, 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.