Tobias Ekholm - Skein valued curve counts and applications

Value of the Information & Strength of the Argument

The talk presents original research that introduces a novel invariant, skein valued curve counts, which addresses long-standing issues in Gromov-Witten theory with Lagrangian boundary conditions. The argumentation is rigorous, with careful handling of wall crossings and using skein relations to achieve invariance. The speaker provides concrete examples and demonstrates how the method simplifies computations that would otherwise be extremely complex. The approach is innovative and opens new avenues in symplectic geometry, contact geometry, and link theory. The reasoning is solid and well-supported by the mathematics, though the video’s audio and visual quality may hinder full comprehension for non-experts.

Scientific Rigor, Source Quality, Title Accuracy

The talk is based on the speaker’s own research, developed with collaborators such as VC Shenda and others, and is presented at a reputable workshop. The only explicit source provided is the workshop page, but the content is clearly grounded in established literature (skein theory, Gromov-Witten theory, contact geometry). The title accurately reflects the content. The technical level is high, and the speaker demonstrates depth and precision. The absence of detailed references in the talk is typical for a seminar, but the mathematical rigor is evident. There is no marketing or sponsorship segment. The video is poorly viewed but this does not affect the scientific value.

The title accurately reflects the content, as the talk focuses on skein valued curve counts and their applications to contact geometry and cluster algebras.

9/10

The presentation is a formal research talk by a recognized expert (Uppsala University) at a prestigious institute (IPAM), based on peer-reviewed work. The content is rigorous and technically detailed, though the video quality and transcript are imperfect.

Markers derived by PSI from the transcript: the creator did not define chapters.

• 00:00Introduction: talk overview and outline
• 05:00Definition of skein module and skein relations
• 15:00Wall crossing phenomenon and resolution via skein counting
• 25:00Example: unknot conormal and counting annuli
• 35:00Curves at infinity and computation via operators for solid torus
• 45:00Application to trace lifting and skein interpretation

• Workshop II: Contact Geometry, Cluster Algebras and Skein Theory — The talk was presented at this workshop; the page provides context of the workshop structure and topics.