October 26, 2023: Ivan Dynnikov "Rectangular diagrams of taut foliations in knot complements"

Abstract: TBA

October 19, 2023: Sergey Melikhov "Isotopy of knots and the 2-variable Conway polynomial"

Abstract: TBA

September 28, 2023: Matthew Harper "Seifert-Torres Formulas for the Alexander Polynomial of Links from Quantum sl2"

Abstract: In this talk, I will recall how the Alexander polynomial, a classical knot invariant, can be constructed as a quantum invariant from quantum sl2 at a fourth root of unity. I will then discuss the development of a diagrammatic calculus based on further investigation of quantum sl2 representations. Applying this calculus in the context of the Alexander polynomial allows us to compute the invariant for certain families of links using quantum algebraic methods, rather than using methods of classical topology.

September 14, 2023: Evgeniy Scepin "Application of topology to optical recognition of handwritten characters"

Abstract: Every handwritten symbol consists of several lines. These lines may intersect. Therefore, each symbol corresponds to a graph whose vertices correspond to the intersection points of the lines and their ends, and the edges correspond to the line segments enclosed between the vertices. A scanned image of a symbol representing a Boolean matrix is fed to the input of the recognition program. On the image matrix, the lines become "thick", interference also occurs there. The report will tell you how to reduce the image so as to get a correct graph of the symbol, whose edges on the matrix are represented by thin (pixel-thick) lines that preserve the shape of the original ones.