トポロジー火曜セミナー

過去の記録 ~06/25次回の予定今後の予定 06/26~

開催情報 火曜日 17:00~18:30 数理科学研究科棟(駒場) 056号室
担当者 河澄 響矢, 北山 貴裕, 逆井卓也
セミナーURL http://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index.html

2024年05月28日(火)

17:00-18:00   オンライン開催
参加を希望される場合は、下記URLから参加登録を行って下さい。
Andreani Petrou 氏 (沖縄科学技術大学院大学)
Knot invariants and their Harer-Zagier transform (ENGLISH)
[ 講演概要 ]
The Harer-Zagier (HZ) transform is a discrete Laplace transform that can be applied to knot polynomials, mapping them into a rational function of two variables $\lambda$ and $q$. The HZ transform of the HOMFLY-PT polynomial has a simple form, as it can be written as a sum of factorised terms. For some special families of knots, it can be fully factorised and it is completely determined by a set of exponents. There is an interesting relation between such exponents and Khovanov homology. Moreover, we conjecture that there is an 1-1 correspondence with such factorisability and a relation between the HOMFLY-PT and Kauffman polynomials. Furthermore, we suggest that by fixing the variable $\lambda= q^n$ for some "magical" exponent $n$, the HZ transform of any knot can obtain a factorised form in terms of cyclotomic polynomials. Finally, the zeros of the HZ transform show an interesting behaviour, which shall be discussed.
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html