2021年度 第１回セミナー
題目：楕円 Ruijsenaars 差分作用素の固有函数
講師：野海正俊 氏 （KTH / 神戸大）
場所：オンラインセミナー（参加希望の方は数理物理センターのメンバーにコンタクトしてください）
日時：2021年4月21日(水) 17:20--18:50
概要：Edwin Langmann 氏(KTH・物理)，白石潤一氏(東大・数理)との共同研究に基いて，楕円 Ruijsenaars 差分作用素の可換族の同時固有値問題についての，最近の研究の内容を報告する．特に，Macdonald 多項式の楕円変形を与える対称函数解と， いわゆる漸近自由解の２つクラスの解の構成について述べる．また，白石氏の非定常型 Ruijsenaars 函数との関連 についても触れたい．
2021年度 第２回セミナー
題目：Random geometry approach to TTbar-deformed conformal field theory
講師：Prof. Shinji Hirano (University of the Witwatersrand)
場所：オンラインセミナー（参加希望の方は数理物理センターのメンバーにコンタクトしてください）
日時：2021年5月12日(水) 17:10--18:40
概要：In this talk I discuss the TTbar deformation of conformal field theory in two dimensions and develop a geometric method proposed by Cardy to study matter and stress tensor correlators. Along the way I present the TTbar-deformed Polyakov-Liouville conformal anomaly action as well as the TTbar deformation of the stress tensor OPEs. If time permits, I comment on an alternative description of the TTbar-deformed CFT, namely, the undeformed CFT on the operator/state-dependent TTbar-deformed space. I also discuss the gravity dual of the TTbar deformed CFT, translating the random geometry method into the language of AdS/CFT, and comment on its relation to the cutoff AdS interpretation.
2021年度 第３回セミナー
題目：Positive temperature free fermions and solvable models in the KPZ class
講師：Matteo Mucciconi 氏 (東京工業大学)
場所：オンラインセミナー（参加希望の方は数理物理センターのメンバーにコンタクトしてください）
日時：2021年6月23日(水) 17:10--18:40
概要：During the last two decades the study of solvable stochastic systems in the KPZ universality class has attracted much attention. A typical feature of these solvable models is their connection with special symmetric polynomials, which characterize their probability distribution. In numerous cases, utilizing Macdonald difference operators or Bethe Ansatz, one point functions have been expressed in the form of Fredholm determinants or pfaffians, leading to precise asymptotic analysis.
In this talk we aim to describe the origin of such determinantal and pfaffian formulas, relating the theory of solvable KPZ models with that of positive temperature free fermions in one dimension.
We accomplish this by establishing new identities between restricted Cauchy sums of skew Schur polynomials and q-Whittaker polynomials (i.e. Macdonald polynomials with t=0). This result is a consequence of a new bijective q-deformation of the celebrated RSK correspondence we introduce. Our arguments pivot around a combination of various theories that include Kirillov-Reshetikhin crystals, Demazure modules and the Box-Ball system.
This is a joint work with Takashi Imamura and Tomohiro Sasamoto.