报告题目 (Title)：On connection problems and algebraic equations over fields of elliptic functions: I, II（Q4方程的tau函数）
报告人 (Speaker)：Pieter Roffelsen副教授 (悉尼大学，澳大利亚）
报告时间 (Time)：I. 2024年09月28日; 下午14:00-15:30
II. 2024年09月29日; 下午14:00-15:30
报告地点 (Place)：校本部GJ303
邀请人(Inviter)：张大军
报告摘要：Jimbo (1982) showed that the problem of relating the asymptotic behaviours of Painlevé VI transcendents at distinct critical points, the connection problem, reduces to a set of equations involving a cubic surface, the gamma function and trigonometric functions, under the Riemann-Hilbert correspondence. After revisiting this result, we will analyze the analog for q-Painlevé VI. In that case, we will see that the connection problem reduces to a set of equations involving a Segre surface, the q-gamma function and elliptic functions. Whilst this is certainly a reduction in complexity, the reduced problem is still very rich and gets to some deep questions about integrable difference equations that we will explore.