报告题目：Total positivity of three types: conjectures and observations

报 告 人：Bishal Deb 博士后（清华大学丘成桐数学科学中心）

报告时间：2025年12月17日（星期三）15:00—16:00

报告地点：数学科学学院114（小报告厅）      

校内联系人：陈曦 副教授         联系方式：84708351-8504

报告摘要：Given a lower-triangular matrix of real numbers, one can ask the following four total-positivity questions: total positivity of the triangle itself; total positivity of its row-reversal; Toeplitz-total positivity of its row sequences (equivalent to negative-real-rootedness of the row-generating polynomials); and coefficientwise Hankel-total positivity of the sequence of row-generating polynomials.
In this talk we introduce two infinite families of lower-triangular matrices generalising the Stirling cycle and subset triangles, parametrised by an integer r≥1; we call these the rth-order Stirling cycle and subset numbers. We then ask the foregoing four questions for each of these triangles, leading us to several conjectures.

报告人简介：Bishal Deb is a postdoctoral researcher based at the Yau Mathematical Sciences Center, Tsinghua University where his mentor is Nicolai Reshetikhin. He finished his PhD in 2023 at University College London (UK) under the supervision of Alan Sokal. He then spent a year as a postdoctoral researcher working at Sorbonne University (France) and was employed by the CNRS. His primary research interest is in enumerative combinatorics, in particular questions on total positivity in enumerative combinatorics. More recently, he has been working on the dimer model in statistical physics.