报告题目1：Partitions Weighted by the Parities of Several Statistics

报告摘要：This talk begins with Euler's classical pentagonal number theorem, which serves as a prototype illustrating the central role that parity phenomena play in the theory of partitions. We then investigate partitions weighted by the parity of statistics such as the crank and the minimal excludant, and present related results on partitions with designated summands and restricted overpartitions weighted by the parity of their length.

报告人简介：林丽双，博士毕业于南开大学组合数学中心，现为集美大学教授、博士生导师，研究方向是整数分拆、q-级数。已在Ramanujan Journal、European J. Combinatorics、Discrete Mathematics、Journal of Number Theory等期刊上发表学术论文近50篇，获批两项国家自然科学基金面上项目。

报告时间：2026.10.28上午9:00-10:00

报告题目2：Normalized skew Schur polynomials are Lorentzian

报告摘要：We prove the conjecture of Huh, Matherne, Mészáros, and St.~Dizier that the normalization of every skew Schur polynomial in finitely many variables is Lorentzian. We first realize every nonzero skew Schur polynomial in finitely many variables as a specialization of a Schubert polynomial and prove that it is dually Lorentzian. The dual Jacobi--Trudi identity then identifies its normalization with the finite dual of a skew Schur polynomial obtained by rectangular complementation. As a consequence, skew Kostka numbers satisfy log-concavity inequalities along the root directions.

报告人简介：

张彪、教授、博士生导师，主要从事组合数学中单峰型理论和对称函数理论的研究工作。2015年6月博士毕业于南开大学，2018年8月至2019年8月到美国宾夕法尼亚大学访问。在《J.Comb.Theory Ser. A》、《Adv. Appl. Math.》、《SIAM J. Discrete Math.》、《Bull. Lond. Math. Soc.》、《Proc. Amer. Math. Soc.》等期刊发表学术论文三十余篇，主持国家自然科学基金3项、天津市自然科学基金1项。解决了John Stembridge、Francesco Brenti、Christos Athanasiadis、叶永南等人提出的多个猜想；关于实根多项式的结果被Tom Braden和Nicholas Proudfoot 在他们的国际数学家大会邀请报告中列为拟阵Kazhdan-Lusztig多项式实根性猜想的"重要证据(significant evidence)"；与合作者定义的多项式被Luis Ferroni等人(Adv. Math., 2024)称为“Haglund-Zhang多项式”，并部分验证了Fields奖得主June Huh提出的拟阵增广周环Hilbert级数的实根性猜想在均匀拟阵上的情况。担任天津市数学会理事、天津市工业与应用数学学会理事、中国运筹学会图论组合分会青年理事。

报告时间：2026.10.28上午10:00-11:00

报告题目3：Sharp bounds of bounded ratio for Lorentzian matrices

报告摘要：In this talk, we investigate the bounded ratio for Lorentzian matrices. We give the sharp bounds for several kinds of bounded ratio. As consequences, we give an affirmative answer to a conjecture proposed by Huang, Huh, Soskin and Wang for order six. For some types, we give the upper bound and lower bound. For hypermetric types, we find the maximum cases.

报告人简介：王星炜，南开大学组合数学中心，教授。主要从事于分析组合学，代数组合学，极值集合论等领域的研究，在Trans. Amer. Math. Soc.，Math. Comp.，Israel J. Math., Canad. J. Math., J. Combin. Theory A, Constr. Approx., SIAM J. Discrete Math.，Adv. Appl. Math.等期刊发表论文三十余篇。

报告时间：2026.10.30上午10:00-11:00

报告题目4：Infinite Log-Concavity of the Boros–Moll Polynomials

报告摘要：The Boros–Moll polynomials arise from the evaluation of a quartic integral. Boros and Moll conjectured that their coefficient sequences are infinitely log-concave: every iterate under the transformation L(a)_k = a_k^2 - a_{k-1}a_{k+1} remains nonnegative. In this talk, we present a proof of this conjecture, focusing on the real-rootedness approach. We show that the generating polynomial obtained after the first transformation has simple negative zeros that strictly interlace with those of the Narayana polynomial. Brändén’s preservation theorem then yields infinite log-concavity. The key step is to determine the signs of the transformed polynomial at the Narayana zeros through Jacobi polynomial expansions, summation by parts, and recurrence relations. We conclude with a brief discussion of an analytic approach based on complex-analytic estimates for the nonlinear iteration and its applications to other combinatorial sequences。

报告人简介：解红叶，天津理工大学教授。2018 年博士毕业于南开大学组合数学中心。主要研究方向为对称函数理论与单峰型问题，近几年主要从事拟阵 Kazhdan–Lusztig 多项式及其相关不变量的计算方法与对数凹性、实根性等性质的研究。在 Journal of Combinatorial Theory, Series A/B、Journal of Combinatorial Algebra、Advances in Applied Mathematics、SIAM Journal on Discrete Mathematics、Bulletin of the London Mathematical Society 等期刊发表学术论文多篇，先后主持国家自然科学基金青年科学基金项目及面上项目。

报告时间：2026.10.31上午10:00-11:00

报告地点：数学楼322