报告题目1：关于组合计数与枚举

报告人：王军教授，上海师范大学

报告时间：2023年11月11日（周六）8:30-11:50

报告地点：雷迪森广场酒店5楼通悦厅

报告摘要：主要介绍组合计数与枚举的内容、意义与方法，以及本人对所谓“Enumerative combinatorics”的理解和体会。

报告题目2：On the q-rational Taylor expansion

报告人：刘治国教授，华东师范大学

报告时间：2023年11月11日（周六）8:30-11:50

报告地点：雷迪森广场酒店5楼通悦厅

报告摘要：In 1973, Carlitz proved the q-rational Maclaurin expansion. Almost thirty years later, Carlitz’s theorem was extended to the q-rational Taylor formula, which finds many important applications to q-series and number theory. With the help of q-rational series, we can overcome some extremely difficult problems in q-mathematics. In this talk, I will introduce some applications the q-rational Taylor expansions. 

报告题目3：The (α,β)-Eulerian Polynomials and DescentStirling Statistics on Permutations

报告人：季青教授，天津大学

报告时间：2023年11月11日（周六）8:30-11:50

报告地点：雷迪森广场酒店5楼通悦厅

报告摘要：Carlitz and Scoville introduced the polynomials An(x, y|α, β), which we refer to as the (α, β)-Eulerian polynomials. These polynomials count permutations based on Eulerian-Stirling statistics, including descents, ascents, left-to-right maxima, and right-to-left maxima. Carlitz and Scoville obtained the generating function for these polynomials. In this talk, we present a new family of polynomials, Pn(u1, u2, u3, u4|α, β), defined on permutations, which incorporate descent-Stirling statistics including valleys, exterior peaks, right double descents, left double ascents, left-to-right maxima, and right-to-left maxima. By employing the grammatical calculus introduced by Chen, we establish the connection between the generating function of Pn(u1, u2, u3, u4|α, β) and the generating function of the (α, β)- Eulerian polynomials An(x, y|α, β). This connection can be specialized to derive many formulas involving the Eulerian polynomials and the peak polynomials and the double descent polynomials given by David-Barton, Elizalde and Noy, Entringer, Gessel, Kitaev, Stembridge, Petersen, Branden and so on. 

报告题目4：Log-concavity of sequences from total positivity

报告人：祝宝宣教授，江苏师范大学

报告时间：2023年11月11日（周六）8:30-11:50

报告地点：雷迪森广场酒店5楼通悦厅

报告摘要：Log-concave sequences occur often in combinatorics, analysis, algebra, geometry, probability and statistics. It is often a difficult problem to show log-concavity. In combinatorics, log-concavity has always been of great interest to researchers. Especially, June Huh was awarded the Fields Medal in 2022 because he brought the Hodge theory to log-concavity problems in combinatorics in recent years. Total positivity of matrices is a powerful tool and has many applications in different branches of mathematics. In this talk, we will report some results for log-concavity from total positivity.

报告题目5：Fast Numerical Evaluation of Generalized Todd Polynomials

报告人：辛国策教授，首都师范大学

报告时间：2023年11月11日（周六）8:30-11:50

报告地点：雷迪森广场酒店5楼通悦厅

报告摘要：The Todd polynomials $td_k=td_k(\beta_1,\beta_2,...)$ are defined by their generating functions $\sum_{k\geq0} td_ks^k=\prod_{i\geq1}\frac{\beta_is}{e^{\beta_is-1}}$. It appears as a basic block in Todd class of a toric variety, which is important in the theory of lattice polytopes and in number theory. We find generalized Todd polynomials arise naturally in MacMahon's partition analysis, especially in Erhart series computation. We give fast evaluation of generalized Todd polynomials for numerical $\beta_i$'s. As a test, we recompute the Erhart series of magic squares of order 6, which was first solved by the first named author. The running time is reduced from 70 days to about 1 day.

报告题目6：Total positivity of matrices that enumerate labeled trees and partial functional digraphs 

报告人：陈曦副教授，大连理工大学

报告时间：2023年11月11日（周六）8:30-11:50

报告地点：雷迪森广场酒店5楼通悦厅

报告摘要：A matrix is called totally positive if all its minors are nonnegative. Such matrices have a wide variety of applications across pure and applied mathematics. In this talk, we study some matrices that enumerate rooted labeled trees and partial functional digraphs. We show that these matrices are totally positive, and their row generating functions are coefficientwise Hankel-totally positive. This is joint work with A.D. Sokal. 

报告题目7：Inertia indices and eigenvalue inequalities for Hermitian matrices 

报告人：王毅教授，大连理工大学

报告时间：2023年11月11日（周六）14:00-17:50

报告地点：雷迪森广场酒店5楼通悦厅

报告摘要：We present a characterization of eigenvalue inequalities between two Hermitian matrices by means of inertia indices. As applications, we deal with some classical eigenvalue inequalities for Hermitian matrices, including the Cauchy interlacing theorem and the Weyl inequality, in a simple and unified approach. We also give a common generalization of eigenvalue inequalities for (Hermitian) normalized Laplacian matrices of simple (signed, weighted, directed) graphs.

报告题目8：On some counting problems in Archimedean tilings

报告人：苑立平教授，河北师范大学

报告时间：2023年11月11日（周六）14:00-17:50

报告地点：雷迪森广场酒店5楼通悦厅

报告摘要：A plane tiling T is a countable family of closed sets with non-empty interiors T1, T2......,which cover the plane without gaps or overlaps. Every closed set T1 in T is called a tile of T. We consider the special case in which each tile is a polygon. If the corners and sides of a polygon coincide with the vertices and edges of the tiling, we call the tiling edge-to-edge. A so-called type describes the neighbourhood of any vertex of the tiling. We consider plane edge-to-edge tilings in which all tiles are regular polygons, and all vertices are of the same type. Thus, the vertex-type defines our tiling up to similarity. There exist precisely eleven such tilings, which are called Archimedean tilings. In this talk we’ll discuss some counting problems in Archimedean tilings. 

报告题目9：Counting and signed counting permutations by descent-based statistics

报告人：林志聪教授，山东大学

报告时间：2023年11月11日（周六）14:00-17:50

报告地点：雷迪森广场酒店5楼通悦厅

报告摘要：The original motivation of this paper was to find the context-free grammar for the joint distribution of peaks and valleys on permutations. Although such attempt was unsuccessful, we can obtain noncommutative symmetric function identities for the joint distributions of several descent-based statistics, including peaks, valleys and even/odd descents, on permutations via Zhuang’s generalized run theorem. Our results extend in a unified way several generating function formulae exist in the literature, including formulas of Carlitz–Scoville (1973, 1974), Stanley (1976), Zhuang (2017) and Pan–Zeng (2019, 2023). As applications of these generating function formulas, Wachs’ involution and Foata–Strehl action on permutations, we also investigate the signed counting of even and odd descents, and of descents and peaks. This talk is based on joint work with Yao Dong.

报告题目10：存在准符号图的一般理论吗？

报告人：陈仪朝教授，苏州科技大学

报告时间：2023年11月11日（周六）14:00-17:50

报告地点：雷迪森广场酒店5楼通悦厅

报告摘要：在上个世纪 80 年代初期，Stahl引入了置换划分对的概念，上述概念是图和图嵌入的一般推广（Permutation-partition pairs），在本报告中我们将引入符号图以及符号图嵌入的推广—准符号图（Pre-signed graphs), 并介绍这个概念的一些基本性质，以及一些在图嵌入中的应用。 

报告题目11：Counting regions of hyperplane arrangements

报告人：王岁杰教授，湖南大学

报告时间：2023年11月11日（周六）14:00-17:50

报告地点：雷迪森广场酒店5楼通悦厅

报告摘要：In this talk, we will introduce a formulae on numbers of regions for hyperplane arrangements of Catalan type and semi-order type.

报告题目12：A group action on cyclic compositions and gamma positivity

报告人：傅士硕教授，重庆大学

报告时间：2023年11月11日（周六）14:00-17:50

报告地点：雷迪森广场酒店5楼通悦厅

报告摘要：We introduce a group action on the set of dominant cyclic compositions. This leads to a combinatorial proof of a recent gamma positivity result obtained by Bóna et al. 

报告题目13：Puzzles in Schubert Calculus

报告人：范久瑜副教授，四川大学

报告时间：2023年11月11日（周六）14:00-17:50

报告地点：雷迪森广场酒店5楼通悦厅

报告摘要：In 2004, Knutson, Tao and Woodward introduced puzzle models for the structre constants of the cohomology of Grassmannians. From then on, various puzzle formulas were found in Schubert Calculus. In this talk, we shall first recall the known puzzle rules in the literature and then introduce our puzzle formula for the triple Schubert Calculus of separated descent equivariant K-theory. This talk is based on joint work with Peter Guo and Rui Xiong.

报告题目14：On series involving harmonic numbers 

报告人：孙智伟教授，南京大学

报告时间：2023年11月12日（周日）8:00-11:50

报告地点：雷迪森广场酒店5楼通悦厅

报告摘要：In this talk we introduce various conjectures and results on evaluations of series with summands involving harmonic numbers. We will leave many open series identities for further research. 

报告题目15：A new q-analogue of a “divergent” Ramanujantype supercongruence 

报告人：郭军伟教授，淮阴师范学院

报告时间：2023年11月12日（周日）8:00-11:50

报告地点：雷迪森广场酒店5楼通悦厅

报告摘要：Guillera and Zudilin proved the following ``divergent Ramanujan-type supercongruence: for any odd prime $p$,$$\sum_{k=0}^{p-1} \frac{(\frac{1}{2})_k^3}{k!^3}(3k+1)2^{2k} \equiv p\pmod{p^3}.$$Sun further conjectured that the above supercongruence is also true modulo $p^4$ for $p>3$, and a $q$-analogue of this result was given by the author in an early paper. In this paper, we establish a new $q$-analogue of Sun's supercongruence by employing the method of “creative microscoping”, developed by the author and Zudilin in 2019.

报告题目16：Proofs of Mizuno’s conjectures on rank two Nahm sums

报告人：王六权教授，武汉大学

报告时间：2023年11月12日（周日）8:00-11:50

报告地点：雷迪森广场酒店5楼通悦厅

报告摘要：Recently, Mizuno studied Nahm sums associated with symmetrizable matrices. He provided 14 sets of candidates of modular Nahm sums in rank two and justified four of them. We prove the modularity for eight other sets of candidates and present conjectural formulas for the remaining two sets of candidates. This is achieved by finding Rogers-Ramanujan type identities associated with these Nahm sums. We also prove Mizuno’s conjectural modular transformation formula for a vector-valued function consists of Nahm sums. Meanwhile, we find some new non-modular identities for some other Nahm sums associated with the matrices in Mizuno’s candidates. This talk is based on a joint work with Boxue Wang.

报告题目17：Riordan Numbers and Pattern-avoiding Matchings 

报告人：杜若霞副教授，华东师范大学

报告时间：2023年11月12日（周日）8:00-11:50

报告地点：雷迪森广场酒店5楼通悦厅

报告摘要：In this talk we will introduce some recent work on enumerations of matchings, alternating mathchings and reverse alternating mathchings avoiding a given pattern. Many of the results can be represented as combinations of Riordan numbers. 

报告题目18：The Lambda-positivity of e-positive graphs 

报告人：王国亮教授，北京理工大学

报告时间：2023年11月12日（周日）8:00-11:50

报告地点：雷迪森广场酒店5楼通悦厅

报告摘要：We present Lambda-positive noncommutative analogs of the chromatic symmetric function of some graphs, which implies both the e-positivity and Schur positivity of the graphs. It often turns out that certain noncommutative analog has a concise formula, which implies a convenient way of calculating explicit e-coefficients and a new approach of confirming the epositivity of graphs of special structures.

报告题目19：Partition inequalities based on partition statistics 

报告人：林丽双教授，集美大学

报告时间：2023年11月12日（周日）8:00-11:50

报告地点：雷迪森广场酒店5楼通悦厅

报告摘要：In this talk, we first introduce some basic results on partitions. Then, we present some inequalities in partitions and bipartitions related to certain statistics. 

报告题目20：q-unimodality and Catalan combinatorics

报告人：邱敦副教授，南开大学

报告时间：2023年11月12日（周日）8:00-11:50

报告地点：雷迪森广场酒店5楼通悦厅

报告摘要：Parking functions play an important role in Catalan combinatorics, such as the combinatorial side of the shuffle theorem. We discuss the q-unimodality property of polynomials related to parking functions, which generalize q-binomial polynomials. The q-unimodality property implies the Schur positivity of LLT polynomials.