
Time: Monday, June 30, 2014 at 15:00 –16:00 p.m. Room: N514
Title: General Soliton Solution to the Vector Nonlinear Schrödinger Equation
Speaker: Baofeng Feng (University of TexasPan American, USA)
Abstract: In the present talk, we consider general soliton solution to the vector nonlinear Schrödinger (NLS) equation of all possible combinations of nonlinearities including allfocusing, alldefocusing and mixed types. By using the KPhierarchy reduction method based on the Sato theory, we construct a general formula in Gramtype determinants for the vector NLS equation. The condition for the reality of the soliton solution with all possible combinations of nonlinearities is elucidated.

Time: Tuesday, July 22, 2014 at 9:30 –10:30 a.m. Room: N226
Title: The Theory and Applications of TSplines
Speaker: Thomas W. Sederberg (Brigham Young University, USA)
Abstract: TSplines were invented in 2003 to address the major limitations of the NURBS freeform surface representation which is the industry standard in computer aided. TSplines provide a watertight model of arbitrary topology that allows for local refinement. TSplines also simplify the model creation procedure for designers. In addition, TSplines are emerging as the representation of choice for IsoGeometric Analysis.

Time: Monday, July 28, 2014 at 10:00 –11:00 a.m. Room: N420
Title: Classification of Restricted Lattice Walks in 3D
Speaker: Manuel Kauers (RISC, Johannes Kepler University, Austria)
Abstract: We consider walks in the positive octant $N^3$ that start at the origin and consist of exactly n steps, where each step is taken from some prescribed step set $S$. Depending on the choice of $S$, the generating function for such walks may be $D$finite or not. Together with Alin Bostan, Mireille BousquetMelou, and Steve Melczer, we have started to classify the step sets $S$ according to the nature of the generating function. In the talk, we present the results we have obtained so far, and we explain the computational and combinatorial tools we employed to obtain these results.

Time: Thursday, August 7, 2014 at 10:00 –11:00 a.m. Room: N420
Title: A Survey of Alternating Permutations
Speaker: Richard Stanley (MIT, USA)
Abstract: A permutation $a_1,a_2,\dots,a_n$ of $1,2,\dots,n$ is called alternating if $a_1>a_2< a_3 > a_4 < \cdots$. The number of alternating permutations of $1,2,\dots,n$ is denoted $E_n$ and is called an Euler number. The most striking result about alternating permutations is the generating function $$ \sum_{n\geq 0}E_n\frac{x^n}{n!} = \sec x+\tan x, $$ found by Désiré André in 1879. We will discuss this result and how it leads to the subject of "combinatorial trigonometry''. We will then survey some further aspects of alternating permutations, including some other objects that are counted by $E_n$, the use of the representation theory of the symmetric group to count certain classes of alternating permutations, and the statistical properties of the longest alternating subsequence of a random permutation.

Time: Thursday, August 7, 2014 at 15:00 –16:00 p.m. Room: N420
Title: Essentially Optimal Interactive Certificates in Linear Algebra
Speaker: Erich Kaltofen (North Carolina State University, USA)
Abstract: Certificates to a linear algebra computation are additional data structures for each output, which can be used by apossibly randomizedverification algorithm that proves the correctness of each output. The certificates are essentially optimal if the time (and space) complexity of verification is essentially linear in the input size $N$, meaning $N$ times a factor $ N^{o(1)} $, that is, a factor $N^{\eta(N)}$ with $\lim_{N\to \infty} \eta(N) = 0$.
We give algorithms that compute essentially optimal certificates for the positive semidefiniteness, Frobenius form, characteristic and minimal polynomial of an $n\times n$ dense integer matrix A. Our certificates can be verified in MonteCarlo bit complexity $(n^2 \log A)^{1+o(1)}$, where $\log A$ is the bit size of the integer entries, solving an open problem in [Kaltofen, Nehring, Saunders, Proc. ISSAC 2011] subject to computational hardness assumptions.
Second, we give algorithms that compute certificates for the rank of sparse or structured $n\times n$ matrices over an abstract field, whose Monte Carlo verification complexity is 2 matrixtimesvector products + $n^{1+o(1)}$ arithmetic operations in the field. For example, if the $n\times n$ input matrix is sparse with $n^{1+o(1)}$ nonzero entries, our rank certificate can be verified in $n^{1+o(1)}$ field operations. This extends also to integer matrices with only an extra $\logA^{1+o(1)}$ factor.
All our certificates are based on interactive verification protocols with the interaction removed by a FiatShamir identification heuristic. The validity of our verification procedure is subject to standard computational hardness assumptions from cryptography. Our certificates improve on those by Goldwasser, Kalai and Rothblum 2008 and Thaler 2012 for our problems in the prover complexity, and are independent of the circuit that computes them thus detecting programming errors in them.
This is joint work with JeanGuillaume Dumas at the University of Grenoble. 
Time: Tuesday, August 26, 2014 at 15:00 –16:00 p.m. Room: N210
Title: Verified Computation Based on Finite Element Method: From Qualitative Error Analysis to Quantitative One
Speaker: Xuefeng Liu (Waseda University, Japan)
Abstract: In computerassisted proof for nonlinear differential equations, verified computation based on the finite element method plays an important role. Particularly, the quantitative error analysis is much more important than the classical qualitative one. That is, not only the convergence order but also the explicit error estimation of approximate solutions are desired. This talk contains the following topics. a) Verified computation and interval arithmetic computation; b) The quantitative error estimation for the finite element method in solving partial differential equations; c) The technique of hypercircle equation from PragerSynge’s theorem to deal with the singularity of solutions; d) The error estimation for various interpolation error constants, which are reduced to eigenvalue problems.

Time: Wensday, August 27, 2014 at 15:00 –16:00 p.m. Room: N210
Title: Verified Eigenvalue Bounds for Selfadjoint Differential Operators
Speaker: Xuefeng Liu (Waseda University, Japan)
Abstract:In this talk, a uniform framework to provide guaranteed eigenvalue bounds for selfadjoint differential operators is proposed. In this framework, both conforming and nonconforming finite element methods (FEMs) are adopted to construct explicit eigenvalue bounds, even in the case that the eigenfunction has a singularity around the reentrant corners of domains.
As concrete examples, the conforming Lagrange finite element is used to give eigenvalue bounds for the Laplacian defined over polygonal domains of general shapes. The CrouzeixRaviart FEMs and the FujinoMorley FEMs, along with explicit a priori error estimation, are used to provide explicit eigenvalue bounds for the Laplacian and the Biharmonic operators, respectively. Further, LehmannGoerisch’s theorem is applied to give dramatically improved highprecision eigenvalue bounds. As the computation is performed under the interval arithmetic, the obtained eigenvalue bounds are mathematically correct and thus can be used in solution existence verification for certain nonlinear partial differential equations. 
Time: Thursday, August 28, 2014 at 15:00 –16:00 p.m. Room: N210
Title: Solution Verification for Nonlinear Elliptic Partial Differential Equations
Speaker: Xuefeng Liu (Waseda University, Japan)
Abstract: The computerassisted proof based on verified computation is becoming a powerful tool to investigate the solution existence and uniqueness of nonlinear partial differential equations (PDEs). For the nonlinear elliptic PDEs, several methods have proposed to verify the solution existence, for example, the methods of M. Plum, M. Nakao, S. Oishi, respectively. Each of these methods is based on the fixedpoint theorem and the spectrum estimation for elliptic partial differential operators. In this talk, I would like to give a brief introduction of these methods and more efforts are paid to the spectrum estimation and the quantitative error estimation.

Time: Thursday, September 25, 2014 at 15:00 –16:00 p.m. Room: N205
Title: Minimal Universal Denominators for Linear Difference Equations
Speaker: Qinghu Hou (Nankai University, China)
Abstract: We provide minimal universal denominators for linear difference equations with fixed leading and trailing coefficients. In the case of firstorder equations, they are factors of Abramov’s universal denominators. While in the case of higher order equations, we show that Abramov’s universal denominators are minimal.

Time: Thursday, October 30, 2014 at 15:00 –16:00 p.m. Room: N219
Title: Mixed Volume Computation and Solving Polynomial Systems
Speaker: Tien Yien Li (Michigan State University, USA)
Abstract: In the last few decades, the homotopy continuation method has been established in the U.S. for finding the full set of isolated zeros to a polynomial system numerically. The method involves first solving a trivial system, and then deforming these solutions along smooth paths to the solutions of the target system. Recently, modeling the sparse structure of a polynomial system by its Newton polytopes leads to a major computational breakthrough. Based on an elegant method for computing the mixed volume, the new polyhedral homotopy can find all isolated zeros of a polynomial system much efficiently. The method has been successfully implemented and proved to be very powerful in many occasions, especially when the systems are sparse. We will elaborate the method in this talk.

Time: Wensday, November 19, 2014 at 10:00 –11:00 p.m. Room: N420
Title: The Algorithmic Revolution in Geometry of Numbers
Speaker: Phong Nguyen (INRIA, France and Tsinghua University, China)
Abstract: In the past 30 years, there has been significant progress in the study of algorithmic questions in geometry of numbers. This research has used or revisited many classical mathematical results. In this talk, we survey the connection between algorithmic and mathematical aspects of geometry of numbers. Examples include random lattices and distributions, worstcase to averagecase reductions and lattice algorithms.

Time: Thursday, November 20, 2014 at 15:00 –16:00 p.m. Room: N205
Title: Computer Aided Analysis for the Global Stability and the Existence of Limit Cycles of ODE's
Speaker: Zhengyi Lu (Sichuan Normal University, China)
Abstract: Symbolic computation for dealing with the global stability and the existence of periodic orbits of ODE's are shown.
Wu's well ordering principle is applied to the preypredator chain systems. An algorithm for real root isolation of polynomial systems is proposed and used to check the uniqueness of a positive equilibrium which implies the global stability of the corresponding monotone systems. The positive definiteness of a class of polynomials from the global stability analysis of discrete di usion systems is proved. Small amplitude limit cycles for Kolmogorov systems are constructed based on the Liapunov method and the algorithm for real root isolation. Center and focus problems and the algorithmic construction for multiple limit cycles for 3D systems are mentioned.. 
Time: Monday, December 15, 2014 at 15:00 –16:00 p.m. Room: N205
Title: Melham's Conjecture on Sums of Odd Powers of Fibonacci Numbers
Speaker: Arthur L. B. Yang (Center for Combinatorics, Nankai University, China)
Abstract: Let $F_n$ denote the $n$th Fibonacci number and $L_n$ denote the $n$th Lucas number. Melham conjectured that for any $n, m\geq 1$, the sum $$ L_1L_3L_5\cdots L_{2m+1}\sum_{r=1}^n F_{2r}^{2m+1} $$ can be expressed as $(F_{2n+1}1)^2P(F_{2n+1})$, where $P(x)$ is a polynomial of degree $2m1$ with integer coefficients. Based on a formula due to Prodinger, we give an affirmative answer to Melham's conjecture.
This is a joint work with Brian Y. Sun and Matthew H.Y. Xie. 
Time: Tuesday, Juanary 20, 2015 at 15:00 –16:00 p.m. Room: N205
Title: Incidence Geometry and Erdös Type Problems
Speaker: Oliver RocheNewton (RICAMLinz, Austrian Academy of Sciences, Austria)
Abstract: A famous problem of Erdös in the field of discrete geometry is the following: given a set of $n$ points in the plane, what lower bounds can we obtain for the number of distinct distances determined by pairs of points from the set. One can generate many other interesting questions about bounds for certain configurations determined by a finite set of points  these are often described as "Erdöstype problems" and most of the best answers that have been obtained have come from progress in the field of incidence geometry. This talk will give an introduction to these two closely related areas, and touch upon some new results of this nature in the finite field setting.

Time: Thursday, August 27, 2015 at 15:00 –16:00 p.m. Room: N205
Title: Gammapositivity for the Eulerian distribution on separable permutations
Speaker: Shishuo Fu (College of Mathematics and Statistics, Chongqing Univeristy, China)
Abstract: In this talk, we introduce the descent polynomial on separable permutations (3142 and 2413 avoiding). We prove that it is gammapositive, which implies both unimodality and symmetry. Moreover, we find a combinatorial interpretation for its gammacoefficients which is comparable with that of Eulerian polynomials. This is joint work with Zhicong Lin and Jiang Zeng.

Time: Tuesday, December 6, 2016 at 9:30 –10:30 a.m. Room: N420
Title: Multidimensional Wavelets and Framelets
Speaker: Bin Han (University of Alberta, Canada)
Abstract: One of the current active research directions in wavelet analysis is on multidimensional wavelets and framelets, which are of interest for highdimensional problems such as image processing and computer graphics. The study of multidimensional wavelets and framelets is closely related to multivariate Laurent polynomials, algebraic geometric, symbolic computing, and symmetry groups. In this talk, we first introduce some basic theory on multidimensional wavelets and framelets. Then we shall present some recent progresses on their constructions. Next we shall discuss some major tools and techniques used from other areas in mathematics for the study of multivariate wavelets and framelets. Finally we shall address some difficulties and challenges on the construction of multidimensional wavelets and framelets as well as some open problems on this topic.

Time: Tuesday, December 6, 2016 at 10:45 –11:45 a.m. Room: N420
Title:GaussNewton Method for Phase Retrieval
Speaker: Zhiqiang Xu (Academy of Mathematics and Systems Science, CAS, China)
Abstract: In this talk, we introduce a concrete algorithm for phase retrieval, which we refer to as GaussNewton algorithm. In short, this algorithm starts with a good initial estimation, which is obtained by a modified spectral method, and then update the iteration point by a GaussNewton iteration step. We prove that a resampled version of this algorithm quadratically converges to the solution for the real case with the number of random measurements being nearly minimal. Numerical experiments also show that GaussNewton method has better performance over the other algorithms.

Time: Monday, Feburary 20, 2017 at 14:00 –15:00 p.m. Room: N210
Title:Polynomials with only real zeros in combinatorics
Speaker: Yi Wang (Dalian University of Technology, China)
Abstract: Polynomials with only real zeros arise often in combinatorics. Our interest in such polynomials was originally due to its implication about unimodality and logconcavity. In this talk we establish some sufficient conditions to the reality of zeros of polynomial sequences satisfying certain recurrence relations and then apply them to solve several open problems.

Time: Monday, March 27, 2017 at 14:00 –15:00 p.m. Room: N205
Title:Smith normal form and combinatorics
Speaker: Lili Mu (Liaoning Normal University, China)
Abstract: This talk surveys some combinatorial aspects of Smith normal form. The discussion includes Smith normal form of Laplacian matrices, random integer matrices and matrices associated with Youngs Lattice and partitions. we then give some examples of Smith normal form arising from three interesting cases of Varchenko matrices of hyperplane arrangements.

Time: Tuesday, April 18, 2017 at 10:00 –11:00 a.m. Room: N202
Title:The Riemann Hypothesis in terms of eigenvalues of certain almost triangular Hankel matrices
Speaker: Yuri Matiyasevich (St.Petersburg Department of Steklov Institute of Mathematics of Russian Academy of Sciencies, Russia)
Abstract: The famous Riemann Hypothesis (RH) is one of the most important open problem in Number Theory. As many other outstanding problems, RH has many equivalent statements. Ten years ago the speaker reformulated the Riemann Hypothesis as statements about the eigenvalues of certain Hankel matrices, entries of which are defined via the Taylor series coefficients of Riemann's zeta function. Numerical calculations revealed some very interesting visual patterns in the behaviour of the eigenvalues and allowed the speaker to state a number of new conjectures related to the RH.
Recently computations have been performed on supercomputers. This led to new conjectures about the finer structure of the eigenvalues and eigenvectors and to conjectures that are (formally) stronger than RH. Further refinement of these conjectures would require extensive computations on more powerful computers than those that were available to the speaker.
More information can be found at http://logic.pdmi.ras.ru/~yumat/personaljournal/zetahiddenlife. 
Time: Tuesday, April 18, 2017 at 11:00 –12:00 a.m. Room: N202
Title:Further results on Hilbert's Tenth Problem
Speaker: ZhiWei Sun (Nanjing University, China)
Abstract: Hilbert's Tenth Problem (HTP) asks for an effective algorithm to test whether an arbitrary polynomial equation $P(x_1, ... ,x_n)=0$ (with integer coefficients) has solutions over the ring $\mathbb{Z}$ of the integers. This was finally solved by Matiyasevich in 1970 negatively. In this talk we introduce the speaker's further results on HTP. In particular, we present a sketch of the proof of the speaker's main result that there is no effective algorithm to determine whether an arbitrary polynomial equation $P(x_1, ... ,x_{11})=0$ (with integer coefficients) in 11 unknowns has integral solutions or not.

Time: Thursday, May 4, 2017 at 14:00 –15:00 p.m. Room: N205
Title:密码学中几类非线性序列综述
Speaker: 戚文峰 (解放军信息工程大学)
Abstract: 整数剩余类环上导出序列，特别是应用于祖冲之算法（即ZUC算法）中序列源；带进位反馈移位寄存器（FCSR）序列，重点介绍极大周期FCSR序列及其伪随机性质；非线性反馈移位寄存器（NFSR）序列，重点介绍NFSR的串联和线性子簇问题。

Time: Monday, June 5, 2017 at 14:00 –15:00 p.m. Room: N202
Title:On the summability of formal solutions of singular PDEs
Speaker: Changgui Zhang (Université de Sciences et Technologies de Lille, France)
Abstract: Via the Stokes phenomenon, the BorelLaplace summation method plays a central role for the analytic description of the Galois differential group associated with a singular linear ODE. In the talk, we deal with a family of totally characteristic type PDEs, establishing the summability of their formal solutions in suitable Gevrey spaces. This is a joint work with Chen H. and Luo Z..

Time: Monday, June 5, 2017 at 15:30 –16:30 p.m. Room: N202
Title:Algebraic and computational aspects of tensors
Speaker: Ke Ye (Univsersity of Chichago, USA)
Abstract: Tensors are direct generalizations of matrices. They appear in almost every branch of mathematics and engineering. Three of the most important problems about tensors are: 1) compute the rank of a tensor 2) decompose a tensor into a sum of rank one tensors 3) Comon’s conjecture for symmetric tensors. In this talk, I will try to convince the audience that algebra can be used to study tensors. Examples for this purpose include structured matrix decomposition problem, bilinear complexity problem, tensor networks states, Hankel tensors and tensor eigenvalue problems. In these examples, I will explain how algebraic tools are used to answer the three problems mentioned above.

Time: Monday, June 19, 2017 at 14:00 –15:00 p.m. Room: N202
Title:Automation in interactive theorem proving
Speaker: Bohua Zhan (MIT, USA)
Abstract: Interactive theorem proving involves using proof assistants to verify, with human guidance, proofs of either mathematical theorems or correctness of computer programs. In this talk, I will give a brief overview of the history of this field, with an emphasis on automation techniques. I will then discuss my own work on a new heuristic theorem prover called auto2 for the proof assistant Isabelle.

Time: Monday, August 21, 2017 at 9:00 –10:00 a.m. Room: N205
Title: 等几何造型与分析新进展
Speaker: 徐岗 (杭州电子科技大学计算机学院)
Abstract: 等几何分析(isogeometric analysis)是一种基于CAD 模型的精确几何表示进行模拟仿真的新型技术，为实现CAD/CAE 的无缝融合提供了新途径. 其所面临的几何瓶颈问题也为已趋成熟的CAGD领域开辟了“等几何造型”这一新的研究方向. 本报告将重点介绍我们最近在等几何造型与分析领域所做的一些工作，包括复杂计算域参数化、拓扑一致模型的分析重用方法、基于等几何分析的中轴计算方法等。

Time: Wensday, September 6, 2017 at 14:00 –15:00 p.m. Room: N210
Title: Several Combinatorial Problems Concerning Tableaux
Speaker: Peter L. Guo (南开大学)
Abstract: Tableaux have numerous applications in combinatorics, representation theory and algebraic geometry. In this talk, we shall discuss several combinatorial problems related to tableaux. For example, are there tableau formulas for Schubert/Grothendieck polynomials? We also talk about some our recent work on tableaux.

Time: Wensday, September 6, 2017 at 15:30 –16:30 p.m. Room: N210
Title: Over and Under Approximations of Reachable Sets Within HamiltonJacobi Framework
Speaker: 佘志坤 (北京航空航天大学)
Abstract: For dynamical systems, reachable sets can be described by solutions of HamiltonJacobi equations. In this paper, we discuss a methodology to compute approximations, defined by zero sublevel sets of polynomials, of timebounded reachable sets (i.e., flowpipes) with arbitrary bounded errors for polynomial dynamical systems via solving derived HamiltonJacobi equations with inequality constraints. We start with evolution functions for describing the flowpipes of systems, and find their explicit Taylor expansions with respect to time. Then, we prove the existence of polynomial approximations to evolution functions with arbitrary bounded errors by investigating solutions of corresponding partial differential equations with derived inequality constraints, which shows the applicability of this methodology to obtain both over and under approximations of reachable sets with arbitrary precisions in Hausdorff metric. Afterwards, we propose two methods to compute polynomial template based evolution functions with constraints via using sumofsquares decomposition and quantifier elimination, respectively. We test these two methods on some examples with comparisons to the advection operator based method. The computation and comparison results show that the QE based method to certain extent has better performance than the SOS based method and the advection operator based method.

Time: Wensday, September 13, 2017 at 9:30 –10:30 a.m. Room: N205
Title: Tropical geometry and its applications
Speaker: Yue Ren (Max Planck Institute for Mathematics in the Sciences,Germany)
Abstract: Tropical varieties are balanced polyhedral complexes that arise in several contexts. In Geometry, they are commonly regarded as combinatorial shadows of their algebraic counterparts; in combinatorics, they appear in the study of realizable matroids; and in optimization, they appear as parameter domains in which the optimal solution is not unique.
In this talk, we will discuss the different equivalent definitions for tropical varieties and the different applications of tropical geometry that they entail. Moreover, we will discuss how tropical varieties can be computed, and, in doing so, highlight some breadandbutter techniques of computer algebra. 
Time: Tuesday, October 10, 2017 at 15:00 –16:00 p.m. Room: N205
Title: On $q$series and the $q$partial differential equations
Speaker: 刘治国 (华东师范大学)
Abstract: A $q$partial derivative of a function of several variables is its $q$derivative with respect to one of these variables, regarding other variables as constants. A $q$partial differential equation is an equation containing unknown multivariable functions and their $q$partial derivatives, which is a $q$extension of the ordinary partial differential equation. The $q$partial differential equation is a completely new research topic, which reveal some surpring connections between $q$series and the analytic functions of several complex variables. In this talk, I will intoduce some research results in the $q$partial differential equations.

Time: Monday, October 30, 2017 at 15:00 –16:00 p.m. Room: N205
Title:Some generalizations of a supercongruence of van Hamme
Speaker: 郭军伟 (淮阴师范学院)
Abstract: In 1997, van Hamme conjectured that Ramanujan's formula for $1/\pi$ has a nice $p$analogue. This result was proved by Mortenson using a $6F5$ transformation, and was reproved by Zudilin via the Wilf–Zeilberger method. In this talk, we propose a conjectural generalization of van Hamme's supercongruence and prove some special cases.

Time: Tuesday, November 21, 2017 at 14:00 –15:00 p.m. Room: N205
Title:深度学习在图像视频处理中的应用
Speaker: 刘偲 (中国科学院信息工程研究所)
Abstract: 近年来，基于深度学习的图像视频分析技术取得了巨大成功。本报告首先介绍一些深度学习在图像视频处理方面的进展，包括图像分类、检测、推荐和检索等。其次，相比于传统的物体分类识别技术，图像的像素级语义理解，又称语义分割，能提供更加丰富的像素级信息, 因而成为一个新的研究热点。本报告以语义分割的三个典型实例，即场景解析，人脸解析以及人像解析为切入点，重点介绍我们在语义分割方面做出的工作。