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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the transcendental Morse inequality
先验 莫尔斯不等式 射影流形 可动锥 对偶性
2023/5/4
We report the work “Duality between the pseudoeffective and the movable cone of a projective manifold” of Witt Nystrom, where he proved the transcendental Morse inequality for projective manifolds.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Fields with a generic multiplicative endomorphism
通用乘法 自同态 域
2023/5/4
The theory of fields expanded by a unary function symbol for a multiplicative endomorphism admits a model-companion, we denote it ACFH. It is a new example of an NSOP1 theory which is not simple. I wi...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Arnold conjecture and advances in Floer theory
阿诺德猜想 弗洛尔理论 哈密顿微分同胚
2023/5/4
In 1960s, Arnold conjectured that the number of fixed points of a Hamiltonian diffeomorphism of a symplectic manifold should be (much) greater than its counterpart for a general diffeomorphism. This c...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On forward/inverse spectral problems, approximation problems and multiple integral formulae for non-smooth solitons
非光滑孤子 正/逆谱问题 近似问题 多重积分公式
2023/4/28
A class of nonlinear integrable PDEs admit non-smooth solitary wave solutions as certain special weak solutions. These solutions can be used to capture main attributes of solutions of these PDEs, e.g....
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Boundary expansion in the Loewner-Nirenberg problem
Loewner-Nirenberg problem 边界展开 利玛窦曲率
2023/4/28
We first review some classical results of the Loewner-Nirenberg problem. Then we discuss the characteristics of boundary expansion and its applications in studying the negativity of Ricci curvatures o...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Optimization-inspired deep unfolding correction-distillation network for CS-MRI reconstruction
优化启发 CS-MRI 重建深度展开 校正-蒸馏网络
2023/4/27
In this talk, we discuss a unifying deep unfolding multi-sampling-ratio interpretable CS-MRI framework. The combined approach offers more generalizability than the existing deep-learning-based CS-MRI ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Kazdan-Warner equations on compact Riemann surfaces
紧黎曼曲面 卡兹丹-华纳方程 数学
2023/4/28
In this talk, we shall review firstly the study history of Kazdan-Warner equations on compact Riemann surfaces, which was proposed by Kazdan and Warner on Annals of Math on 1974. Then we shall show th...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A New Framework for SIMD Bootstrapping in Polynomial Modulus
多项式 模数 SIMD自举 新框架
2023/4/28
In this series of work, we aim at improving the bootstrapping paradigm for fully homomorphic encryption (FHE). Our main goal is to show that the amortized cost of bootstrapping within a polynomial mod...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Capsule Aggregated Attention for Vehicle Routing Problems
车辆 路径问题 胶囊聚合 关注
2023/4/27
Deep learning based methods have shown great potential for solving Vehicle Routing Problems (VRPs) in recent years. In the current learning based models, attention mechanism plays an important role an...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Solving hidden number problem with lattice sieving
晶格筛分 隐数问题 格约简算法
2023/4/28
Lattice reduction algorithms have been proved to be one of the most powerful and versatile tools in public key cryptanalysis. In this talk, we primarily concentrate on lattice attacks against (EC)DSA ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：First-order factors of linear Mahler operators
线性 Mahler operators 一阶因子
2023/4/27
We develop and compare two algorithms for computing first-order right-hand factors in the ring of linear Mahler operators l_r M^r+?+l_1 M+l_0 where l_0,…,l_r are polynomials in x and Mx=x^b M for some...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Dynamic inference for left behind probabilities on congested metro routes
动态推理 拥挤地铁路线 落后概率
2023/4/26
Passengers left behind is an important measure to describe the degree of congestion in metro systems. Note that passengers' left behind probabilities are different for their different tap-in times. Th...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Integral equations with bubble-type kernel via the method of moving spheres
运动球体 气泡型核 积分方程
2023/4/27
In this talk, I will describe a moving sphere approach to a class of integral equations with bubble-type kernel. This class of equations comes from higher-order elliptic equations on the standard sphe...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Machine learning methods for forward and inverse PDEs
正反向 偏微分方程 机器学习
2023/4/27
本报告介绍我们近期的两项工作。(1) 求解PDE的PINN方法在处理时间发展方程时往往遇到难以收敛的困难。我们发展了时间方向的预训练PINN方法及自适应步长方法，解决了收敛性困难，使PDE求解精度能够得到系统性提高。我们在一系列时间发展方程上获得了比文献报道更精确的训练结果。(2) 辐射调源问题是一个典型的反问题，要求调整辐射输运方程的边条件(源)，使解满足特定设计目标。我们针对辐射输运方程的时序...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Multiple solutions for semilinear subelliptic Dirichlet problem
半线性 次椭圆 狄利克雷问题 多种解
2023/4/27
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Multiple solutions for semilinear subelliptic Dirichlet problem。