即将开课！BIMSA秋学期公开课一览

Sergio Cecotti   (Research Fellow)

10:40 - 12:15,   Mon,Wed

1110

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Graduate

English

Yes

Basic mathematics (calculus, algebra, etc.); a textbook knowledge of General Relativity and Quantum Field Theory (including the very basics facts about supersymmetry); the elementary notions of differential geometry (Riemannian geometry, bundles, connections, etc.), Lie groups, and algebraic topology (homology & cohomology groups,etc.).

A comprehsive course in String Theory. String Theory I covers the foundations of the theory, the construction of the various string theories, with emphasis on the supersymmetric ones, and the basic computational techniques. The emphasis is on SUSY string theories, the bosonic string is used mainly as a didactical laboratory where we introduce basic ideas and techniques in the simplest possible context. While the approach is meant to be didactical, one tries to be mathematically precise, and self-contained. Conformal field theory in two-dimensions is introduced from scratch, with the topics relevant to string theory discussed in detail. String Theory II covers the physics of the supersymmetric strings, from the perturbative regime to the non-perturbative one. The theory of supergravity and anomalies are reviewed from a geometric perspective. BPS objects and non-renormalization theorems are described from different viewpoints. Calabi-Yau compactifications are discussed in detail. The course covers also some advanced stuff such as the basic ideas of M- and F-theory, black hole entropy, and so on.

Sergio Cecotti graduated in physics at the University of Pisa in 1979 and has worked at the Harvard University, the University of Pisa, CERN, etc.. In 2014, he became a full professor at SISSA. He has published about 100 papers with total number of citations 7260. His h-index is 44.

Song Cheng   (Assistant Research Fellow)

15:20 - 18:40,   Tue

1129B

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Graduate

Chinese

No

Quantum Mechanics

This course will focus on the basic concepts and representative algorithms of tensor networks. For 1D tensor networks, we will introduce the Matrix Product State(MPS) and its Density Matrix Renormalization Group algorithm(DMRG), Time Evolution Block Decimation algorithm(TEBD), etc. For high-dimensional tensor networks, we will include the Projected Entangled Pair States (PEPS) and its various Tensor Renormalization Group algorithms, as well as the Corner Transfer Matrix Renormalization Group algorithm, variational algorithms, etc. We will also involve some machine learning algorithms and quantum simulation algorithms based on tensor networks if time permits.

程嵩，现任北京雁栖湖应用数学研究院助理研究员，曾任鹏城实验室量子计算中心助理研究员，博士毕业于中科院物理所理论物理专业。他的研究方向是张量网络算法，研究兴趣主要集中于开发张量网络在凝聚态物理，机器学习，量子计算等方向的新算法。

Jintai Ding   (Research Fellow)

18:40 - 20:55,   Tue

JCY-1

Graduate

Chinese

No

This will be on Tuesday night where we give an introduction class for the basics of modern cryptography including symmetric cryptography, public key cryptography and post-quantum cryptography.

Jintai Ding received a Ph.D. degree from Yale University and used to work as a professor of William Taft at the University of Cincinnati. Currently, he is a double-appointed professor at Yau Mathematical Sciences Center, Tsinghua University, and Yanqi Lake Beijing Institute of Mathematical Sciences and Applications (BIMSA). In the early days, he was engaged in the research of quantum affine algebra and representation theory, while his current research direction is post-quantum cryptography. Moreover, he has served as the co-chairman of the International Conference on Post-Quantum Cryptography for three times and is one of the prominent scholars of multivariate cryptography in the world.

William Donovan   (Associate Professor)

13:30 - 15:05,   Tue,Thu

1110

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Graduate

English

Yes

Some representation theory or algebraic geometry would be helpful.

Quiver representations are a useful tool in diverse areas of algebra and geometry. Recently, they have furthermore been used to describe and analyze neural networks. I will introduce quivers, their representations, and a range of applications, including to the theory of machine learning.

Will Donovan joined Yau MSC, Tsinghua U in 2018. Since 2021 he is an Associate Professor, and Adjunct Associate Professor at BIMSA. His focus is geometry, in particular applying ideas from physics and noncommutative algebra to study varieties, using tools of homological algebra and category theory. He studied at Cambridge U, completed his PhD at Imperial College London, and was postdoctoral researcher at Edinburgh U, UK. From 2014-18 he was research fellow at Kavli IPMU, U Tokyo, where he is now Visiting Associate Scientist. His work is published in journals including Communications in Mathematical Physics and Duke Mathematical Journal. He is supported by China Thousand Talents Plan, and received a Japan Society for Promotion of Science Young Scientist grant award.

Babak Haghighat   (Associate Professor)

10:40 - 12:15,   Fri

1118

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Graduate

English

Yes

Quantum Mechanics, Linear Algebra

In this course, I present a self-consistent review of fault-tolerant quantum computation using the surface code. The course covers everything required to understand topological fault-tolerant quantum computation, ranging from the definition of the surface code to topological quantum error correction and topological operations on the surface code. In the process, basic concepts and powerful tools, such as universal quantum computation, quantum algorithms, stabilizer formalism, and measurement-based quantum computation, are also introduced.

Associate Professor, research interests are string theory, quantum field theory and topological field theory.

Liyan Han   (Research Fellow)

13:30 - 15:05,   Wed,Fri

1110

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Undergraduate

Chinese

Yes

如何完善宏观经济指导与调控、优化宏观经济政策和市场资源配置？如何形成可持续经济增长和高质量发展的创新能力？如何稳步地消除贫富差距，而实现社会均富？《宏观经济学十二讲：中国情景》是一本中级宏观经济学教材。本书结合中国特色社会主义市场经济建设实践，以及西方宏观经济学理论，从国际比较的视角，系统、全面地构建了宏观经济学的知识体系与理论框架。书中凝结了两位作者数十年教学、理论研究成果，在介绍宏观经济学理论的同时，融入大量中国及其他经济体的发展实例，从实践出发辩证地解读宏观经济学理论。本书可作为本科、硕士和MBA的宏观经济学课程教材，也是大众读者全面理解国际主流宏观经济学理论及其在中国的思辨、实践的绝佳选择。

Dr. Han Liyan, Research fellow at Beijing Yanqi Lake Institute of Applied Mathematics, Lab of Digital Economy. He once worked as a chief professor of economics in Beihang University for 20 years. He was awarded as Beijing Renowned Teacher, Distinguished Fellow in Chinese Quantitative Economics, and Special government allowances of the State Council. His doctorate research focused on fuzzy information and knowledge engineering in 1990s, and now his research interests focus on fintech, foreign exchange rate combined with monetary policy, and green finance as well.   

Lynn Heller   (Research Fellow)

19:20 - 20:55,   Wed

JCY-3

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Undergraduate

English

No

In this course we look at the life and work of some of the most influential Mathematicians including David Hilbert, Felix Klein, Emmy Noether and Bernhard Riemann. The aim is twofold. On the one hand, we would like to introduce the historical figures and convey the flavor of how Mathematics were conducted at that time, on the other hand, I would also like to show how (in a possibly modern interpretation) their work continue to be influencial today. Along the way we will also be encountering some specifics of the German culture and in particular the different educational and academic system.

I was born in Wuhan and grew up in the little German town Göttingen, which was home to an extraordinary amount of great Mathematicians (and Nobel prize winners) including all the Mathematicians discussed in the course.   I studied economics at the FU Berlin and Mathematics at TU Berlin from 2003-2007 and obtained my PhD from Eberhard Karls University  Tübingen in 2012. Thereafter, I stayed in Tübingen as a Postdoc till I got a Juniorprofessorship in 2017 at the Leibniz University in Hannover.

Sebastian Heller   (Research Fellow)

10:40 - 12:15,   Mon,Wed

JCY-3

Zoom: 293 812 9202   PW:BIMSA

Undergraduate

English

Yes

It is necessary to be familiar with the basic concepts of linear algebra and calculus. In order to be able to follow the course throughout, it is beneficial to have some basic knowledge about differential geometry or manifolds, and to be familiar with some complex analysis. However, it is also possible to make up for this within the course.

The investigation and construction of  surfaces with special geometric properties has always been an important subject in differential geometry. Of particular interest are minimal surfaces and constant mean curvature (CMC) surfaces in space forms. Global properties surfaces were first considered by Hopf, showing that all CMC spheres are round. This result was generalized by Alexandrov [2] in the 1950s, who showed that the round spheres are the only embedded compact CMC surfaces in $\mathbb R^3$, while there do not exist any compact minimal surfaces in euclidean space and hyperbolic 3-space due to the maximum principle. In contrast, there are many compact and embedded minimal surfaces in the 3-sphere, the best known examples being the Clifford torus and the Lawson surfaces, in addition to the totally geodesic 2-sphere, and a full classification is beyond the current knowledge. One reason for the beauty and depth of minimal surface theory is that there are many different methods and tools with which to construct, study, and classify these surfaces. In this course we will first derive basic properties of minimal surfaces in $\mathbb R^3$ and introduce some general techniques, and then move on to CMC surfaces in $\mathbb R^3$ and minimal surfaces in $\mathbb S^3.$ We mainly use differential geometric and complex analytical methods in this course.

PhD in 2008, Humboldt Universitat Berlin, Germany Habilitation in 2014, Universitat Tubingen, Germany Researcher at Universities of Heidelberg, Hamburg, Hannover, 2014-2022 Research Fellow at Beijing Institute of Mathematical Sciences and Applications from September 2022 on Research interests: minimal surfaces, harmonic maps, Riemann surfaces, Higgs bundles, moduli spaces, visualisation and experimental mathematics

Chuangqiang Hu   (Assistant Research Fellow)

13:30 - 15:05,   Tue,Thu

Sanya

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Undergraduate

Chinese

Yes

homological algebra

This lecture explores Hochschild cohomology as a Gerstenhaber algebra in detail, the notions of smoothness and duality, algebraic deformation theory, infinity structures,  and connections to the Hochschild-Kostant-Rosenberg decomposition. Useful homological algebra background is provided as well.

Hu chuangqiang joined Bimsa in the autumn of 2021. The main research fields include: coding theory, function field and number theory, singularity theory. In recent years, he has made a series of academic achievements in the research of quantum codes, algebraic geometric codes, Drinfeld modules, elliptic singular points, Yau Lie algebras and other studies. He has published 13 papers in famous academic journals such as IEEE Trans. on IT., Final Fields and their Applications, Designs, Codes and Cryptography. He has been invited to attend domestic and international academic conferences for many times and made conference reports.

Sergei Ivanov   (Research Fellow)

10:40 - 12:15,   Tue,Fri

1129B

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Graduate

English

Yes

Basic theory of rings and modules, basic group theory, basic category theory

Such concepts as homology and cohomology of algebraic objects, spaces and varieties have become an integral part of modern mathematics. This course is dedicated to introducing this range of ideas from the side of algebra.

Hanru Jiang   (Assistant Research Fellow)

15:20 - 16:55,   Tue,Thu

1118

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Graduate

Chinese

No

Discrete math.

In this course, we introduce basic concepts in graph theory and complexity theory, then study graph algorithms with a focus on matching and network flows.

蒋瀚如于2019年在中国科学技术大学取得计算机科学与技术博士学位，2019-2020年在鹏城实验室量子计算研究中心担任助理研究员，2020年加入BIMSA任助理研究员。他的主要研究方向为程序语言理论、编译器的形式化验证和量子计算中的程序语言问题。作为并发程序分离编译验证工作CASCompCert的主要完成人，获得程序语言领域顶级会议PLDI 2019的Distinguished Paper Award。

Kotaro Kawai   (Associate Research Fellow)

10:40 - 15:05,   Fri

1120

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Graduate

English

Yes

Linear algebra, basics of Riemmanian geometry

The classification of Riemannian manifolds with special holonomy contains two “exceptional” cases: G2 and Spin(7). Manifolds with holonomy contained in G2 or Spin(7) are called G2-manifolds or Spin(7)-manifolds, respectively. In this course, I will introduce various topics of G2 and Spin(7) geometry, mainly focusing on the G2 case. We start from the linear algebra in G2 geometry. Then we study topics such as the structure of a G2-manifold and calibrated geometry/ gauge theory/mirror symmetry on a G2-manifold.

Kotaro Kawai got a bachelor's degree and a master's degree from the university of Tokyo, and received his Ph.D from Tohoku university in 2013. He was an assistant professor at Gakushuin university in Japan, then he moved to BIMSA this year. Gakushuin University was established as an educational institution for the imperial family and peers, and even today, some members of the imperial family attend this university. There are many eminent professors and Kunihiko Kodaira worked at this university. He majors in differential geometry, focusing on manifolds with exceptional holonomy. These manifolds are considered to be analogues of Calabi-Yau manifolds, and higher dimensional analogues of gauge theory are expected on these manifolds. This topic is also related to physics, and he think that this is an exciting research field.

Pengyu Le   (Assistant Research Fellow)

08:50 - 10:35,   Mon,Wed

1129B

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Graduate

Chinese

No

Multivariable Calculus, Ordinary Differential Equation, Basics of Riemannian Geometry (optional)

The course will cover various comparison theorems under different curvature conditions in Riemannian geometry.

Jingyan Li   (Assistant Research Fellow)

13:30 - 15:05,   Mon,Wed

1118

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Graduate

Chinese

No

Simplicial complex theory and simplicial set theory.

The notion of fibre bundle first arose out of questions posed in the 1930s on the topology and geometry of manifolds. By the year 1950, the definition of fibre bundle had been clearly formulated, the homotopy classification of fibre bundles achieved, and the theory of characteristic classes of fibre bundles developed by several mathematicians: Chern, Pontrjagin, Stiefel, and Whitney. Fiber bundle theory is not only important in topology and differential geometry, but also is widely used in other branches of mathematics and physics. This course mainly introduces some basic concepts of fiber bundles and the application of fiber bundles in homology theory in comparison with the geometric level and the simple level.

Assistant Reserch fellow Jingyan Li received a PhD degree from the Department of Mathematics of Hebei Normal University in 2007. Before joining BIMSA in September 2021, she has taught in the Department of Mathematics and Physics of Shijiazhuang Railway University and the School of Mathematical Sciences of Hebei Normal University as an associate professor. Her research interests include topology data analysis and simplicial homology and homotopy.

Zhen Li   (Assistant Research Fellow)

08:50 - 10:35,   Tue,Thu

1110

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Graduate

Chinese

No

Political economy, Macroeconomics, Microeconomics, Accounting, etc

Facing the complicated global economic and financial changes, this course applies the modern economics theory to tell the history of financial development in China, integrates the basic principles of finance and the financial practice of China, and rationally integrates micro-finance and macro-finance, forming a systematic and complete logical framework and knowledge system. It mainly includes five parts: currency, credit and finance; financial intermediary and financial market; monetary equilibrium and macro-policy; micro-mechanism of financial operation; financial development and stability mechanism. This course is intended for college students who need to understand and master financial knowledge systematically.

Dr. Zhen Li is an assistant research fellow at the BIMSA. He is also a visiting research fellow at the Chongyang Institute for Financial Studies, Renmin University of China, the International Monetary Institute, Renmin University of China, and the Alibaba Research Center for Rural Dynamics. He was a postdoctoral fellow from 2020-2022 at the School of Data Science, Fudan University, and an assistant research fellow from 2013-2016 at the Chongyang Institute for Financial Studies, Renmin University of China. Dr. Li received his Ph.D. in Finance, M.A. in Statistics, and B.A. in Finance from the Renmin University of China, and B.E. in Software Engineering from the Nanjing University. He was a visiting scholar from 2019-2020 at the School of Business, George Washington University. His current research focuses on FinTech, commercial banking, and financial risk management, and other fields. Dr. Li has published more than 30 articles in some important academic journals such as Journal of Financial Research, Statistical Research, China Economic Review , etc.

Bei Liang   (Assistant Research Fellow)

18:40 - 20:55,   Thu

JCY-1

Graduate

Chinese

No

This class will be on Thursday night and we will cover advanced topics including Secure  Multi-Party Computation, Fully Homomorphic Encryption, etc. It will also bring in speakers, including students and postdocs, to give lectures on their current research topics and results, and it encourages students to give presentations in any interesting topics they choose.

Dr. Bei Liang received Ph.D. in information security from the Institute of Information Engineering, Chinese Academy of Sciences. She was a postdoc researcher at Chalmers University of Technology, Sweden. Currently, she is an assistant researcher at the BIMSA. Her main research interest is theoretical cryptography. She has published more than 20 papers in international journals or conferences, and won the ISC2019 Best Paper Award and the ProvSec2015 Best Student Paper Award. She participated in two National Key Research and Development Programs and undertook one Beijing Natural Science Foundation.

Qingfu Liu   (Professor)

09:50 - 12:15,   Fri

1110

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Graduate

Chinese

No

在监管新规下，为实现对金融风险的有效管理，本课程在总结经典风险管理建模方法的基础上，从大数据、人工智能和区块链出发，系统给出金融市场风险、信用风险、操作风险和流动性风险的先进风险管理方法及其工具。课程内容包括但不限于金融监管新规与风险内涵、特性与分类，金融监管大数据及其挖掘技术，金融市场风险管理论及其测度方法，金融信用风险管测度方法与技术，基于人工智能技术的智能风控，异常交易的监控技术与市场化管理工具，以及风险管理策略及其模型优化。为加深理解，课程将增设国内外经典案例讲授与软件编程实现。课程一般适用于拥有一定数理基础的高年级本科生、硕士和博士研究生。

Qingfu Liu, the professor and doctoral supervisor at School of Economics, Fudan University, was awarded as Shanghai Pujiang Scholar. Prof. Liu obtained a doctorate in management science and engineering from Southeast University, was a postdoctoral fellow at Fudan University, and also a visiting scholar at Stanford University. Prof. Liu is now the executive dean of Fudan-Stanford Institute for China Financial Technology and Risk Analytics, the academic vice dean of Fudan-Zhongzhi Institute for Big Data Finance and Investment, and the vice dean of Shanghai Big Data Joint Innovation Lab. Prof. Liu's research interests mainly include financial derivatives, big data finance, quantitative investment, RegTech, green finance and non-performing asset disposal. He has published more than 80 papers in the Journal of economics, Journal of International Money and Finance, Journal of Management Sciences in China and other important journals at home and abroad, published three monographs, and presided over more than 20 national and provincial research projects. He is currently an associate editor at Digital Finance and an editor at World Economic Papers.

Sixu Liu   (Assistant Research Fellow)

15:20 - 18:40,   Mon

1110

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Graduate

Chinese

Yes

basic knowledge of measure theory, stochastic process, functional analysis and topology

We will introduce basis knowledge of ergodic theory, and its  relationship with dynamical systems. This course includes topics on measure-preserving transformation, entropy and  topological entropy.

刘思序于2019年获得北京大学博士学位，之后在清华大学任博士后，并于2022年加入BIMSA任助理研究员。主要研究方向为动力系统与遍历论，统计试验设计。

Yong Suk Moon   (Assistant Research Fellow)

13:30 - 15:05,   Wed,Fri

1129B

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Graduate

English

No

Algebraic geometry (background in algebraic number theory will be helpful)

Prismatic cohomology, which is developed in a recent work of Bhatt-Scholze, is a cohomology theory for schemes over p-adic rings. It is considered to be an overarching cohomology theory in p-adic geometry, unifying etale, de Rham, and crystalline cohomology. Due to wide-ranging applications in p-adic Hodge theory and p-adic Galois representations, it is one of the central topics of active research. In this course, we will start by going over motivational background in p-adic cohomology theories, and then give a rough overview of main ideas and results in the paper "Prisms and prismatic cohomology" by Bhatt-Scholze. If time permits, we will also briefly discuss how the prismatic theory may reveal a deeper understanding of p-adic Galois representations.

Yong Suk Moon joined BIMSA in 2022 fall as an assistant research fellow. His research area is number theory and arithmetic geometry. More specifically, his current research focuses on p-adic Hodge theory, Fontaine-Mazur conjecture, and p-adic Langlands program. He completed his Ph.D at Harvard University in 2016, and was a Golomb visiting assistant professor at Purdue University (2016-19) and a postdoctoral researcher at University of Arizona (2019 - 22).

Sebastien Palcoux   (Assistant Research Fellow)

15:20 - 16:55,   Mon,Tue

1120

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Undergraduate

English

Yes

Category theory

This is the sequel of the course "On Fusion Categories II" given last semester.It introduces to the notion fusion category, which can be seen as a representation theory of the (finite) quantum symmetries. The notes and videos of the first and second parts are available at: Part I: http://www.bimsa.cn/newsinfo/526244.html Part II: https://www.bimsa.cn/newsinfo/601271.html

2010年于 Institut de Mathématiques de Marseille (I2M)取得数学博士学位 2014-2016 于 Institute of Mathematical Sciences (IMSc)任博士后 2020-至今于北京雁栖湖应用数学研究院任助理研究员 主要研究兴趣：量子代数，量子对称，子因子平面代数和融合范畴。在Advances in Mathematics, Quantum Topology等多个杂志上发表学术论文。

Yuval Peres   (Research Fellow)

15:20 - 16:55,   Wed,Fri

1129B

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Graduate

English

Yes

Undergraduate Probability and Linear Algebra, some measure theoretic probability: Conditional expectation, Laws of large numbers. The first chapter of Durrett’s graduate text or taking  the course “Probability 1” given by Prof. Hao Wu at Tsinghua will provide ample background. That course can be taken in parallel with this course. The textbook for the course is “Markov chains and mixing times”, second edition, PDF is available from https://www.yuval-peres-books.com/markov-chains-and-mixing-times/ In the last part of the course, we will see new material that is not in that book, and explore open problems and directions of current research.

Background: The modern theory of Markov chain mixing is the result of the convergence, in the 1980's and 1990's, of several threads: For statistical physicists, Markov chains become useful in Monte Carlo simulation  The mixing time determines the running time for simulation.  Deep connections were found between rapid mixing and spatial properties of spin systems. In theoretical computer science, Markov chains play a key role in sampling and approximate counting algorithms. At the same time, mathematicians were intensively studying random walks on groups. Both spectral methods and probabilistic techniques, such as coupling, played important roles. Ingenious constructions of expander graphs (on which random walks mix especially fast) were found. The connection  between eigenvalues and expansion properties was first discovered in differential geometry, but then became central to the study of Markov chain mixing.

Yuval Peres obtained his PhD  in 1990 from the Hebrew University, Jerusalem. He was a postdoctoral fellow at Stanford and Yale, and  was then a Professor of Mathematics and Statistics in Jerusalem and in Berkeley. Later, he was a Principal researcher at Microsoft. Yuval has published more than 350 papers in most areas of probability theory, including random walks, Brownian motion, percolation, and random graphs. He has co-authored  books on Markov chains, probability on graphs, game theory and Brownian motion, which can be found at https://www.yuval-peres-books.com/ . His presentations are available at https://yuval-peres-presentations.com/  Dr. Peres is a recipient of the Rollo Davidson prize and the Loeve prize. He has mentored 21 PhD students including Elchanan Mossel (MIT, AMS fellow),  Jian Ding (PKU, ICCM gold medal and Rollo Davidson prize),  Balint Virag and Gabor Pete (Rollo Davidson prize). Dr. Peres was an invited speaker at the 2002 International Congress of Mathematicians in Beijing, at the 2008 European congress of Math,  and at the 2017 Math Congress of the Americas. In 2016, he was elected to the US National Academy of Science.

Zaijiu Shang   (Professor)

09:50 - 12:15,   Mon

1118

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Graduate

Chinese

Yes

This course is a continuation of last semester and will cover the following topics: 1) Normal forms of Hamiltonian systems and bifurcation theory; 2) Averaging methods of classical perturbation theory; 3) KAM stability of Hamiltonian systems; 4) Effective stability of nearly integrable systems; 5) Numerical stability of symplectic geometric methods.

Zaijiu Shang is a Professor of the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and a Post Teacher at the University of Chinese Academy of Sciences (2015-). He was the deputy director (2003-2011) and the director (2012-2016) of the Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences. He has been  served as a member of editorial boards of  Acta Math. Appl. Sinica (2007-), Acta Math. Sinica (2009-), Science China: Mathematics (2013-), and Applied Mathematics (HUST 2013-). He is working in the fields of dynamical systems and geometrical numerical methods. He won the second prize in “the Science and Technology Progress Award of the State Education Commission (1993)”. He was one of the core members of the project “Symplectic Geometric Algorithms of Hamiltonian Systems” which won the first prize of the National Natural Science Awards (Kang Feng etc., 1997), and his representative achievements include stability theory of symplectic algorithms and volume-preserving algorithms for source-free systems.

Artan Sheshmani   (Research Fellow)

08:50 - 10:35,   Wed,Fri

Online

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Graduate

English

Yes

Commutative Algebra (Atiyah McDonald or Rottman), Algebraic Geometry (Hartshorne or Grothendieck’s EGA/SGA)

Derived Algebraic Geometry is a machinery regarded as an extension of algebraic geometry, whose goal is to study exotic geometric settings and situations that might occur in algebraic geometry where algebraic geometry might not be able to rigorously study. Take for instance the example of intersection of two subvarieties, X, Y, in a fixed ambient smooth algebraic variety Z. We have the notion of "nice intersection" (or generic intersection) of X and Y in Z, which is equivalent to transverse intersection of the X and Y. In this case the span of the tangent space generated by tangent spaces of X and Y is equal to the tangent space of Z and their locus of intersection X∩Y will be of expected dimension. Now take for instance a “bad intersection” of X and Y, that is non-generic or non-transverse intersection of X and Y in Z. The latter situation might occur if X and Y intersect over points or loci with higher multiplicities or when their locus of intersection is not of expected dimension. Certainly such situation has been addressed in algebraic geometry, using cohomology theory, that is, one realizes the locus of intersection, X∩Y, as a cohomology class in the ambient cohomology theory of Z (for instance an element in de Rham cohomology of Z, or in complex cobordism ring of Z, or an element of the K-theory in the intersection ring of Z) and studies the intersection of X and Y cohomologically. The drawback of this approach is that X ∩Y is realized only as a cohomology class and not as a geometric object any more. The Derived Algebraic Geometry allows one to construct a geometric object associated to the non-generic locus of intersection of X and Y, which is called the “Derived Scheme”. It is roughly speaking the homotipical perturbation of the naive locus of intersection of X and Y, and contains the data of higher multiplicity components of X∩Y or components with defects of expected dimension. The machinery of homotopy theory in derived algebraic geometry enables one to identify the points in derived intersection of X and Y as points which lie in X and Y respectively, together with certain continuous homotopy maps between them (as opposed to generic intersection of X and Y where points in X∩Y are given by points which lie both in X and Y simultaneously). Similarly taking “bad” quotients of algebraic schemes/varieties by non-proper or non-free actions is yet another example which can be modeled geometrically and rigorously by derived algebraic geometry. In usual setting the points in quotient of a variety X by the action of a free proper group G are the ones that lie in the orbit space of elements of G. However in instances where the group G is acting non-freely on X, the derived algebraic geometry enables one to realize the points in the "bad quotient" as points which lie in the orbit of elements of G up to homotopy, that is two points, a and b, lie in the orbit of an element of G if they are related to each other by a homotopy path or a path with homotopical structure in that orbit. The course sets foundations to such theory of derived schemes, and follows by discussing the derived moduli spaces, and specially the derived structure of the moduli spaces of coherent sheaves, and some applications of derived geometry in enumerative geometry (specially the Donaldson-Thomas theory) of Calabi-Yau 3 folds and 4 folds will be discussed at the end.

I am a Professor of pure Mathematics, specialized in Algebraic geometry, Differential Geometry and Mathematics of String Theory. I am a Full Research Fellow (equivalent to Full Professor in the US and Europe) at Yanqi Lake Beijing Institute of Mathematical Sciences and Applications in Beijing, as well as a senior member at Harvard University CMSA, and a visiting professor at Institute for the Mathematical Sciences of the Americas at University of Miami. During the past 5 years I have been a senior personnel at Simons Collaboration Program for Homological Mirror Symmetry at Harvard University Center for Mathematical Sciences and Applications (CMSA), as well as Harvard Physics department (2020-2021), and an Associate Professor of Mathematics at Institut for Mathematik and Center for Quantum Geometry of Moduli Spaces at Aarhus University in Denmark. My work is mainly focused on Gromov Witten theory, Donaldson Thomas theory, Calabi-Yau geometries, and mathematical aspects of String theory. I study geometry of moduli spaces of sheaves and curves on Calabi Yau spaces, some of which arise in the study of mathematics of string theory. In my research I have worked on understanding dualities between geometry of such moduli spaces over complex varieties of dimension 2,3,4 and currently I am working on extension of these projects from derived geometry and geometric representation theory point of view. In joint work with Shing-Tung Yau (BIMSA, YMSC, Tsinghua, Harvard Math, Harvard CMSA, and Harvard Physics departments), Cody Long (Harvard Physics), and Cumrun Vafa (Harvard Math and Physics departments) I worked on geometry moduli spaces of sheaves with non-homolomorphic support and their associated non-BPS (non-holomorphic) counting invariants. In 2019 I recieved IRFD "Research Leader" grant (approx $1M) on my project "Embedded surfaces, dualities and quantum number theory". The project has additionally been co-financed by Harvard University CMSA (Approx total. $400K). Detail of IRFD "Research Leader" grant ($1M). --The grant has recently been extended until 2027!

Congwei Song   (Assistant Research Fellow)

17:05 - 18:40,   Mon,Wed

1118

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Graduate

Chinese

Yes

线性代数、实分析、概率论、统计学

统计学习是一种主流机器学习范式，它主张一切机器学习模型都派生自统计模型。介绍统计学习基础知识、常用模型和应用。配合以算法实现、作品展示、论文解读。还会简单讲解统计学习相关计算机语言和包的使用。希望大家在学习过程中有所收获，有所领悟。

Congwei Song received the master degree in applied mathematics from the Institute of Science in Zhejiang University of Technology, and the Ph.D. degree in basic mathematics from the Department of Mathematics, Zhejiang University, worked in Zhijiang College of Zhejiang University of Technology as an assistant from 2014 to 2021, from 2021 on, worked in BIMSA as asistant researcher. His research interests include machine learning, as well as wavelet analysis and harmonic analysis.

Benjamin Sudakov   (Professor)

15:20 - 17:20,   Thu

Online

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Graduate

English

Yes

The goal of this course is to give students an overview over the most fundamental concepts and results in modern graph theory. The topics which we plan to cover include:  Basic notions: graphs, graph isomorphism, adjacency matrix, paths, cycles, connectivity Trees, spanning trees, Cayley's formula, Vertex and edge connectivity, 2-connectivity, Mader's theorem, Menger's theorem Eulerian graphs, Hamilton cycle, Dirac's theorem Matchings, Hall's theorem, Kőnig's theorem, Tutte's condition Planar graphs, Euler's formula, basic non-planar graphs, platonic solids Graph colourings, greedy colourings, Brooks' theorem, 5-colourings of planar graphs, Gallai-Roy theorem Large girth and large chromatic number, edge colourings, Vizing's theorem, list colourings Matrix-tree theorem, Cauchy-Binet formula Hamiltonicity: Chvátal-Erdős theorem, Pósa's lemma, tournaments Ramsey theory Turán's theorem, Kővári-Sós-Turán theorem

Benny Sudakov received his PhD from Tel Aviv University in 1999. He had appointments in Princeton University, the Institute for Advanced Studies and in University of California at Los Angeles. Sudakov is currently professor of mathematics in ETH, Zurich. He is the recipient of a Sloan Fellowship, NSF CAREER Award, Humboldt Research Award, is Fellow of the American Math. Society and was invited speaker at the 2010 International Congress of Mathematicians. He authored more than 300 scientific publications and is on the editorial board of 14  research journals.  His main scientific interests are combinatorics and its applications to other areas of mathematics and computer science.

Funaki Tadahisa   (Research Fellow)

08:50 - 10:35,   Mon,Wed

1110

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Graduate

English

Yes

It is desirable that the audience is familiar with Modern Probability Theory and some tools in Stochastic Analysis such as martingales and stochastic differential equations. But I will try to briefly explain these in my course. For example, Parts I and II of my course given at Yau Mathematical Sciences Center from March to June, 2022 fit to this purpose; see slides of Lect-1 to Lect-20 posted on the web page of YMSC.

I explain our recent results on the derivation of interface motion such as motion by mean curvature or free boundary problem from particle systems in some details.  The core of these results was presented in my talk at vICM2022 [5], [6].

Funaki Tadahisa was a professor at University of Tokyo and then at Waseda University in Japan. His research subject is probability theory mostly related to statistical physics, specifically interacting systems and stochastic PDEs, whose importance increases as several Fields medals are given to this area.

Kazuyuki Tanaka   (Research Fellow)

10:40 - 12:15,   Tue,Thu

1110

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Graduate

English

Yes

Completion of undergraduate course on logic, set theory or automata theory is recommended. But all interested students are welcome.

This is an advanced undergraduate and graduate-level course in mathematical logic and theory of computation. Topics to be presented in the first semester include: computable functions, undecidability, propositional logic, NP-completeness, first-order logic, Goedel's completeness theorem, Ehrenfeucht-Fraisse games, Presburger arithmetic.

In the second semester, we will move on to Goedel's incompleteness theorems, second-order logic, infinite automata, determinacy of infinite games, etc.

Kazuyuki Tanaka received his Ph.D. from U.C. Berkeley. Before joining BIMSA in 2022, he taught at Tokyo Inst. Tech and Tohoku University, and supervised fifteen Ph.D. students. He is most known for his works on second-order arithmetic and reverse mathematics, e.g., Tanaka's embedding theorem for WKLo and the Tanaka formulas for conservation results.  For more details: https://sendailogic.com/tanaka/

Ke Tang   (Professor)

09:50 - 12:15,   Wed

1118

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Graduate

Chinese

No

Probability theory

随着金融市场的发展，传统金融产品无法满足日益增加的金融需求，衍生品市场（如期货、期权）在我国发展非常迅速。数理工具在新型金融产品设计及新型设施开发中发挥了巨大作用，以衍生品为基础的金融工程也成为金融学中重要的学科分支。本课程将介绍金融工程中核心的数理基础知识并系统总结衍生品市场中的金融理论与模型。课程内容包括套利、对冲及B-S模型等基础衍生品理论，和泊松市场模型、随机波动率模型以及随机过程的基础理论等更深入的衍生品模型。本课程旨在让同学们系统了解金融工程中运用的基本数理工具，以及它们在衍生品市场中如何发挥作用。课程适用于学习过概率论的高年级本科生、硕士和博士研究生。

Ke Tang is a professor and director of the Institute of economics, School of Social Sciences, Tsinghua University. His main research includes commodity market (including digital assets), financial technology and digital economy. He has published many papers on top English journals such as Journal of Finance, Review of Financial Studies, Management Science, and currently serves as an executive editor of Quantitative Finance, and an associate editor of Journal of Commodity Markets. His research has been reported by the CFTC, the United Nations Commodity Report etc. He is in the Elsevier highly cited scholar list of China in 2020 and 2021.

Xinxing Tang   (Assistant Research Fellow)

13:30 - 15:05,   Mon,Tue

1120

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Graduate

Chinese

No

representation theory of simple Lie algebra, basic knowledge of differential geometry and algebraic topology

We continue the related topics of KZ equations in the last semseter, including the various invariants, the Gaudin model and the Bethe Ansatz. Then we switch to the genus 1 case, and talk about the corresponding results of KZB equations. We try to collect and discuss the well-known results and recent developments.

2009-2013 四川大学数学学院基础数学 本科 2013-2018 北京大学北京国际数学研究中心 博士 2018-2021 清华大学丘成桐数学科学中心 博士后 2021- 北京怀柔应用数学研究院 助理研究员 研究兴趣：1. 可积系统，特别是GW理论、LG理论中出现的无穷维可积系统，兴趣在于理解其中的无穷个对称性的代数结构和相关计算。2. 其他兴趣：mixed Hodge structure，quantum group and KZ equation, W-algebra and W-symmetry, augmentation representation

Chengdong Tao   (Assistant Research Fellow)

15:20 - 16:55,   Wed,Fri

1110

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Graduate

Chinese

No

Mordern Cryptography, Coding Theory, C Programming Language

The most widely used nowadays are the number theoretical based cryptosystems such as RSA, DSA, and ECC. However, due to Peter Shor's Algorithm, such cryptosystems would become insecure if a large Quantum computer is built. We need to develop a new family of cryptosystems that can resist quantum computers attacks. Researchers usually use Post-Quantum Cryptography (PQC) to denote this new family. In the course, we will talk about Post-Quantum Cryptography.

Dr. Chengdong Tao got his Ph.D from South China University of Technology in 2015. Then he became an engineer at Shenzhen Huawei Technology Co., Ltd., and Executive Director and General Manager at Guangzhou Liangjian Technology Co., Ltd.. From 2020, he has been an Assistant Research Fellow of Yanqi Lake Beijing Institute of Mathematical Sciences and Applications. Research Interests include Computational Algebra, Post-quantum Cryptography, Fast Implementation.

Arnav Tripathy   (Assistant Research Fellow)

15:20 - 16:55,   Mon,Wed

1118

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Graduate

English

Yes

Differential geometry, basic complex analysis.

Hyperkahler manifolds form an extremely symmetric class of manifolds of great importance throughout mathematics and physics. I'll introduce their basic properties before indicating many examples of known constructions. Finally, I hope to detail Gaiotto-Moore-Neitzke's conjectural description of Hitchin moduli spaces.

Dr. Tripathy is a researcher interested in the geometry of string theories and supersymmetric field theories.

Bart Vlaar   (Associate Research Fellow)

15:20 - 16:55,   Tue,Thu

1110

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Graduate

English

Yes

Dr. Bart Vlaar has joined BIMSA in September 2022 as an Associate Research Fellow. His research interests are in algebra and representation theory and applications in mathematical physics. He obtained a PhD in Mathematics from the University of Glasgow. Previously, he has held postdoctoral positions in Amsterdam, Nottingham, York and Heriot-Watt University. Before coming to BIMSA he visited the Max Planck Institute of Mathematics in Bonn.Dr. Bart Vlaar has joined BIMSA in September 2022 as an Associate Research Fellow. His research interests are in algebra and representation theory and applications in mathematical physics. He obtained a PhD in Mathematics from the University of Glasgow. Previously, he has held postdoctoral positions in Amsterdam, Nottingham, York and Heriot-Watt University. Before coming to BIMSA he visited the Max Planck Institute of Mathematics in Bonn.

Zheyan Wan   (Assistant Research Fellow)

10:40 - 12:15,   Mon,Wed

1129B

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Graduate

Chinese

Yes

basic algebraic topology

The first half covers some classical topics in bordism, including spectra and Pontryagin-Thom isomorphism. The second half covers the computation of bordism groups using the Adams spectral sequence.

本科和博士毕业于中国科学技术大学，之前是清华大学丘成桐数学科学中心博士后，现在是北京雁栖湖应用数学研究院助理研究员，研究兴趣是用拓扑方法（cobordism）研究理论物理（anomaly）。

Yilong Wang   (Assistant Research Fellow)

08:50 - 12:15,   Tue

1120

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Graduate

Chinese

No

Graduate level algebra.

In this course, we give a brief introduction to Hopf algebras and their representation categories. We will then generalize such categories and study the abstract theory of tensor categories.

Yilong Wang graduated from The Ohio State University in 2018. After working in Louisiana State University as a postdoc researcher, he joined BIMSA as an assistant research fellow in 2021. His research interests include modular tensor categories and topological quantum field theories.

Yu Wang   (Assistant Research Fellow)

08:50 - 10:35,   Tue,Thu

Sanya

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Graduate

Chinese

No

Advanced algebra, complex analysis, functional analysis, probability theory, quantum mechanics

In this semester, we will introduce how to represent and transmit information by quantum states. We will also introduce how to characterize the process with quantum channel in open quantum system. Several special quantum noise channel will be discussed and the some error correction methods will be given. Then we will discuss the measure of the information similarity of two quantum states. We will also introduce the differences of quantum and classical entropy, and related study. Finally, we will introduce some research directions in quantum information.

Yu Wang received his PhD degree in computer software and theory from the Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences in 2019. After graduation, he worked at Pengcheng Laboratory in Shenzhen. In December 2020, he joined the Yanqi Lake Beijing Institute of Mathematical Science and Applications. The main research area is about quantum information and quantum computation. Specifically, the current research is focuses on quantum state tomography, in order to optimize the measurement and computation resouce to read out the unknown quantum states. Besides, it is also studied to design new quantum communication protocols by different quantum walk models.

Jie Wu   (Research Fellow)

13:30 - 16:55,   Thu

1120

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Graduate

Chinese

Yes

Algebraic Topology

Topological data analysis is a new-born research area that explores topological approaches in data science, where persistent homology has been proved as an effective mathematical tool in data analytics with various successful applications. This course will discuss the mathematical foundations of (higher) topological structures on graphs, aiming to explore new topological approaches beyond the classical persistent homology.

Jie Wu received a Ph.D. degree in Mathematics from the University of Rochester and worked as a postdoc at Mathematical Sciences Research Institute (MSRI), University of California, Berkeley. He was a former tenured professor at the Department of Mathematics, National University of Singapore. In December 2021, he joined the Yanqi Lake Beijing Institute of Mathematical Sciences and Applications (BIMSA). His research interests are algebraic topology and applied topology. The main achievements  in  algebraic topology are to establish the fundamental relations between homotopy groups and the theory of braids, and the fundamental relations between loop spaces and modular representation theory of symmetric groups. In terms of applied topology, he has obtained various important results on topological approaches to data science. He has published more than 90 academic papers in top mathematics journals such as “the Journal of American Mathematical Society”, “Advances in Mathematics”, etc. In 2007, he won“the Singapore National Science Award”. In 2014, his project was funded by the “Overseas Joint Fund of National Natural Science Foundation” (Jieqing B).

Jinsong Wu   (Research Fellow)

13:30 - 16:55,   Thu

JCY-1

Graduate

Chinese

No

Functional Analysis

We will continue talking about quantum Fourier analysis on many finite dimensional quantum symmetries such as fusion rings, fusion categories, subfactors, planar algebras and their connections. Many applications are also involved.

Jinsong Wu, a research fellow at the Yanqi Lake Beijing Institute of Mathematical Sciences and Applications. He obtained Ph. D. from Academy of Mathematics and Systems Sciences, CAS. He is interested in Functional Analysis, Operator Algebra and their applications in Quantum Information. He together with his collaborators initiate Quantum Fourier analysis for quantum symmetries. The subject provides mathematical tool for quantum information. He was PI for grants from NSFC and his work was published in top journals such as PNAS, Adv Math, Comm Math Phys, J Func Anal, Sci China Math.

Haihua Xie   (Assistant Research Fellow)

17:05 - 18:40,   Wed,Fri

1110

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Graduate

Chinese

Yes

Computer Science, Machine Learning, Python

Natural Language Processing (NLP) is an important research area in Artificial Intelligence. NLP mainly studys how to use computer technology to process linguistic texts. The specific research problems in NLP includes recognition, classification, extraction, transformation and generation of lexical, syntactic, semantic and pragmatic information. This course will introduce the basic concepts and methods in NLP, as well as some classical algorithms and models.

Dr. Haihua Xie receives a Ph.D. in Computer Science at Iowa State University in 2015. Before joining BIMSA in Oct. 2021, Dr. Xie worked in the State Key Lab of Digital Publishing Technology for many years. His research interests include Natural Language Processing and Knowledge Service. He published more than 20 papers and obtained 5 invention patents. In 2018, Dr. Xie was selected in the 13th batch of overseas high-level talents in Beijing and was hornored as a "Beijing Distinguished Expert".

(female) Fan Yang   (Research Fellow)

09:50 - 11:25,   Mon,Tue

JCY-1

Level

Graduate

Chinese

No

(male) Fan Yang   (Associate Research Fellow)

13:30 - 15:05,   Wed,Fri

JCY-3

Tencent: 615 0642 7295   PW:

Graduate

Chinese

Yes

Fan Yang is an Associate Professor of YMSC at Tsinghua University and an Associate Research Fellow at BIMSA. Prior to joining YMSC and BIMSA, he was a postdoctoral researcher with the Department of Statistics and Data Science at the University of Pennsylvania from 2019 to 2022. He received the Ph.D. degree in mathematics from the University of California, Los Angeles in 2019, the Ph.D. degree in physics from the Chinese University of Hong Kong in 2014, and the Bachelor degree from Tsinghua University in 2009. His research interests include probability and statistics, with a focus on random matrix theory and its applications to mathematical physics, high-dimensional statistics, and machine learning. He has published multiple papers in leading journals in mathematics and statistics, including Communications in Mathematical Physics, Probability Theory and Related Fields, Annals of Statistics, and IEEE Transactions on Information Theory.

Nanjun Yang   (Assistant Research Fellow)

09:50 - 12:15,   Thu

1120

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Graduate

Chinese

No

Algebraic topology and algebraic geometry

Steenrod operations are natural transformations of cohomology groups of spaces being compatible with suspensions, which play an important role especially in homotopy theory, for example, the Hopf invariant one problem and Adams spectral sequence. In this course, we introduce the Steenrod operations for both singular cohomologies and motivic cohomologies, focusing on constructions and basic properties. In particular, we prove the Adem relations and give the Hopf algebra (algebroid) structure of Steenrod algebra and its dual.

Nanjun Yang got my doctor and master degree in University of Grenoble-Alpes, advised by Jean Fasel, and bachelor degree in Beihang University. Currently he is a assistant researcher in BIMSA. His research interests are motivic cohomology and Chow-Witt ring. He proposed the theory of split Milnor-Witt motives, which applies to the computation of the Chow-Witt ring of fiber bundles. The corresponding results have been published independently on journals such as Camb. J. Math and Doc. Math.

Xiaoming Zhang   (Research Fellow)

09:50 - 12:15,   Thu

1118

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Undergraduate

Chinese

No

Basic knowledge on numerical methods for partial differential equations and machine learning methods

This course reviews the publications of the recent years on using machine learning methods to solve partial differential equations, such as Physics Informed Neural Network (PINN).  The course will cover the materials on forward method, inverse method, reduced order modeling, and the assimilation of observational data to the scientific principles.

Dr. Zhang Xiaoming, a native of Zhejiang province, is a national specially-appointed expert. He received his bachelor's, master's, and doctor's degrees from Zhejiang University, Peking University, and Massachusetts Institute of technology. At present, he is an industrial and application researcher of Beijing Institute of Mathematical Sciences and Applications and the head of the artificial intelligence and big data team. Before returning to China, Dr. Zhang served as a technology executive of several well-known American enterprises. After returning to China, he served as director of the Textile Industry Big Data Center of Zhejiang China Light Textile City Group Co., Ltd., researcher of Data Science Research Institute of Tsinghua University, visiting professor of East China Normal University, and part-time professor of Zhejiang University of Technology. As a Principal Investigator, he has won and presided over 20 research projects funded and awarded by the governments and major corporations. He has published more than 30 papers in international professional journals, of which two have been published in Nature subsidiary journals. He led his group won the first place in the Micro Array Quality Control (MAQC) competition hosted by the US Food and Drug Administration, twice the first places in the Alibaba Qianlima Industrial Big Data Competition, the second place and the third place in the First and Second China Industrial Internet Competitions respectively. Dr. Zhang led the development of the digital and intelligent service platform "Printing and Dyeing Brain", and is known as the "Godfather of intelligent printing and dyeing" in the industry. Dr. Zhang has been engaged in the research, development and application of artificial intelligence methods to the prediction and resource optimization and allocation for a long time. At present, his work focuses on the research and development of digital twins and process twins in the industrial field, which are used to optimize the process flow, help enterprises improve the yield and production efficiency, reduce energy consumption and pollution, improve product grade and increase their core competitiveness.

Hui Zhao   (Assistant Research Fellow)

13:30 - 16:55,   Wed

1120

Graduate & Undergraduate

Chinese

No

Differentials Geometry, Linear Algebra, Topology

This course introduces the algorithms and philosophy of Computational Discrete Global Geometric Structures. There are six components in this course: 1) the mathematical theory of global geometric structures on smooth manifolds; 2) their discrete counterparts; 3) the algorithms to compute them; 4) the programming and coding techniques for the implementaitons of the algorithms; 5) the visualization techniques to demonstrate these geometry structures; 6) besides computer graphcis, the possible discussion of their potential applications in other inter-discipline fields, and so on. Computational discrete global geometric structures(CDGGS) is pioneered by Prof. Shing-Tung Yau and Prof Xianfeng Gu with the classic Gu-Yau algorithm to compute discrete harmonic one-form around 2000. After twenty year's research by mathematicians and computer scientists, currently, CDGGS can handle many other discrete global geometric structures, such as holomorphic one-form, foliation, holomorphic quadratic differentials, conformal structures, and so on, and play an important role in the application of geometry modeling and meshing.

Hui Zhao is an assistant research fellow in Yanxi Lake Beijing institute of mathematical sciences and applications, he had been a visiting scholar in Harvard university and YMSC, Tsinghua university. His research focuses on the theory and algorithms of computational conformal geometry, computational discrete global geometric structures, computer graphics, geometry modeling and their applications in medical images, materials, CAD, virtual reality, Metaverse, and so on. He published fives computer graphics books and dozens of papers in related journals.