日程安排8.21-8.25 博远楼201
短课程：
主讲人：荆一凡博士（俄亥俄州立大学）
课程：Arithmetic Combinatorics
简介：The aim of this course is to explore fundamental results in additive and
multiplicative combinatorics. The course is divided into two parts. In the first part, we
will delve into additive combinatorics, focusing on notable theorems such as Roth's
theorem on three-term progressions, combinatorial inequalities involving sumset
estimates, sum-product theorems, and the Freiman theorem. The second part of the
course will delve into multiplicative combinatorics, where we will investigate
combinatorial problems within the realm of groups. Topics covered will include basic
estimates for product sets, Kneser and Kemperman type inequalities, the concept of
good models, expanders, quasirandomness, and the product theorem in groups.
Throughout the course, we will draw upon tools from various mathematical
disciplines. However, prerequisites will be minimal, as we will develop all necessary
concepts from scratch.
主讲人：刘西之博士（华威大学）
课程：Mini-course on Extremal Hypergraph Theory
简介：Extremal Hypergraph Theory is a fascinating branch of combinatorics that
focuses on understanding the structural properties and behavior of hypergraphs, which
are generalizations of graphs that allow for the representation of complex relationships
involving more than two vertices. This mini-course delves into the fundamental
principles, classical results, and standard techniques in Extremal Hypergraph Theory,
providing students with a comprehensive understanding of this vibrant field.
目标：This course aims to equip students with the theoretical foundations, analytical
tools, and problem-solving skills necessary to explore and contribute to the exciting
world of Extremal Hypergraph Theory. By the end of the course, students should be
able to: Grasp the key concepts and terminologies associated with hypergraphs and their
extremal properties. Understand and prove classical theorems in Extremal Hypergraph
Theory, such as the K ̋ovari–S ́os–Tur ́an theorem, the Zarankiewicz problem, the
Tur ́an problem, and more. Gain insights into techniques like the Stability Method of
Simonovits, Hypergraph Lagrangian, and the use of shifting, symmetrization, and other
standard tools. Analyze and solve problems related to hypergraph extremal properties.
大纲：
1. Introduction to Hypergraphs
➢ Definitions and notations
➢ Hypergraph families (uniform, r-partite, matching, star, etc.)
➢ Tur ́an type problem
➢ Inducibility problem
2. Classical Extremal Results
➢ K ̋ovari–S ́os–Tur ́an theorem
➢ Zarankiewicz problem
➢ Erd ̋os–Stone–Simonovits theorem and Tur ́an problem for hypergraphs
➢ Erd ̋os–Ko-Rado theorem
➢ Kruskal–Katona Theorem
3. Standard Techniques
➢ Stability Method of Simonovits
➢ Shifting technique
➢ Symmetrization arguments
➢ Hypergraph Lagrangian
主讲人：周正春教授（西南交通大学）
课程：面向现代通信和雷达的新型序列编码
简介：序列是有限域/复数域上的有限维向量，在通信、雷达和信息安全等领域
具有重要应用，与Hadamard 矩阵、差集（族）、Bent 函数等数学对象之间具有深
刻的联系。
大纲：
1. 序列的基本概念
2. 现代通信和雷达中序列性能的度量指标
3. 序列性能指标的理论界
4. 几类经典序列
5. 面向新应用场景的新型序列
6. 一些开放问题
邀请报告：
报告人：姜子麟 Assistant Professor（亚利桑那州立大学）
报告地点：腾讯会议：548-364-395 会议密码：821103
报告时间：北京时间2023/08/21 10:30-11:30
报告题目：Forbidden subgraphs and spherical two-distance sets
报告摘要：A set of unit vectors in a Euclidean space is called a spherical two-distance
set if the pairwise inner products of these vectors assume only two values α and β. It is
known that the maximum size of a spherical two-distance grows quadratically as the
dimension of the Euclidean space grows. However when the values α and β are held
fixed, a very intricate behavior of the maximum size emerges. Building on our recent
resolution in the equiangular case, that is β = −α, we make a plausible conjecture which
connects this behavior with spectral theory of signed graphs in the regime β < 0 ≤ α,
and we confirm this conjecture when α + 2β < 0 or (1 − α)/(β − α) < 2.0198. Joint work
with Alexandr Polyanskii, Jonathan Tidor, Yuan Yao, Shengtong Zhang and Yufei Zhao.
报告人：刘鸿首席科学家（Institute for Basic Science）
报告地点：腾讯会议：791-682-090 会议密码：821143
报告时间：北京时间2023/08/21 14:30-15:30
报告题目：Tur\'{a}n problem for graphs from geometric shapes
报告摘要： While Tur\'{a}n type problem is the most studied topic in extremal
combinatorics, some of the most basic bipartite degenerate Tur\'{a}n problems remain
elusive. In this talk, I will discuss some recent advancements on this topic and new
results on bipartite graphs arising from geometric shapes and periodic tilings
commonly found in nature, including even prisms, planar hexagonal tiling and
quadrangulations of plane, cylinder and torus. This is joint work with Jun Gao, Oliver
Janzer, and Zixiang Xu.
报告人：李抒行 Assistant Professor（特拉华大学）
报告地点：腾讯会议：604-870-433 会议密码：824083
报告时间：北京时间2023/08/22 08:30-09:30
报告题目：Group rings and character sums --- a tutorial
报告摘要：Group rings serve as potent instruments for representing and analyzing
diverse combinatorial objects. Combining group rings and character sums, fruitful
results have been obtained in the captivating exploration of a wide of difference-sets-
related objects. In this talk, we aim to present an elementary and illustrative tutorial
outlining the fundamentals of group rings and character sums. This talk is based on a
joint expository paper with Jonathan Jedwab.
报告人：郭赫博士（以色列理工大学）
报告地点：腾讯会议：557-399-773 会议密码：822143
报告时间：北京时间2023/08/22 14:30-15:30
报告题目：Prague dimension of random graphs
报告摘要：The Prague dimension of graphs was introduced by Nesetril, Pultr and Rodl
in the 1970s. Proving a conjecture of Furedi and Kantor, we show that the Prague
dimension of the binomial random graph is typically of order n/log n for constant edge-
probabilities. The main new proof ingredient is a Pippenger-Spencer type edge-coloring
result for random hypergraphs with large uniformities, i.e., edges of size O(log n). Joint
work with Lutz Warnke and Kalen Patton.
报告人：顾玉杰 Assistant Professor（九州大学）
报告地点：腾讯会议：949-694-438 会议密码：823143
报告时间：北京时间2023/08/23 10:30-11:30
报告题目：Secure codes for multimedia fingerprinting
报告摘要： Multimedia fingerprinting is a forensic technology used to protect
multimedia content from unauthorized redistribution. In this talk, we will introduce the
recent progress on combinatorial secure codes that defend against collusion attacks in
multimedia fingerprinting.
学员报告：
报告人：叶智恺博士（英属哥伦比亚大学）
报告地点：博远楼201
报告时间：北京时间2023/08/23 8:30-9:00
报告题目：Sperner systems with restricted differences modulo $q$
报告摘要：Let F be a family of subsets of [n] and L be a subset of [n]. We say F is an
L-differencing Sperner system if |A\B|\in L for any distinct A,B\in F. Let p be a prime
and q be a power of p. Frankl first studied p-modular L-differencing Sperner systems
and showed an upper bound of the form \sum_{i=0}^{|L|}\binom{n}{i}. In this talk, I
will explain how ideas from elementary p-adic analysis and polynomial method lead to
new upper bounds on q-modular L-differencing Sperner systems. In particular, we
provide a significant improvement on a result of Felszeghy, Heged\H{u}s, and
R\'{o}nyai. This is a joint work with Zixiang Xu.
报告人：李国栋博士（山东大学）
报告地点：博远楼201
报告时间：北京时间2023/08/23 9:10-9:40
报告题目：Adjacent-Bits-Swapped Polar codes: A new code construction to speed up
polarization
报告摘要：The construction of polar codes with code length n=2^m involves m layers
of polar transforms. In this talk, we observe that after each layer of polar transforms,
one can swap certain pairs of adjacent bits to accelerate the polarization process. More
precisely, if the previous bit is more reliable than its next bit under the successive
decoder, then switching the decoding order of these two adjacent bits will make the
reliable bit even more reliable and the noisy bit even noisier. Based on this observation,
we propose a new family of codes called the Adjacent-Bits-Swapped (ABS) polar codes.
We add a permutation layer after each polar transform layer in the construction of the
ABS polar codes. In order to choose which pairs of adjacent bits to swap in the
permutation layers, we rely on a new polar transform that combines two independent
channels with 4-ary inputs. This new polar transform allows us to track the evolution
of every pair of adjacent bits through different layers of polar transforms, and it also
plays an essential role in the Successive Cancellation List (SCL) decoder for the ABS
polar codes. Extensive simulation results show that ABS polar codes consistently
outperform standard polar codes by 0.15dB-0.3dB when we use CRC-aided SCL
decoder with list size 32 for both codes. The implementations of all the algorithms in
this paper are available at //github.com/PlumJelly/ABS-Polar
报告人：黄和祥博士（山东大学）
报告地点：博远楼201
报告时间：北京时间2023/08/23 9:50-10:20
报告题目：Construction of storage codes of rate approaching one on triangle-free
graphs
报告摘要：Consider an assignment of bits to the vertices of a connected graph Γ(V, E)
with the property that the value of each vertex is a function of the values of its neighbors.
A collection of such assignments is called a storage code of length |V| on Γ. In this talk
we construct an infinite family of linear storage codes on triangle-free graphs with rates
arbitrarily close to one.