Extremal and Additive Combinatorics, Spring 24
Instructor
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Tuan Tran
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Office: 1409, Management Building, East Campus
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E-mail: trantuan [at] ustc [dot] edu [dot] cn
Time
Tuesday 15:55-18:20 and Thursday 14:00-15:35, in 5502 (the 5th teaching building).
Lecture notes
Reading papers
- Samuel Kutin, Constructing Large Set Systems with Given Intersection Sizes Modulo Composite Numbers. pdf
- Boris Bukh and Ting-Wei Chao, Sharp density bounds on the finite field Kakeya problem. pdf
- Christian Elsholtz, Laura Proske, and Lisa Sauermann, New lower bounds for three-term progression free sets in $F_p^n$. pdf
- Matija Bucic, Shoham Letzter, Benny Sudakov, Tuan Tran. Minimum saturated families of sets. pdf
- Asaf Shapira and Mykhaylo Tyomkyn, Weakly saturated hypergraphs and a conjecture of Tuza. pdf
- Benjamin Gunby, Xiaoyu He, Bhargav Narayanan, and Sam Spiro, Antichain Codes. pdf
- Domagoj Bradac, Matija Bucic, and Benny Sudakov, Turan numbers of sunflowers. pdf
- Keith Frankston, Jeff Kahn, and Bhargav Narayanan, On regular 3-wise intersecting families. pdf
- Marcelo Campos, A new proof of the efficient container lemma. Chapter 4 in pdf
- Omar Alrabiah and Venkatesan Guruswami, Near-Tight Bounds for 3-Query Locally Correctable Binary Linear Codes via Rainbow Cycles. pdf
- Matija Bucic, Stefan Glock, and Benny Sudakov, The intersection spectrum of 3-chromatic intersecting hypergraphs. pdf
- Peter Keevash, Jason Long, Bhargav Narayanan, and Alex Scott, A universal exponent for homeomorphs. pdf
- David Ellis, Maria-Romina Ivan, and Imre Leader, Turan densities for daisies and hypercubes. pdf
- Benny Sudakov and Istvan Tomon, The Turan number of bipartite graphs with no $K_{t,t}$. pdf
- Ernie Croot, Izabella Laba, and Olof Sisask, Arithmetic progressions in sumsets and $L_p$-almost-periodicity. pdf
- Jacques Verstraëte, On The Number Of Sets Of Cycle Lengths. pdf
Seminar
Date |
Title |
Speakers |
May 22 (Wed), 6-7 |
Sharp density bounds on the finite field Kakeya problem |
Wang Xuanzhe, Luo Yufan |
May 22 (Wed), 8-9 |
New lower bounds for three-term progression free sets in $\mathbb{F}_p^n$ |
Liu Jingyuan, Lin Zhihao, Pavel Maria Descamps |
May 30 (Thu), 2-3 |
Minimum saturated families of sets |
Zhang Ting, Zhao Mintong, Yue Yunfan |
May 30 (Thu), 4-5 |
Antichain Codes |
Zhou Zihan, Wang Malong |
June 7 (Fri), 6-7 |
Turan densities for daisies and hypercubes |
Yang Yuang, Yang Dilong, Zhu Tianming |
June 7 (Fri), 8-9 |
The Turan number of bipartite graphs with no $K_{t,t}$ |
Luo Tao, Zhu Yifang |
June 13 (Thu), 6-7 |
Arithmetic progressions in sumsets and $L_p$-almost-periodicity |
Xie Shengjie, Geng Ruohan |
Topics of the course
- Algebra methods
- Bollobas set-pairs inequality
- Sunflowers and Kahn-Kalai conjecture
- Dependent random choice
- Sum-product problem
Prerequisites
Linear Algebra, Graph Theory.
Requirements
Here you can read the requirements and formalities
of the course.
Literature
Some of the lectures will mostly follow the two fantastic books listed below. Other lectures will be based on original papers.
- Laszlo Babai and Peter Frankl, Linear Algebra Methods in Combinatorics
- Yufei Zhao, Graph Theory and Additive Combinatorics: Exploring Structure and Randomness