Extremal and Additive Combinatorics, Spring 24


  • Tuan Tran

  • Office: 1409, Management Building, East Campus

  • E-mail: trantuan [at] ustc [dot] edu [dot] cn


Tuesday 15:55-18:20 and Thursday 14:00-15:35, in 5502 (the 5th teaching building).

Lecture notes

Reading papers

  1. Samuel Kutin, Constructing Large Set Systems with Given Intersection Sizes Modulo Composite Numbers. pdf
  2. Boris Bukh and Ting-Wei Chao, Sharp density bounds on the finite field Kakeya problem. pdf
  3. Christian Elsholtz, Laura Proske, and Lisa Sauermann, New lower bounds for three-term progression free sets in $F_p^n$. pdf
  4. Matija Bucic, Shoham Letzter, Benny Sudakov, Tuan Tran. Minimum saturated families of sets. pdf
  5. Asaf Shapira and Mykhaylo Tyomkyn, Weakly saturated hypergraphs and a conjecture of Tuza. pdf
  6. Benjamin Gunby, Xiaoyu He, Bhargav Narayanan, and Sam Spiro, Antichain Codes. pdf
  7. Domagoj Bradac, Matija Bucic, and Benny Sudakov, Turan numbers of sunflowers. pdf
  8. Keith Frankston, Jeff Kahn, and Bhargav Narayanan, On regular 3-wise intersecting families. pdf
  9. Marcelo Campos, A new proof of the efficient container lemma. Chapter 4 in pdf
  10. Omar Alrabiah and Venkatesan Guruswami, Near-Tight Bounds for 3-Query Locally Correctable Binary Linear Codes via Rainbow Cycles. pdf
  11. Matija Bucic, Stefan Glock, and Benny Sudakov, The intersection spectrum of 3-chromatic intersecting hypergraphs. pdf
  12. Peter Keevash, Jason Long, Bhargav Narayanan, and Alex Scott, A universal exponent for homeomorphs. pdf
  13. David Ellis, Maria-Romina Ivan, and Imre Leader, Turan densities for daisies and hypercubes. pdf
  14. Benny Sudakov and Istvan Tomon, The Turan number of bipartite graphs with no $K_{t,t}$. pdf
  15. Ernie Croot, Izabella Laba, and Olof Sisask, Arithmetic progressions in sumsets and $L_p$-almost-periodicity. pdf
  16. Jacques Verstraëte, On The Number Of Sets Of Cycle Lengths. pdf


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


Linear Algebra, Graph Theory.


Here you can read the requirements and formalities of the course.


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