
Recent Posts
Archives
 August 2021 (1)
 March 2021 (2)
 November 2020 (1)
 October 2020 (1)
 September 2020 (3)
 August 2020 (2)
 January 2020 (2)
 December 2019 (1)
 September 2019 (1)
 July 2019 (1)
 May 2019 (1)
 September 2018 (1)
 April 2018 (1)
 March 2018 (1)
 November 2017 (2)
 August 2017 (2)
 July 2017 (1)
 April 2017 (2)
 September 2016 (1)
 July 2016 (1)
 May 2016 (2)
 December 2015 (1)
 October 2015 (1)
 August 2015 (2)
 June 2015 (1)
 May 2015 (1)
 April 2015 (1)
 March 2015 (4)
 January 2015 (1)
 September 2014 (3)
 August 2014 (1)
 July 2012 (3)
Categories
 Coding Theory (2)
 Combinatorics (38)
 Extremal Combinatorics (18)
 Ramsey Theory (7)
 Spectral Graph Theory (6)
 Conferences (1)
 Finite Geometry (28)
 Incidence Geometry (13)
 Job openings (1)
 Number Theory (1)
 Polynomial Method (15)
 Real Analysis (1)
 References (1)
 Research Diary (1)
 Uncategorized (2)
Blogs I Follow
 I Can't Believe It's Not Random!
 Random Permutations
 What's new
 Manu S Pillai
 cgroenland.wordpress.com/
 Radimentary
 Cosmin Pohoata
 Sleepless in Seattle
 Bloag
 Jagriti is professoring
 Math3ma
 Aparajita's blog
 The Intrepid Mathematician
 Ratio Bound – A Combinatorics Blog
 all the women
 ellipticnews
 Becoming My Better Self
 Points And Lines
 Some Plane Truths
 Gentzen translated
 E. Kowalski's blog
 Quomodocumque
 Short, Fat Matrices
 Combinatorics and more
 Yufei Zhao
 Abhishek Khetan
 urduwallahs
 Gaurish4Math
 Jerusalem Combinatorics Seminar
 Personal Blog
Category Archives: Spectral Graph Theory
Kopparty’s graph
Alon’s construction of optimal pseudorandom graphs from 1994 is useful for obtaining several interesting combinatorial results in various areas of mathematics, some of which are highlighted in this survey of Noga from last year (also see my previous post). In … Continue reading
Spectral proofs of theorems on the boolean hypercube
In a recent breakthrough Hao Huang proved the sensitivity conjecture, that had remained open for past 30 years despite some serious effort from various computer scientists and mathematicians. The proof can be described in a single tweet (if you have … Continue reading
Pseudorandom cliquefree graphs
Pseudorandom graphs are graphs that in some way behaves like a random graph with the same edge density. One way in which this happens is as follows. In the random graph , with , a direct application of Chernoff bound … Continue reading
Posted in Combinatorics, Extremal Combinatorics, Spectral Graph Theory
Tagged alon, pseudorandom, pseudorandom graphs
5 Comments
Incidence Bounds and Interlacing Eigenvalues
The Szemerédi–Trotter theorem is one of the central results in discrete geometry which gives us a (tight) bound on the number of incidences, i.e., the number of pointline pairs with the point lying on the line, between finite sets of points and lines … Continue reading