My Survey on Cameron-Liebler Classes & Low Degree Functions in Vector Spaces
Earlier this year there was a conference in Budapest, Hungary, named Sum(m)it280, to honor the cumulative 280th birthday of the Péter Frankl, Zoltán Füredi, Ervin Győri and János Pach. There the organizers asked participants for survey articles for a conference volume on extremal problems in combinatorics and geometry. Now I have worked a reasonably amount […]
The Twisted $D_{5,5}(q)$ Graph
One of the greatest discovery of in the theory of distance-regular graphs has been the twisted Grassmann graph by Edwin van Dam and Jack Koolen. Here I want to describe a small variation of their construction for the twisted $ {D_{5,5}(q)}$ graph. This post mostly to preserve my blackboard on the topic. (I tend to […]
Ramsey numbers, polar spaces, and oddtowns
I have uploaded a preprint which concludes a joint work with John Bamberg and Ferdinand Ihringer that started last year during their visit to TU Delft. In this work, we have done one of my favorite things in mathematics research: combining unrelated topics to create something new in each of them. Here is a quick […]
Love in Projective Planes, Chinese Valentine’s Day & Phonotactics
A few days ago China celebrated one of many Chinese Valentine’s days: the 20th of May. Why is this a special day in China? Chinese has around 30 to 36 phonemes which is plenty, but Chinese phonotactics dictate that you can only make around 1200 syllables out of them, for instance, see this video. English […]
Classifying Cameron-Liebler Sets/Boolean Degree 1 Functions
This week I put two new preprint on the arXiv. Both are on a similar theme, so I will discuss them together. One is with Morgan Rodgers on regular sets of lines in rank 3 polar spaces. The other one is solves a problem which I have been thinking about very regularly since November 2017: […]
Interlacing and the Second Largest Eigenvalue
Apparently, I described a very elegant argument to give a lower bound on the second largest eigenvalue of the adjacency matrix of a regular graph last year. This was pointed out in two recent preprints by Eero Räty, Benny Sudakov, and Istvan Tomon. This blog post is to describe the very short argument and how […]
Poll: Grants & Attributions in Mathematics
Yesterday I received the feedback by referees on one of my grant proposals. Two of the three referee reports were very positive, but, sadly, one was just positive. Hence, I did not receive the highest grade in the evaluation system of the grant agency, only the second highest (that particular grant agency has 7 grades). […]
Finite Geometry Beats the Random Process
I am very happy about today’s result by Sam Mattheus and Jacques Verstraete proving an almost tight bound on the off-diagonal Ramsey number r(4, t). This beats the bound by Bohman and Keevash using the random process. See Anurag’s post above for details. Just yesterday I gave a plenary talk at CanaDAM about off-diagonal Ramsey […]