Author Archives: Anurag Bishnoi

About Anurag Bishnoi

A mathematician working at TU Delft. I am broadly interested in combinatorics and finite geometry.

A short video on Ramsey numbers

I was recently involved in making a 1 minute maths video for a contest organised by Veritasium. Here is the main requirement for the video We are looking for videos that clearly and creatively explain complex or counterintuitive concepts in … Continue reading

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A postdoc position at TU Delft

I would like to advertise a 3 year postdoc position at my research group. Please apply if you are interested in the kind of research that Dion and I do (https://anuragbishnoi.wordpress.com/publications/). The deadline is April 15 2021. Here are some … Continue reading

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A coding theoretic application of the Alon-Füredi theorem

The Alon-Füredi theorem is something that I have written a lot about in this blog. I spent a considerable amount of time on this theorem during my PhD. In fact, it’s generalisation that I obtained and it’s applications in finite … Continue reading

Posted in Coding Theory, Combinatorics, Extremal Combinatorics, Finite Geometry, Polynomial Method | Tagged , , , , , | 2 Comments

Bilinear forms and diagonal Ramsey numbers

The recent breakthrough of Conlon and Ferber has shown us that algebraic methods can be used in combination with probabilistic methods to improve bounds on multicolour diagonal Ramsey numbers. This was already shown for the off-diagonal Ramsey numbers by Mubayi … Continue reading

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Covering the binary hypercube

A finite grid is a set , where is a field and each is a finite subset of . The minimum number of hyperplanes required to cover can easily be shown to be , with the hyperplanes defined by , … Continue reading

Posted in Combinatorics, Extremal Combinatorics, Finite Geometry, Polynomial Method | Tagged , , , , , , , , , , | 1 Comment

Improved lower bounds for multicolour diagonal Ramsey numbers

Big news in combinatorics today: David Conlon and Asaf Ferber have posted a 4-page preprint on arXiv that gives exponential improvements in the lower bounds on multicolour diagonal Ramsey numbers, when the number of colours is at least (also see … Continue reading

Posted in Combinatorics, Extremal Combinatorics, Finite Geometry, Incidence Geometry, Ramsey Theory | Tagged , , , , , , | 20 Comments

The dual version of Ryser’s conjecture

I talked about our new results related to Ryser’s conjecture in a previous post (also see an even earlier post). The conjecture, and its variants, have some interesting equivalent formulations in terms of edge colourings of graphs. While I was … Continue reading

Posted in Combinatorics, Extremal Combinatorics, Uncategorized | Tagged , , , , , , , , , , | Leave a comment

Heisenberg groups, irreducible cubics and minimal Ramsey

As I mentioned in a previous post, we recently improved the upper bound on a Ramsey parameter, in collaboration with John Bamberg and Thomas Lesgourgues. My favourite thing about this work is how it ends up using the properties of … Continue reading

Posted in Combinatorics, Extremal Combinatorics, Finite Geometry, Incidence Geometry, Ramsey Theory | Tagged , , , , , , , , | 2 Comments

Generalized polygons in extremal combinatorics

Jacques Tits invented generalized polygons to give a geometrical interpretation of the exceptional groups of Lie type. The prototype of these incidence geometries already appears in his 1956 paper, while they are axiomatically defined in his influential 1959 paper on … Continue reading

Posted in Combinatorics, Extremal Combinatorics, Finite Geometry, Incidence Geometry, Ramsey Theory, Uncategorized | Tagged , , , , , , , , , , | Leave a comment

Minimal Ramsey problems

Thanks to Anita Liebenau, I have recently been introduced to some very interesting questions in Ramsey theory and I have been working on them for the past few months in collaboration with various people. In my recent joint work with … Continue reading

Posted in Combinatorics, Extremal Combinatorics, Finite Geometry, Incidence Geometry, Ramsey Theory | Tagged , , , , , , | 2 Comments