Automatic differentiation

Posted on 2018-06-03

Posted on 2018-04-29

It has been 9 months since I last wrote about open (maths) research. Since then two things happened which prompted me to write an update.

The Mathematical Bazaar

Posted on 2017-08-07

In this essay I describe some problems in academia of mathematics and propose an open source model, which I call open research in mathematics.

Open mathematical research and launching toywiki

Posted on 2017-04-25

As an experimental project, I am launching toywiki.

A $$q$$-Robinson-Schensted-Knuth algorithm and a $$q$$-polymer
(Latest update: 2017-01-12) In Matveev-Petrov 2016 a $$q$$-deformed Robinson-Schensted-Knuth algorithm ($$q$$RSK) was introduced. In this article we give reformulations of this algorithm in terms of Noumi-Yamada description, growth diagrams and local moves. We show that the algorithm is symmetric, namely the output tableaux pair are swapped in a sense of distribution when the input matrix is transposed. We also formulate a $$q$$-polymer model based on the $$q$$RSK and prove the corresponding Burke property, which we use to show a strong law of large numbers for the partition function given stationary boundary conditions and $$q$$-geometric weights. We use the $$q$$-local moves to define a generalisation of the $$q$$RSK taking a Young diagram-shape of array as the input. We write down the joint distribution of partition functions in the space-like direction of the $$q$$-polymer in $$q$$-geometric environment, formulate a $$q$$-version of the multilayer polynuclear growth model ($$q$$PNG) and write down the joint distribution of the $$q$$-polymer partition functions at a fixed time.