Georgia Institute of Technology College of Sciences

Let us discuss how to use generative AI to help with math and coding.

My presentation features two scenarios:

Coding in LaTeX. Suppose you have a raw draft of what potentially could be a math paper. We will consider and apply simple AI tools that may help realizing the potential.

Coding in CAS. Suppose you have a raw idea for a package in a Computer Algebra System; your raw idea may be limited to a rough description of the input/output of a method you would like to implement. How far can an AI assistant take you? Can it autonomously code a working software package?   

We will start with a presentation by Elanor Moore and continue with a free discussion.

We will start with a presentation by Griffin Edwards and continue with a free discussion.

 Let A be a subset of the integer lattice of positive upper density. Roth' theorem in this setting states that there are points x,x+y,x+2y in A with the length of the gap y arbitrary large. We show that the lengths of the gaps y contain an infinite arithmetic progression, as long as one measures the length in lp for p>2 even, while this not true for the Euclidean distance.

Such results have been previously obtained in the continuous settings for measurable subsets of Euclidean spaces using methods of time-frequency analysis, as opposed our approach is based on some ideas from additive combinatorics such as uniformity norms and arithmetic regularity lemmas. If time permits, we discuss some other results that can be obtained similarly.