**TRIPODS-STEMORALL2023**

It is never too early to start planning the next summer research
program, and this one will be of a slightly different flavor than
the previous three. We are going to take the aspects of the material
from several advanced undergraduate courses such as Linear Algebra,
Multi-Variable Calculus, Analysis, Algebra, Combinatorics and Number
Theory and focus on the aspects of the material covered in those
classes that are susceptible to an effective analysis using modern
big data techniques. As a result, we are going to both deepen our
understanding of the subject matter in those courses and develop the
skills that are valued in Big Data. In the coming weeks and months,
we are going to start posting sketches of the type of problems we
are going to consider in this program and links to the study
materials, both theoretical and computational. Stay tuned!

It is my hope that at least a few undergraduate students would be
interested in getting started on the projects outlined below during
the 2022-2023 academic year, long before Tripods/StemForAll2023
actually begins.

**Preliminary list of topics:**

**Title:** Reinforcement learning and tensors of 1's and 0's

**Description:** A classical result due to Erdos says that if an
n by n matrix of 1's and 0's has the property that no rectangles
with vertices that are all 1's are allowed, then the total number of
1's in this matric cannot exceed n raised to the power of 3/2 and
this exponent is known to be best possible. Similar results can be
obtained for n by n by ... by n tensors, but here there is a
considerable gap between counter-examples and the known bounds. We
are going to use computational methods, including reinforcement
learning to search for examples.