Abstract: Let X and Y be two finite multisets of integers. When do they have equal sums of squares? If we know one example, does this help us find others? Three easy examples are X = {3, 4}, Y = {5} and X = {1, 2, 2}, Y = {3} and X = {5, 5}, Y = {1, 7}. We shall discuss a matrix which transforms any such X and Y into another, so yields infinitely many solutions. Indeed if the difference between the sums of squares of X and Y is r, not necessarily zero, the matrix transformation gives a new pair X' and Y' with sums of squares that again differ by r.
The talk will present these matters in a geometric context and shed some light on the problem of finding multisets X and Y with equal sums of squares.