Here is a pared down example of some 3D data that I want to make dynamic and add locators to each set of points.  Is that possible?

dimension1 = {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
              {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1},
              {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2},
              {3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3},
              {4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4},
              {5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5},
              {6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6},
              {7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7},
              {8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8},
              {9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9},
              {10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10}};

dimension2 = {{2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2},
              {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2},
              {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2},
              {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2},
              {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2},
              {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2},
              {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2},
              {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2},
              {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2},
              {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2},
              {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2}};

dimension3 = {{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10},
              {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10},
              {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10},
              {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10},
              {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10},
              {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10},
              {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10},
              {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10},
              {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10},
              {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10},
              {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}};

firstDimension = ListPlot3D[dimension1, BoxRatios -&gt; {1, 1, 1}, 
  PlotStyle -&gt; {Cyan, Opacity[0.2]}, Background -&gt; White];

secondDimension = ListPlot3D[dimension2, BoxRatios -&gt; {1, 1, 1}, 
  PlotStyle -&gt; {Magenta, Opacity[0.2]}, Background -&gt; White];

thirdDimension = ListPlot3D[dimension3, BoxRatios -&gt; {1, 1, 1}, 
  PlotStyle -&gt; {Yellow, Opacity[0.2]}, Background -&gt; White];

Show[firstDimension, secondDimension, thirdDimension]




The locators should move the points on the grid, and affect the other surrounding points depending on a variable.


Question: How to choose between multiple math postdocs offers?
Answer: At the end of the day, the quality of your research is more important than prestige.  I would go with the university that is a better research match.

As for what makes a good postdoc supervisor.  I think this depends completely on the individual and how one conducts research.  The two extremes are: hands off -- I have plenty of ideas and give me something to work on.

The best is a combination of the two.  This shows you are able to work independently and work well with others.