Draft:Gerald Reisner

Gerald Reisner is an American mathematician who receievd his PhD from Uiversity of Minnesota under the direction of Prof. Melvin Hochster in 1974. (https://mathgenealogy.org/id.php?id=7693). He is known for his role in what are now known as Stanley-Reisner rings (https://en.wikipedia.org/w/index.php?title=Special:Search&search=Stanley%E2%80%93Reisner+ring&wprov=acrw1_0).

In his doctoral dissertation, Reisner did fundamental work on the properties of a ring, an algebraic object, associated over a given choice of base field with a finite simplicial complex, which gives a combinatorial description, not unique, of a geometric object. Reisner characterized when such rings, now called Stanley-Reisner rings, are Cohen-Macaulay, enabling Richard Stanley to prove the Upper Bound Conjecture in combinatorics for triangulations.