Dr. Gablehauser is responsible for running the physics department smoothly. He introduced the child prodigy Dennis Kim to the university in "The Jerusalem Duality" (S01E12), though his time there was short lived. He also hosts the Physics Bowl in "The Bat Jar Conjecture" (S01E13). He is later asked to settle one of many arguments between Sheldon and Leslie Winkle in "The Barbarian Sublimation" (S02E03).
Dr. Gablehauser makes a point of calling Howard "Mr. Wolowitz", while referring to Sheldon, Leonard and Raj as "Dr. Cooper", "Dr. Hofstadter" and "Dr. Koothrappali", respectively. Once Raj receives accolades for the discovery of a planetary body he believes he has discovered a star in Dr. Koothrappali and reveals the business of the university is to make money in "The Griffin Equivalency" (S02E04). He has also described Sheldon as "nuts" on at least one occasion, as in "The Jerusalem Duality" (S01E12). He was also mentioned in "The Bath Item Gift Hypothesis" (S02E11).
Relationship to Sheldon Cooper
Sheldon dislikes having a boss like Gablehauser who, according to him, has done no original research in the last 25 years and has spent his career writing books which reduce scientific concepts to anecdotes, "each one dumbed down to accommodate the duration of an average bowel movement".
But Sheldon takes things too far when he introduces himself to Gablehauser as "an actual real scientist", which is followed by a series of insults. As a result, Gablehauser fires Sheldon, but re-hires him some time later, not because of Sheldon's apology (which never actually takes place), but because Gablehauser has a soft spot for Sheldon's mother, as told in "The Luminous Fish Effect" (S01E04).