The Torah introduces Korah by recounting his lineage -- "ben Yitzhar ben Kehas ben Levi". Rashi asks why the Torah did not go one step further and trace Korach's ancestry back to Ya'akov Avinu. He answers that Ya'akov davened that his name should not be joined in partnership with evil.
The Torah usually does not trace back the lineage of heroes or villains all the way to the Patriarchs. Why here does Rashi see the omission of Ya'akov's name as significant? And even if Ya'akov's name is not mentioned, don't we all know that he is the father of Levi and therefore the great-great-grandfather of Korach?
Maharal explains that the Torah here is not simply introducing Korach, but condemning him. Because Korach was a descendant of a prominent family within the prominent tribe of Levi, his guilt is that much worse. Korach had excellent role models to learn from and failed to follow their example. That failure might have been further emphasized by highlighting Korach's failure to live up to the model of Ya'akov Avinu. However, Ya'akov did not want to be associated with the condemnation of his descendants, and therefore he is not mentioned.
How does a Korach come out of such an illustrious family? The Maharal explains that every tzadik has elements of "psoles" -- there are imperfections, however slight, in the character of even the greatest people. Children absorb everything, and flaws in a parent can be magnified many times over when passed to the next generation. Korach's parents and grandparents in this way all contributed in some way to shaping his flawed character. The only exception is Ya'akov Avinu, who reached a degree of perfection that did not allow for defects to pass to his children. The lineage which shaped Korach stops at Levi, for Ya'akov had no part in the flaws which later emerged.
Lost opportunities and the failure to live up to expectations can create a devastating burden of guilt. Yet, beneath those layers of failure there always remains the pure spark of Ya'akov Avinu that does not condemn. There is always a point within each person that remains disassociated from past failure which -- if the person chooses -- can be the foundation for new growth.
The Shem m'Shmuel (1910) writes that each of our Shabbos meals and tefilos correspond to one of the Avos: Friday night=Avraham; Shabbos morning=Yitzchak; Shalosh Seudos=Ya'akov. Unlike Avraham, who was the father of Yishmael as well as Yitzchak, and Yitzchak, who was the father of Eisav as well as Ya'akov, Ya'akov Avinu had no offspring who were outside the fold of Klal Yisrael -- there is no "psoles" that remained in Ya'akov which could corrupt any of his offspring. As a Jew goes through Shabbos, h/she reaches deeper and deeper inside him or herself to connect back to the spritual roots which the Avos planted within each and every Jew. On Friday night a person reaches into him/herself and connects with Avraham; at lunch he/she connects with Yitzchak. In each of these stages there is still something missing, there is still "psoles", there is still the taste of "chol" that interferes with Shabbos. But by Shabbos afternoon a person has absorbed enough kedushas Shabbos so that he/she can reach deeper still and connect to Ya'akov Avinu, a level of spirituality that is untainted and uncorrupted by whatever may have transpired in the previous week. Even though grammatically the third meal should properly be called "seudah shlishis", we refer to it as "shalos seudos", three meals, because this third meal can perfect and correct whatever was missing in the previous seudos and bring us to a mindset of "kulo Shabbos", without "psoles".