A Sefardi yeshiva boy wants to learn in an Ashkenazi yeshiva.
No problem!
But he also wants to eat.
Problem!
Ashkenazim [based on the Rema] hold that if a Jew turns on the fire a gentile may place the food on top. Sefardim [based on the mechaber and the gra agrees] hold that a Jew must also place the food on the fire - otherwise it is bishul akum [food cooked by a gentile, a no-no]. So it emerges that a Separdi boy may not eat the food in an Ashkenazi yeshiva where a gentile is working in the kitchen and preparing the food.
Uh Oh!
So there are two possible arguments [at least - if weren't so tired I'd try to find more:-)] to permit him.
1] The boy now studies for an extended period of time with Ashkenazi teachers. In such an instance he is no longer obligated to follow his family custom because the mechaber didn't intend to be stringent in such a case.
2] Even the mechaber agrees that there are those who permit one to eat food as long as a Jew turned on the fire. So in order to enable this boy to learn Torah in a good yeshiva he would permit him to be lenient.
Conclusion: He may eat.
Bi'teavon and as the Ashkenazim say - LEARN SHTARK!!
[See tshuvos vi'hanhagos 5 p. 378]