▁mother ▁Frances ▁Hall am ▁B ren ner ▁was ▁a ▁city ▁council or ▁and ▁briefly ▁mayor ▁of ▁Pal o ▁Al to , ▁California . ▁His ▁uncle ▁Charles ▁B ren ner , ▁MD ▁was ▁a ▁psych iat rist . ▁ ▁B ren ner ▁received ▁a ▁B . S . ▁from ▁Stan ford ▁University ▁in ▁ 1 9 6 7 , ▁and ▁a ▁Ph . D . ▁from ▁the ▁University ▁of ▁California , ▁Los ▁Angeles ▁( U CLA ) ▁in ▁ 1 9 8 4 . ▁ ▁B ren ner ▁participated ▁in ▁the ▁implementation ▁of ▁A PL \ 3 6 0 ▁and ▁A PL \ 1 1 3 0 , ▁and ▁implemented ▁the ▁trans pose ▁and ▁rotate ▁primitive ▁functions . ▁ ▁More ▁recently , ▁B ren ner ▁special izes ▁in ▁the ▁use ▁of ▁mathematics ▁in ▁DNA ▁analysis . ▁His ▁principal ▁areas ▁of ▁interest ▁and ▁achiev ement ▁in ▁the ▁mathematics ▁of ▁for ens ic ▁DNA ▁are ▁kin ship , ▁rare ▁ha plot ype ▁matching , ▁and ▁DNA ▁mi xt ures . ▁In ▁a ▁couple ▁of ▁Y ▁ha plot ype ▁papers , ▁most ▁recently , ▁he ▁showed ▁why ▁Y ▁ha plot ypes ▁must ▁be ▁much ▁r ar er , ▁and ▁how ▁much ▁r ar er , ▁than ▁their ▁sample ▁frequency ▁in ▁a ▁reference ▁population ▁sample . ▁B ren ner ’ s ▁Symbol ic ▁Kin ship ▁Program , ▁which ▁can ▁for ▁example ▁assess ▁the ▁identification ▁evidence ▁based ▁on ▁DNA ▁profiles ▁from ▁an ▁anonymous ▁body ▁and ▁an ▁arbitrary ▁set ▁of ▁pres umed ▁relatives , ▁has ▁been ▁widely ▁used ▁in ▁mass