»ã±¨±êÌâ (Title)£ºMeasure growth in compact semisimple Lie groups and the Kemperman Inverse Problem£¨½ô°ëµ¥ÀîȺÖеIJâ¶ÈÔö³¤ÓëKempermanÄæÎÊÌ⣩

»ã±¨ÈË (Speaker)£ºChieu-Minh Tran£¨National University of Singapore£©

»ã±¨¹¦·ò (Time)£º2023Äê8ÔÂ7ÈÕ(ÖÜÒ») 15:00-16:00

»ã±¨µØÖ· (Place)£ºÐ£±¾²¿ F309

Ô¼ÇëÈË(Inviter)£ºÏ¯¶«ÃË¡¢Àî½ú¡¢Õŵ¿­

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»ã±¨ÌáÒª£ºSuppose G is a compact semisimple Lie group, ¦Ì is the normalized Haar measure on G, and A, A^2?G are measurable. We show that ¦Ì(A^2)¡Ýmin{1,2¦Ì(A)+¦Ç¦Ì(A)(1-2¦Ì(A))} with the absolute constant ¦Ç>0 (independent from the choice of G) quantitatively determined. This is the continuous counterpart of celebrated product theorems by Helfgott, Pyber-Szabo, and Breuillard-Green-Tao. We also show a more general result for abstractly semisimple connected compact groups and resolve the Kemperman Inverse Problem from 1964. (Joint with Jing Yifan).