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We present the recent developments in exact amplitude-based resummationmethods for non-Abelian gauge theories as they relate to precision LHC physics.We discuss QEDXQCD exponentiation, shower/ME matching, IR-improved DGLAP-CStheory and implications, as developed by one of us (BFLW), for a UV finitetheory of quantum general relativity.

New Developments in Precision LHC Theory: QEDXQCD Exponentiation,  Shower/ME Matching, IR-Improved DGLAP-CS Theory and Implications for UV  Finite Quantum Gravity