Exhibit 32.1

STATEMENT PURSUANT TO 18 U.S.C. §1350, AS ADOPTED

PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

Pursuant to 18 U.S.C. §1350, the undersigned certifies that, to her knowledge, this Quarterly Report on Form 10-Q for the period ended June 30, 2019 fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 and that the information contained in this report fairly presents, in all material respects, the financial condition and results of operations of Infinity Pharmaceuticals, Inc.

Date: July 30, 2019	/s/Adelene Q. Perkins
	Adelene Q. Perkins
	Chief Executive Officer
	(Principal Executive Officer)

A signed original of this written statement required by Section 906 has been provided to Infinity Pharmaceuticals, Inc. and will be retained by Infinity Pharmaceuticals, Inc. and furnished to the Securities and Exchange Commission or its staff upon request.