Geron (GERN) 10-Q 2005 Q2 Quarterly report

EXHIBIT 32.1

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

Pursuant to 18 U.S.C. Section 1350, as created by Section 906 of the Sarbanes-Oxley Act of 2002, the undersigned officer of Geron Corporation (the “Company”) hereby certifies, to such officer’s knowledge, that:

(i) the accompanying quarterly report on Form 10-Q of the Company for the three and six months ended June 30, 2005 (the “Report”) fully complies with the requirements of Section 13(a) or Section 15(d), as applicable, of the Securities Exchange Act of 1934, as amended; and

(ii) the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Dated: August 5, 2005

/s/ THOMAS B. OKARMA

Thomas B. Okarma

President and Chief Executive Officer

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