Ownership Submission
FORM 4
Check this box if no longer subject to Section 16. Form 4 or Form 5 obligations may continue. See Instruction 1(b).
UNITED STATES SECURITIES AND EXCHANGE COMMISSION
Washington, D.C. 20549

STATEMENT OF CHANGES IN BENEFICIAL OWNERSHIP OF SECURITIES

Filed pursuant to Section 16(a) of the Securities Exchange Act of 1934, Section 17(a) of the Public Utility Holding Company Act of 1935 or Section 30(h) of the Investment Company Act of 1940
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(Print or Type Responses)
1. Name and Address of Reporting Person *
GREENWOOD DAVID
  2. Issuer Name and Ticker or Trading Symbol
GERON CORP [GERN]
5. Relationship of Reporting Person(s) to Issuer
(Check all applicable)
_____ Director _____ 10% Owner
__X__ Officer (give title below) _____ Other (specify below)
EVP and CFO
(Last)
(First)
(Middle)
C/O GERON CORPORATION, 230 CONSTITUTION DRIVE
3. Date of Earliest Transaction (Month/Day/Year)
05/23/2008
(Street)

MENLO PARK, CA 94025
4. If Amendment, Date Original Filed(Month/Day/Year)
6. Individual or Joint/Group Filing(Check Applicable Line)
_X_ Form filed by One Reporting Person
___ Form filed by More than One Reporting Person
(City)
(State)
(Zip)
Table I - Non-Derivative Securities Acquired, Disposed of, or Beneficially Owned
1.Title of Security
(Instr. 3)
2. Transaction Date (Month/Day/Year) 2A. Deemed Execution Date, if any (Month/Day/Year) 3. Transaction Code
(Instr. 8)
4. Securities Acquired (A) or Disposed of (D)
(Instr. 3, 4 and 5)
5. Amount of Securities Beneficially Owned Following Reported Transaction(s)
(Instr. 3 and 4)
6. Ownership Form: Direct (D) or Indirect (I)
(Instr. 4)
7. Nature of Indirect Beneficial Ownership
(Instr. 4)
Code V Amount (A) or (D) Price
Common Stock 05/23/2008   F(1)   18,991 (1) D $ 3.92 (1) 152,792 D  
Common Stock 05/28/2008   A   37,500 (2) A $ 0 (2) 190,292 D  

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Table II - Derivative Securities Acquired, Disposed of, or Beneficially Owned
(e.g., puts, calls, warrants, options, convertible securities)
1. Title of Derivative Security
(Instr. 3)
2. Conversion or Exercise Price of Derivative Security 3. Transaction Date (Month/Day/Year) 3A. Deemed Execution Date, if any (Month/Day/Year) 4. Transaction Code
(Instr. 8)
5. Number of Derivative Securities Acquired (A) or Disposed of (D)
(Instr. 3, 4, and 5)
6. Date Exercisable and Expiration Date
(Month/Day/Year)
7. Title and Amount of Underlying Securities
(Instr. 3 and 4)
8. Price of Derivative Security
(Instr. 5)
9. Number of Derivative Securities Beneficially Owned Following Reported Transaction(s)
(Instr. 4)
10. Ownership Form of Derivative Security: Direct (D) or Indirect (I)
(Instr. 4)
11. Nature of Indirect Beneficial Ownership
(Instr. 4)
Code V (A) (D) Date Exercisable Expiration Date Title Amount or Number of Shares
Stock Option (right to buy) $ 3.97 05/28/2008   A   75,000     (3) 05/28/2018 Common Stock 75,000 $ 3.97 1,176,341 D  
Stock Option (right to buy) $ 3.97 05/28/2008   A   181,341     (4) 05/28/2018 Common Stock 181,341 $ 3.97 1,357,682 D  
Stock Option (right to buy) $ 3.97 05/28/2008   A   40,000     (5) 05/28/2018 Common Stock 40,000 $ 3.97 1,397,682 D  

Reporting Owners

Reporting Owner Name / Address Relationships
 Director  10% Owner  Officer  Other
GREENWOOD DAVID
C/O GERON CORPORATION
230 CONSTITUTION DRIVE
MENLO PARK, CA 94025
      EVP and CFO  

Signatures

 /s/ Olivia Bloom for David L. Greenwood   05/28/2008
**Signature of Reporting Person Date

Explanation of Responses:

* If the form is filed by more than one reporting person, see Instruction 4(b)(v).
** Intentional misstatements or omissions of facts constitute Federal Criminal Violations. See 18 U.S.C. 1001 and 15 U.S.C. 78ff(a).
(1) Shares equivalent to the amounts required to satisfy payroll tax withholdings are withheld from distribution to recipient upon vesting of stock award, reducing the vested amount from 53,125 to 34,134 shares. There is no sale of shares.
(2) The shares of restricted stock will remain subject to a repurchase right of Geron over four years, during such time the repurchase right will lapse with respect to 25% of such shares on each anniversary date of the date of grant. The lapse of Geron's repurchase right is conditioned on the employee continuing to provide services to Geron through each vesting date.
(3) This option is exercisable in a series of 48 equal monthly installments commencing May 28 2008 provided the optionee continues to provide services to the Company.
(4) This option is exercisable in a series of 24 equal monthly installments commencing September 18, 2008, provided the optionee continues to provide services to the Company.
(5) This option is exercisable in a series of 24 equal monthly installments commencing September 4, 2008, provided the optionee continues to provide services to the Company.

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