Min/Max Matching Between Ranges

I have a worksheet that's been baffling me for some time now.

I have 2 sheets (see below)

Sheet 1:
Name | MIN Start Date | MAX End Date

Sheet 2:
Name | Start Date | End Date

Named Ranges:
_Est_End_Date_Active_Column (range of all end dates)
_Start_Date_Active_Column (range of all start dates)
_Assignment_Active_Column (range of all names)

What I want to do is match the MIN Start Date where Sheet 1 Name is in the row.

So for example:

Data:
Jason | 1/1/11 | 2/15/11
Tommy | 2/2/11 | 3/15/11
Justin | 3/3/11 | 4/15/11
Sal | 4/4/11 | 5/15/11

Sheet 1:
Justin | 1/1/11 | 2/15/11

What I am getting is:

Justin: 1/1/11 | 5/15/11

Here's the formula I've been working with:

=MAX(IF(_Assignment_Active_Column=$A14,_Est_End_Date_Active_Column))

Not sure what I am doing wrong...