How do I most elegantly express left join with aggregate SQL as LINQ query

A solution, albeit one that defers handling of the null value to the code, could be:

DateTime yesterday = DateTime.Now.Date.AddDays(-1);

var collection=
    from u in db.Universe
    select new
    {
        u.id,
        u.name,
        MaxDate =(DateTime?)
       (
           from h in db.History
           where u.Id == h.Id
           && h.dateCol < yesterday
           select h.dateCol 
       ).Max()
    };

This does not produce exactly the same SQL, but does provide the same logical result. Translating "complex" SQL queries to LINQ is not always straightforward.

var collection=
    from u in db.Universe
    select new
    {
        u.id,
        u.name,
        MaxDate =(DateTime?)
       (
           from h in db.History
           where u.Id == h.Id
           && h.dateCol < yesterday
           select h.dateCol 
       ).Max()
    };

Just youse the above code and this should work fine!