Saying “well since you went to elementary school in a big city you must have gotten the shots” is plain stupid. However, at 45 there is a good chance you have immunity, either from shots or naturally acquired, to several of the vaccine-preventable diseases, and some have become rare enough that they aren’t much of a threat to you, especially at 45, so you may not NEED any shots or tests.
However, the benefit of immunizing you is as much to protect your contacts and your contacts’ contacts, many of whom are infirm, as to protect you, and it would be prudent to ensure that you have protection against several vaccine-preventable diseases.
I would expect that a responsible biomedical research facility would require that you be protected against hepatitis B. The vaccine was not routinely given to kids when you were one. You can get 3 shots or have a blood test and only get three shots if you do not have immunity.
They would probably be wise to require immunity to diphtheria, pertussis, and tetanus. The latter only to protect you and the first two to protect you and your contacts. Although you may well have adequate immunity to diphtheria and tetanus, it is easier to give a booster (recommended every 10 years) than test for immunity. Your pertussis shot wore off years ago but you can now get the new “Tdap” shot which will covers diphtheria, tetanus, and pertussis at the same time.
I would expect that they would want you to have measles, mumps, and rubella immunity. These can be measured by a blood test or you can get a single shot.
You would probably benefit from a 2-shot hepatitis A series if you have not traveled much in countries where one doesn’t drink the water but think you might do such traveling some day. That would be your call and you can test for immunity.
A flu shot every year won’t hurt.
A single polio booster may be recommended if you plan travel to one of the countries where polio still occurs but not otherwise.
It is unlikely that you ever got the now-routine meningococcal meningitis shot but it isn’t generally advised for people your age.
You are probably too old to benefit from the new HPV shot.
You are too old for the now-routine Haemophilus influenzae shot. You are too old for the conjugate Streptococcus pneumoniae shot and too young for the polysaccharide S. pneumoniae shot (unless you have a chronic disease).
There are lots of other shots but they are not recommended routinely.