Broken glass on the bicycle path, what to do? Often I find myself driving with my racing bike on the dedicated bicycle lane in my city. The problem with these bicycle lanes is that there is a lot of broken glass (once every few kilometers). Normally I spot it quite late, drive through the glass, and hope for the best in not getting a puncture.

My question is as follows: How can I minimize the chance of getting a puncture while driving through glass?

I am not really looking for material advice, but rather for tips on how to drive through the glass (i.e. does it help to redistribute weight, speed up, or slow down), and does it make sense to check your tires after driving through the glass (as this answer suggests: What is a good way to keep my tires from going flat easily?). This far, I've not gotten a puncture there, but I would like to keep it that way!
There are three approaches you can use in combination.

Preparation

Tough tires - people have their favorite puncture-proof tires. Kevlar reinforced tires work pretty well.

Hard tires - pump your tires to close to the maximum pressure written on the side wall. This definitely reduces punctures, and can be combined with puncture-proof tires.

At the time

You limit your question "reducing punctures while [riding] though glass". Obviously, if you could avoid the trash you would.

You cannot always go around the trash. If you are able, you could bunny hop over it. This is also not always possible when commuting, due to lack of time, heavy traffic (including other bikes) limiting your options, or carrying a pack or panniers.

Slowing down is often also not an option when commuting because of following traffic. 

After the fact

Brush your tires. It should be acknowledged that there are some who are squeamish about this. But it is very effective at removing foreign objects from your tires. In 35 years since I learned to do it, I've never (seriously) hurt my hand. Of course you should wear gloves. Most gloves have a reinforced patch across the palm to the base of the thumb for this purpose. (Many people mistake this for extra padding :-)

Don't wait: as soon as you hit the trash start brushing your tires. The more revolutions your tires do, the more the trash gets hammered into them. So brush them strait away. It doesn't help to stop to do it; firstly, it interrupts your ride, but mainly because by the time you stop the damage is done.

For the front tire, place your palm (near the base of your thumb) gently on the top of the rotating tire, in front of the brakes. The tire surface must be moving away from anything you could catch your hand in. You only need to keep it there for a few seconds, enough for one or maybe two revolutions of the wheel. Sometimes you feel a slight bump when you have successfully removed something from the tire. Usually, you'll feel nothing.

The back tire is a bit harder to brush, because you have to reach down to an awkward place and if you have to look it means you're not looking where you're going. So you'll want to practice this skill before you use it in traffic. Again, brush your tire in front of the brakes, in front of the back stay, where the tire is moving away from the brakes. Because of the low clearance between the back tire and the down tube on most race bikes, you need to be careful not to let you hand get pulled down into the gap. That hurts. Also avoid poking your finger into the spokes. That hurts too.

After reading this you can see why some people avoid doing it. Just be careful while you are learning, and practice before doing it in traffic. It's a valuable skill to have.