In season 1, episode 19, "The road not taken", Dr. Bishop - the mad scientist just pulled out of a mental institution by Olivia Dunham, an FBI agent for whose Dr. Bishop works as a civilian consultant due to his expertise in an area called Fringe Science (after which the show has been named), explains that there is more than one "reality". Indeed - he explains - what we perceive as linear time, it is not: time, as well as what we define reality, is shaped and changed by the choice we make every day. Due to that, there exists an infinite set of parallel universes, just equal to ours but slightly different, populated by other versions of us. Along with this definition goes the one of dejà-vù's: they're glimpses, little visions of what he calls "the other side". A video on YouTube reports the most significant segment.
In the very following episode, "There's more than one of everything", the explanation of the alternate universe goes on: a multi-billion company CEO, William Bell, theorized that in our world there are "soft spots": areas in which the fundamental law of the nature has began to decay, such as the speed of the light. In those spots, the membrane between the universes is thinner, and it would be possible to "cross" to the other side: one of them is said to be the Bermuda Triangle. A full episode about the "crossing over" theory and application is season 2, episode 16, "Peter": and old-fashioned directed segment in which Dr. Bishop explains is adventure in crossing into the alternate universe several years before; I'm not going to explain more because it's a very significant part of the story, someone may not want such a spoiler; however, the story is briefly reported on Wikipedia.
In season 2, episode 15, "Jacksonville", a building in Manhattan comes from the other side and sets itself over the existing building of over here, violating Pauli's exclusion principle; follow harmonical and geometrical explanations to how to "swap" things between the two universes.
In season 2, episode 18, "White tulip", an MIT astrophysics professor Alistar Peck performed a way to jump back in the past by solving mathematical polynomial equations and implementing on his very body a Faraday cage; it was trying to jump back to the moment in which his fiancé was killed by a car accident.
In season 3, episode 3, "the plateau", the alternate universe's Fringe Team investigates on uncommon murders performed by a guy whose intelligence was enhanced by a medical experiment. This person was able to mentally compute high level differential equation and manage to predict short-time future events.
In season 3, episode 6, "6955 Hz", the Fringe team find itself to investigate on "number stations": radio-frequency transmissions of number sequences that seem to be a code coming by an ancient population: the first people. Lot of amateurs tried to decrypt what appeared to be a code, but that was indeed just covering a signal that made them suffer by amnesia, probably in order to "protect" the code.
Season 4, episode 6, "And those we've left behind", all over Boston time anomalies occur, due to a man trying to encase his house in a time-distorted ball. It turns out that anomalies were following a pattern: they were "drawing" the Fibonacci Golden Spiral.
In season 4, episode 12, "Welcome to Westfield", the two universes become to overlap themselves causing wide distruction; but as in a hurricane, there is a safe place: the eye of the cyclone, where the forces of nature contrast themselves.
I know I mentioned lot of them; actually in very each episode science goes as protagonist; all weird facts are explained in ways that let you think it might really be true.
Hoping that's going to be useful to your work, I want to thank you again for your presentation. Hope to have occasions to meet again.
Best regards, Marco Mele