Sheldon refuses to attend the conference, dismissively viewing the audience as "lesser minds." He forbids Leonard from presenting their work alone, leading to a rift between the two.
Howard posts a photo of Penny asleep on his shoulder and claims she is his girlfriend; Penny reacts by mimicking Sheldon’s "head-exploding" gesture at Howard.
For more details, you can find the full script on the Big Bang Theory Transcripts site or check reviews on IMDb . The Cooper-Hofstadter Polarization - IMDb
In the The Big Bang Theory episode (Season 1, Episode 9), Sheldon and Leonard find themselves at odds after being invited to present their joint research paper, “Paradoxical Movement-of-Inertia Changes Due to Putative Super Solids,” at a physics conference. Key Plot Points
In the opening scene, the guys demonstrate a complicated way to turn on a lamp using a laptop signal sent around the world via the internet, simply "because we can".
Penny tries to mediate the situation, even helping Leonard pick out a suit for the presentation, but her involvement only worsens the tension between the friends.