BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Scott Sheffield (MIT) DTSTART:20261020T190000Z DTEND:20261020T200000Z DTSTAMP:20261026T125255Z UID:MathPic/154 DESCRIPTION:Title: 4D Hex and Baby Yang-Mills\nby Scott Sheffield (MIT) as part of Math ematical Picture Language Seminar\n\nLecture held in Jefferson 368.\n\nAbs tract\nThe 2D O(n) model is a very close analog of 4D lattice Yang-Mills. The quest to understand the former (mass gap\, scaling limit\, etc.) has b een colloquially called the "baby Yang-Mills problem" or the "half million -dollar-problem." Now\, several recent OpenAI papers on the 2D O(n) model (one of which comes with Lean code) claim to have solved much of this prob lem. But how exactly is this relevant to 4D Yang-Mills?\n\nI will review a nd explain how the 2D model derives special properties from the identity 1 +1=2 while the 4D model derives special properties from the identity 2+2=4 . The 2D model is related to random loop ensembles\, while the 4D model is related to random surface ensembles. I will discuss the new proofs and th e challenges involved in constructing analogous proofs in 4D. As a warmup\ , try playing a few games of 2D Hex (players compete to make spanning path s on a 2D board) and 4D Hex (players compete to make spanning surfaces on a 4D board) and think about what makes the second game harder to analyze\n LOCATION:https://researchseminars.org/talk/MathPic/154/ END:VEVENT END:VCALENDAR