Speaker: Matthew Jenssen (King's College London​​​​​​​)Title: Non-existence probabilities and lower tails via Gibbs uniqueness on hypertreesAbstract:Given a graph $H$, what is the probability that $G(n,p)$ contains no copy of $H$ or fewer copies than expected? This is a canonical example of a `lower-tail' large deviation probability that arises naturally in combinatorics. Other examples include the probability that a random subset of $[n]$ avoids $k$-term arithmetic progressions or that a random subset of an abelian group is sum free. In this talk, I will discuss a method for determining the logarithmic asymptotics (or rate function) for such probabilities. The method applies for a range of parameters in the `critical regime': between the regime amenable to hypergraph container methods and that amenable to Janson's inequality. The method works in the general framework of estimating the probability that a $p$-random subset of vertices of a $k$-uniform hypergraph contains fewer hyperedges than expected. We show that under some simple structural conditions on the hypergraph and an upper bound on $p$ determined by a phase transition on an infinite hypertree, this probability can be approximated by a formula derived from a Gibbs measure on the hypertree. This is joint work with Will Perkins, Aditya Potukuchi and Michael Simkin.

Preparing for a research talk, investor pitch, or interview? Eager to polish your three-minute thesis video, podcast, or public talk? In this NEW, six-session workshop series, learn to refine your speaking and presentation skills across a range of contexts. Whether your audience is intimate or enormous, expert or novice, we will help you find strategies to capture and keep their attention. Each interactive session will invite you to implement tips on tailoring your content, delivery, and visual aids to develop your confidence, clarity, and charisma. At the end of six meetings, you will have solid advice and experience with introducing yourself and your topic, tailoring your talk to diverse audiences, structuring your content, streamlining your flow, practicing effectively, and fielding questions.Session 1: Tue, April 1, 4:00-5:30 p.m. First Impressions Session 2: Thu, April 3, 4:00-5:30 p.m. Engage Your Audience Session 3: Tue, April 8, 4:00-5:30 p.m. Structure Your Presentation Session 4: Thu, April 10, 4:00-5:30 p.m. Tell Your Story Session 5: Tue, April 15, 4:00-5:30 p.m. Enhance Your Presentation Session 6: Thu, April 17, 4:00-5:30 p.m. Finish Strong: Conclusions and Q&A

Xiaohong Chen (Yale University)

Quantifying Inefficiency | Yannai Gonczarowski (Harvard)

Have some fun(nel) on a tunnel or sun(nel) walk! Join us for a 30-minute volunteer-led walk either through MIT’s famous tunnel system or around Killian Court. As the weather gets warmer, walk leaders may choose to take the group outside. Is the weather warm and you missed the start? Find the group on Killian Court and join in!Location details: Meet in the lobby with the big mirror, right inside the Collier Memorial entrance to Stata. Location photo below.Sun(nel) Walk Leaders will identify themselves by holding a white flag at the meeting location.Prize Drawing: Attend a walk and scan a QR code from the walk leaders to be entered into a drawing for a getfit canvas boat tote bag at the end of the getfit challenge. The more walks you attend, the more entries you get. Winner will be drawn and notified at the end of April. Winner does not need to be a getfit participant.Disclaimer: These walks are led by volunteers. In the rare occasion when a volunteer isn’t able to make it, we will do our best to notify participants. In the event we are unable to notify participants and a walk leader does not show up, we encourage you to walk as much as you feel comfortable doing so. We recommend checking this calendar just before you head out!Getfit is a 12-week fitness challenge for the entire MIT community. These walks are open to the entire MIT community and you do not need to be a current getfit participant to join.