Speaker: Mehtaab S. Sawhney (Columbia University)Title: Quasipolynomial Bounds for the Corners TheoremAbstract:We prove quasipolynomial bounds for the corners theorem for general abelian groups. The proof draws on a number of themes in additive combinatorics, including recent work of Kelley-Meka on 3-term arithmetic progressions, work on almost periodicity, and work of Conlon, Fox, and Zhao on densification. Based on joint work with Michael Jaber, Yang P Liu, Shachar Lovett and Anthony Ostuni.

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

"The Dynamics of Verification when Searching for Quality" | Jonathan Libgober (USC)

Mikkel Sølvsten (Aarhus University)

Speaker: Melody Chan (Brown)Title: Moduli spaces in tropical geometryAbstract:I intend to give a true introduction, accessible to beginning graduate students, to the topics in the title: what is tropical geometry? What is a moduli space? And how can one be used to study the other? Then I’ll discuss some aspects of joint work with Francis Brown, Søren Galatius, and Sam Payne, in which we identify a Hopf algebraic structure on the weight 0 subspace of the compactly supported cohomology of the moduli space of abelian varieties and deduce a number of consequences.*Pre-colloquium reception at 4:00 pm in 553 Lake Hall.