Speaker: Robert RenTitle: Theoretical Foundations of Flow-based Methods for Sampling and Generative Modeling

Ten minutes for your mind@2:50 every day at 2:50 pm in multiple time zones:Europa@2:50, EET, Athens, Helsinki (UTC+2) (7:50 am EST) https://us02web.zoom.us/j/88298032734Atlantica@2:50, EST, New York, Toronto (UTC-4) https://us02web.zoom.us/j/85349851047Pacifica@2:50, PST, Los Angeles, Vancouver (UTC=7) (5:50 pm EST) https://us02web.zoom.us/j/85743543699Almost everything works better again if you unplug it for a bit, including your mind. Stop by and unplug. Get the benefits of mindfulness without the fuss.@2:50 meets at the same time every single day for ten minutes of quiet together.No pre-requisite, no registration needed.Visit the website to view all @2:50 time zones each day.at250.org or at250.mit.edu

Time: 3:00 PM - 4:00 PMSpeaker: Amanda Burcroff (Harvard)Title: Positivity in cluster algebras and their generalizationsAbstract: This dissertation connects several perspectives on positivity in cluster algebras and scattering diagrams, which are powerful combinatorial tools deeply related to geometry, representation theory, and physics. We prove the Laurent positivity conjecture for generalized cluster algebras via a manifestly-positive combinatorial formula for rank 2 scattering diagrams. We also prove bijective results relating scattering diagrams and Dyck path combinatorics for quantum cluster algebras. Portions of this work are joint with Kyungyong Lee and Lang Mou.____________________________________________________________________________________________________Time: 4:15 PM - 5:15 PMSpeaker: Jiyang Gao (Harvard)Title: Tilted Richardson varietiesAbstract: We introduce and develop the theory of tilted Richardson varieties, a new family of subvarieties of the flag variety that generalize classical Richardson varieties. We establish their fundamental geometric properties, including irreducibility, explicit dimension formulas, and a stratification indexed by tilted Bruhat intervals. We construct a tilted analog of the Deodhar decomposition, leading to a combinatorial formula for tilted Kazhdan--Lusztig R-polynomials. We also develop a theory of total positivity for tilted Richardson varieties, showing that their totally nonnegative parts form a CW complex, thus addressing a question of Björner. Finally, we relate tilted Richardson varieties to quantum Schubert calculus, proving they coincide with minimal-degree two-point curve neighborhoods, and use this to compute their cohomology classes and derive new relations among Gromov--Witten invariants. This dissertation is based on joint work with Shiliang Gao and Yibo Gao.

MIT Program in Polymers and Soft Matter (PPSM) Seminar

The Department of Mathematics welcomes École Polytechnique Fédérale de Lausanne professor Maryna Viazovska to our annual Simons Lecture Series.She will give three lectures April 29-May 1The Sphere Packing Problem Lecture 1: General overview. Lecture 2: Random sphere packings with symmetries Lecture 3: Ideal lattice packings and subconvexity bounds IIEach day, a reception will be held at 4pm in Room 2-290, followed by the 4:30pm lecture in Room 2-190.This annual lecture series features presentations by top mathematicians. Many thanks to the late Jim Simons and his wife, Marilyn Simons, for their continued financial support of these lectures.

Michael Greenstone (University of Chicago)