Extreme Equilibria: The Benefits of Correlation | Fedor Sandomirskiy

Speaker: Alex Lubotzky (Weizmann Institute & the Hebrew University, Simons Distinguished Visiting Professor, MIT)Title: High Dimensional Expanders (HDX) and their applications in pure math and computer scienceAbstract:Expander graphs have been an intensive topic of research in math and CS during the last six decades. In the last two decades a high dimensional theory has emerged with (very different) applications in math & CS.In this series of 8 independent (but related) lectures we present some aspects of the theory of HDX and its applications, a number of open problems and suggestions for further research.A more detailed plan:1. Thursday 2/20/25, 4:30pm, 2-190 (Math Colloquium); refreshments served at 4pm in 2-290  Introduction: three main problems(a) Gromov overlapping property(b) Locally testable codes(c) Are all groups sofic?2. Tuesday 2/25/25, 4:15-5:15pm, 32-G449 (Theory of Computing Colloquium), refreshments served at 4pmGood Locally testable codes3. Wednesday 2/26/25, 9:30-11am, 2-449Expander graphs: combinatorics, spectral gap, representation theory(Kazhdan property (T), property (\tau) and more) and property testing4. Wednesday 3/5/25, 9:30-11am, 2-449Geometric & topological expanders, Coboundary expanders, Random simplicial complexes and Property testing5. Wednesday 3/12/25, 9:30-11am, 2-449From Ramanujan graphs to Ramanujan complexes6. Wednesday 3/19/25, 9:30-11am, 2-449Stability and group approximation, Garland Theorem and the p-adic Deligne central extensionsWednesday 3/26/25 - Spring vacation7. Wednesday 4/2/26, 9:30-11am, 2-449Some more CS: Agreement tests, direct product test; PCP8. Wednesday 4/9/25, 9:30-11am, 2-449Are there non-sofic groups? The Aldous-Lyons conjecture and more

Speaker: Alex Lubotzky (Weizmann Institute & The Hebrew University, Simons Distinguished Visiting Professor, MIT)Title: High Dimensional ExpandersAbstract:Expander graphs have been an intensive topic of research in math and CS during the last six decades. In the last two decades a high dimensional theory has emerged with (very different) applications in math & CS. This colloquium talk is actually the first of 8 independent (but related) lectures about some aspects of the theory of HDX and its applications, as well as a number of open problems and suggestions for further research. This lecture will focus on three main problems (a) Gromov overlapping property, (b) Locally testable codes and (c) Are all groups sofic?*Pre-reception held in 2-290 at 4pm.

Speaker: Mohit Hulse (MIT)Title: Period maps and the Gauss-Manin connectionAbstract:For a family of smooth projective varieties over a number field, we have a complex period map and a $p$-adic period map, and they are both governed by the (algebraic) Gauss-Manin connection. After some preliminaries, we introduce these objects and prove some bounds on the dimensions of their images.Reference:$\bullet$ Lawrence and Venkatesh, Diophantine problems and $p$-adic period mappings, Section 3.For more details:$\bullet$ Deligne, Hodge cycles on abelian varieties, Section 2 (for Gauss-Manin connection).$\bullet$ Voisin, Hodge Theory and Complex Algebraic Geometry I, Part III.$\bullet$ Hotta, Takeuchi and Tanisaki, D-Modules, Perverse Sheaves, and Representation Theory (for more on Riemann-Hilbert).

The List Visual Arts Center will host an artist discussion in celebration of the opening of Pedro Gómez-Egaña: The Great Learning followed by an opening reception.This exhibition marks the first US solo presentation of Pedro Gómez-Egaña, a multimedia artist working in sculpture, performance, video, sound and drawing. Pedro Gómez-Egaña: The Great Learning will feature a number of works and interventions articulated as one temporal, sonic and spatial composition.Following a brief artist presentation, Pedro Gómez-Egaña and curator Natalie Bell will engage in a public dialogue about the presentation at the List Center.