Speaker: Niven AchenjangTitle: The Average Size of 2-Selmer Groups of Elliptic Curves in Characteristic 2Zoom Link: https://mit.zoom.us/j/96646700269?pwd=ST8VE7YDozKVY3AMUBR7pw9dkMFoTo.1

"Getting the Picture" | Robby Akerlof (Warwick)

Speaker: Adel Djellouli (Harvard)Title: Shell buckling for programmable metafluidsAbstract:The pursuit of materials with enhanced functionality has led to the emergence of metamaterials—artificially engineered materials whose properties are determined by their structure rather than composition. Traditionally, the building blocks of metamaterials are arranged in fixed positions within a lattice structure. However, recent research has revealed the potential of mixing disconnected building blocks in a fluidic medium. Inspired by these recent advances, here we show that by mixing highly deformable spherical capsules into an incompressible fluid, we can realize a ‘metafluid’ with programmable compressibility, optical behaviour and viscosity. First, we experimentally and numerically demonstrate that the buckling of the shells endows the fluid with a highly nonlinear behaviour. Subsequently, we harness this behaviour to develop smart robotic systems, highly tunable logic gates and optical elements with switchable characteristics. Finally, we demonstrate that the collapse of the shells upon buckling leads to a large increase in the suspension viscosity in the laminar regime. As such, the proposed metafluid provides a promising platform for enhancing the functionality of existing fluidic devices by expanding the capabilities of the fluid itself.

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

Speaker: Vasudevan Srinivas (Tata and Univ. of Buffalo)Title: Some finiteness results for the etale fundamental group in positive characteristicsAbstract:This talk will discuss some results on etale fundamental groups of varieties over an algebraically closed field of characteristic p > 0, based on joint work with Hélène Esnault and other coauthors. One result, along with Mark Shusterman, is that the tame fundamental group is finitely presented for such a variety which is the complement of an SNC divisor in a smooth projective variety. A second, along with Jakob Stix, is to give an obstruction for a smooth projective variety to admit a lifting to characteristic 0, in terms of the structure of its etale fundamental group as a profinite group. We will finally touch on some open questions.

Speaker: Kevin Ren (Princeton University) - 3 PM until 4 PM in 4-257Speaker: Anshul Adve (Princeton University) - 4:15 PM until 5:15 PM in 2-131➖ ➖ ➖➖ ➖ ➖➖ ➖ ➖➖ ➖ ➖➖ ➖ ➖➖ ➖ ➖Speaker: Kevin Ren (Princeton University)Title: Sharp discretized projection theorem in ℝ3Abstract: For 0 < s < 2, 0 < t < 3, we define f(s, t) to be the largest number such that for every choice of t-dimensional set K in ℝ3 and s-dimensional set E in S2 that does not concentrate in any great circle, there exists a direction 𝓍 ∈ E such that the projection of K onto the plane normal to 𝓍 has dimension at least f(s, t). The multi-linear Kakeya inequality gives f(s, t) ≥2t\3; Weikun He (following Bourgain) proved that f(s, t) ≥2t\3 + ε for some explicit ε (s, t) > 0. We compute the sharp value of f(s, t) for all 0 < s < 2, 0 < t < 3. Joint with Paige Bright and Hong Wang.➖ ➖ ➖➖ ➖ ➖➖ ➖ ➖➖ ➖ ➖➖ ➖ ➖➖ ➖ ➖Speaker: Anshul Adve (Princeton University)Title: Algebraic equations characterizing hyperbolic surface spectraAbstract: Given a compact hyperbolic surface of fixed genus, together with a suitable choice of orthonormal basis of Laplace eigenforms, one can consider two natural spectral invariants: 1) the Laplace spectrum Λ, and 2) the 3-tensor Cijk representing pointwise multiplication (as a densely defined map L2 × L2 → L2) in the given basis. Which pairs (Λ, C) arise this way? Both Λ and C are highly transcendental objects. Nevertheless, we will give a concrete and almost completely algebraic answer to this question, by writing down necessary and sufficient conditions in the form of equations satisfied by the Laplace eigenvalues and the Cijk . This answer was conjectured by physicists Kravchuk, Mazac, and Pal, who introduced these equations (in an equivalent form) as a rigorous model for the crossing equations in conformal field theory.