Speaker: Daniel Spiegel (Harvard Univesity)Title: A Classifying Space for Phases of Matrix Product StatesAbstract: Alexei Kitaev has conjectured that there should be a loop spectrum consist- ing of spaces of gapped invertible quantum spin systems, indexed by spatial dimension 𝑑 of the lattice. Motivated by Kitaev’s conjecture, I will detail a concrete construction of a topological space 𝐵 consisting of translation in- variant injective matrix product states (MPS) of all physical and bond di- mensions, which plays the role of Kitaev’s space in dimension 𝑑 = 1. Hav- ing such a space is a useful tool in the discussion of parametrized phases of MPS; in fact, it allows us to define a parametrized phase as a homotopy class of maps into 𝐵.The space 𝐵 is constructed as the quotient of a contractible space 𝐸 of MPS tensors modulo gauge transformations. The projection map from 𝐸 to 𝐵 is a quasifibration, from which we can compute the homotopy groups of the classifying space 𝐵 by a long exact sequence. In particular, 𝐵 has the weak homotopy type 𝐾(ℤ, 2) × 𝐾(ℤ, 3), shedding light on Kitaev’s conjecture in the context of MPS.

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The irony of artificial intelligence is that it often reveals more about human intelligence than machines themselves.From AI in the home to robots in the workplace, the presence of AI all around us compels us to question its potential and recognize the risks. What has become clear is that the more we advance AI technology and consider machine ability versus human ability, the more we need to mind the gap.Researchers at MIT have been at the forefront of this evolving field. The work presented in this exhibition builds on the pioneering contributions of figures such as Claude Shannon and Seymour Papert, while highlighting contemporary research that spans computer science, mechanical engineering, neuroscience, and the social sciences.As research probes the connections between human and machine intelligence, it also underscores the profound differences. With AI now embedded in everyday life — from smart assistants in our homes to robots in the workplace — we are challenged to ask critical questions about its potential, its risks, and the boundaries between machine ability and human capability.Join us in shining light on the tremendous promise, unforeseen impacts, and everyday misconceptions of AI in this riveting, interactive exhibition.Learn more about the exhibition.