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The wondrous world of hyperfinite subfactors

MATHEMATICAL PICTURE LANGUAGE

March 30, 2021      10:00 am
Speaker: Dietmar Bisch - Vanderbilt University

The hyperfinite II1 factor contains a wealth of subfactors, many of which give rise to new and fascinating mathematical structures. For instance, the standard representation of a subfactor generates a...
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Noncommutative real algebraic geometry and quantum games

MATHEMATICAL PICTURE LANGUAGE

March 23, 2021      10:00 am
Speaker: William Helton - University of California San Diego

The last two decades produced a substantial noncommutative (in the free algebra) real and complex algebraic geometry. The aim of this subject is to develop a systematic theory of equations...
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Exploring new scientific frontiers with programmable quantum systems

MATHEMATICAL PICTURE LANGUAGE

March 16, 2021      10:00 am
Speaker: Mikhail Lukin - Harvard University

I will discuss recent developments at a new scientific interface between quantum optics, quantum many-body physics, information science and engineering. Specifically, I will focus on two examples at this interface...
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Some Analysis Aspects in Subfactor Theory

MATHEMATICAL PICTURE LANGUAGE

March 9, 2021      10:00 am
Speaker: Sorin Popa - UCLA

One of the most fascinating aspects about non-commutative spaces (aka von Neumann algebras), is the way their building data, which is often geometric in nature, impacts on the properties of their...
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Integrability of Liouville Theory

MATHEMATICAL PICTURE LANGUAGE

March 2, 2021      10:00 am
Speaker: Antti Kupiainen - University of Helsinki

Polyakov introduced Liouville Conformal Field theory (LCFT) in 1981 as a way to put a naturalmeasure on the set of Riemannian metrics over a two dimensional manifold. Ever since, the work of Polyakov...
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From multi-photon entanglement to quantum computational advantage

MATHEMATICAL PICTURE LANGUAGE

February 23, 2021      9:30 am
Speaker: Jian-Wei Pan - University of Science and Technology of China

By developing high-performance quantum light sources, the multi-photon interference has been scaled up to implement Boson sampling with up to 76 photons out of a 100-mode interferometer, which yields a...
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Elements of ∞-category theory

MATHEMATICAL PICTURE LANGUAGE

February 16, 2021      10:00 am
Speaker: Emily Riehl - Johns Hopkins University

Confusingly for the uninitiated, experts in infinite-dimensional category theory make use of different definitions of an ∞-category, and theorems in the ∞-categorical literature are often proven "analytically", in reference to...
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Many-body localization near the critical point

MATHEMATICAL PICTURE LANGUAGE

February 9, 2021      10:00 am
Speaker: John Imbrie - University of Virginia

I will examine the many-body localization (MBL) phase transition in one-dimensional quantum systems with quenched randomness. Having demonstrated the existence of the MBL phase at strong disorder, under a level-statistics...
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