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DTSTART;TZID=America/New_York:20230507T090000
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DTSTAMP:20260404T125528
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SUMMARY:Workshop on Global Categorical Symmetries
DESCRIPTION:The CMSA will be hosting a Workshop on Global Categorical Symmetries from May 7 – 12\, 2023 \nParticipation in the workshop is by invitation. \nPublic Lectures \nThere will be three lectures on Thursday\, May 11\, 2023\, which are open to the public.\nLocation:  Room G-10\, CMSA\, 20 Garden Street\, Cambridge MA 02138\nNote: The public lectures will be held in-person only. \n2:00 – 2:50 pm\nSpeaker: Kantaro Ohmori (U Tokyo )\nTitle: Fusion Surface Models: 2+1d Lattice Models from Higher Categories\nAbstract: Generalized symmetry in general dimensions is expected to be described by higher categories. Conversely\, one might expect that\, given a higher category with appropriate structures\, there exist models that admit the category as its symmetry. In this talk I will explain a construction of such 2+1d lattice models for fusion 2-categories defined by Douglas and Reutter\, generalizing the work of Aasen\, Fendley and Mong on anyon chains. The construction is by decorating a boundary of a topological Freed-Teleman-Moore sandwich into a non-topological boundary. In particular we can construct a family of candidate lattice systems for chiral topological orders. \n  \n3:00 – 3:50 pm\nSpeaker: David Jordan (Edinburgh)\nTitle: Langlands duality for 3-manifolds\nAbstract: Originating in number theory\, and permeating representation theory\, algebraic geometry\, and quantum field theory\, Langlands duality is a pattern of predictions relating pairs of mathematical objects which have no clear a priori mathematical relation. In this talk I’ll explain a new conjectural appearance of Langlands duality in the setting of 3-manifold topology\, I’ll give some evidence in the form of special cases\, and I’ll survey how the conjecture relates to both the arithmetic and geometric Langlands duality conjectures. \n3:50 – 4:30 pm\nTea/Snack Break \n4:30 – 5:30 pm\nSpeaker: Ken Intriligator (UCSD)\nColloquium\nTitle: QFT Aspects of Symmetry\nAbstract: Everything in the Universe\, including the photons that we see and the quarks and electrons in our bodies\, are actually ripples of quantum fields. Quantum field theory (QFT) is the underlying mathematical framework of Nature\, and in the case of electrons and photons it is the most precisely tested theory in science. Strongly coupled aspects\, e.g. the confinement of quarks and gluons at long distances\, remain challenging. QFT also describes condensed matter systems\, connects to string theory and quantum gravity\, and describes cosmology. Symmetry has deep and powerful realizations and implications throughout physics\, and this is especially so for the study of QFT. Symmetries play a helpful role in characterizing the phases of theories and their behavior under renormalization group flows (zooming out). Quantum field theory has also been an idea generating machine for mathematics\, and there has been increasingly fruitful synergy in both directions. We are currently exploring the symmetry-based interconnections between QFT and mathematics in our Simons Collaboration on Global Categorical Symmetry\, which is meeting here this week. I will try to provide an accessible\, colloquium-level introduction to aspects of symmetries and QFT\, both old and new.
URL:https://cmsa.fas.harvard.edu/event/globalcomputing23/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Workshop
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DTSTART;TZID=America/New_York:20230512T100000
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DTSTAMP:20260404T125528
CREATED:20230802T171128Z
LAST-MODIFIED:20240215T111609Z
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SUMMARY:Anomalies of (1+1)D categorical symmetries
DESCRIPTION:Quantum Matter Seminar \nSpeaker: Carolyn Zhang (U Chicago) \nTitle: Anomalies of (1+1)D categorical symmetries \nAbstract: We present a general approach for detecting when a fusion category symmetry is anomalous\, based on the existence of a special kind of Lagrangian algebra of the corresponding Drinfeld center. The Drinfeld center of a fusion category $A$ describes a $(2+1)D$ topological order whose gapped boundaries enumerate all $(1+1)D$ gapped phases with the fusion category symmetry\, which may be spontaneously broken. There always exists a gapped boundary\, given by the \emph{electric} Lagrangian algebra\, that describes a phase with $A$ fully spontaneously broken. The symmetry defects of this boundary can be identified with the objects in $A$. We observe that if there exists a different gapped boundary\, given by a \emph{magnetic} Lagrangian algebra\, then there exists a gapped phase where $A$ is not spontaneously broken at all\, which means that $A$ is not anomalous. In certain cases\, we show that requiring the existence of such a magnetic Lagrangian algebra leads to highly computable obstructions to $A$ being anomaly-free. As an application\, we consider the Drinfeld centers of $\mathbb{Z}_N\times\mathbb{Z}_N$ Tambara-Yamagami fusion categories and recover known results from the study of fiber functors.
URL:https://cmsa.fas.harvard.edu/event/qm_51223/
LOCATION:Virtual
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-05.12.23.png
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