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Workshop on Global Categorical Symmetries
May 7, 2023 @ 9:00 am - May 12, 2023 @ 6:00 pm
The CMSA will be hosting a Workshop on Global Categorical Symmetries from May 7 – 12, 2023
Participation in the workshop is by invitation.
There will be three lectures on Thursday, May 11, 2023, which are open to the public.
Location: Room G-10, CMSA, 20 Garden Street, Cambridge MA 02138
Note: The public lectures will be held in-person only.
2:00 – 2:50 pm
Speaker: Kantaro Ohmori (U Tokyo )
Title: Fusion Surface Models: 2+1d Lattice Models from Higher Categories
Abstract: 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.
3:00 – 3:50 pm
Speaker: David Jordan (Edinburgh)
Title: Langlands duality for 3-manifolds
Abstract: 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.
3:50 – 4:30 pm
4:30 – 5:30 pm
Speaker: Ken Intriligator (UCSD)
Title: QFT Aspects of Symmetry
Abstract: 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.