## New Publication by Spiro Karigiannis

Title: Introduction to G2 geometry

Spiro Karigiannis

Abstract: These notes give an informal and leisurely introduction to G2 geometry for beginners. A special emphasis is placed on understanding the special linear algebraic structure in 7 dimensions that is the pointwise model for G2 geometry, using the octonions. The basics of G2-structures are introduced, from a Riemannian geometric point of view, including a discussion of the torsion and its relation to curvature for a general G2-structure, as well as the connection to Riemannian holonomy. The history and properties of torsion-free G2 manifolds are considered, and we stress the similarities and differences with Ka ̈hler and Calabi-Yau manifolds. The notes end with a brief survey of three important theorems about compact torsion-free G2 manifolds.

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## Videos from the Workshop on Dynamics, Randomness, and Control in Molecular and Cellular Networks

Videos from the workshop can be found in the Youtube playlist below. More information can be found on our website.

## New Publication by Enno Keßler, Artan Sheshmani and Shing-Tung Yau

Title: Super $J$-holomorphic Curves: Construction of the Moduli Space
Enno Keßler, Artan Sheshmani and Shing-Tung Yau

Abstract: Let $M$ be a super Riemann surface with holomorphic distribution $\mathcal{D}$ and $N$ a symplectic manifold with compatible almost complex structure $J$. We call a map $\Phi\colon M\to N$ a super $J$-holomorphic curve if its differential maps the almost complex structure on $\mathcal{D}$ to $J$. Such a super $J$-holomorphic curve is a critical point for the superconformal action and satisfies a super differential equation of first order. Using component fields of this super differential equation and a transversality argument we construct the moduli space of super $J$-holomorphic curves as a smooth subsupermanifold of the space of maps $M\to N$.

Arxiv: 1911.05607

## Recent Publications by Juven Wang

##### Phys. Rev. D 100, 085012 – Published 21 October 2019

Title: Quantum 4d Yang-Mills theory and time-reversal symmetric 5d higher-gauge topological field theory

Zheyan Wan,  Juven Wang , and Yunqin Zheng

Abstract: We explore various 4d Yang-Mills gauge theories (YM) living as boundary conditions of 5d gapped short-/long-range entangled (SRE/LRE) topological states. Specifically, we explore 4d time-reversal symmetric pure YM of an SU(2) gauge group with a second-Chern-class topological term at θ=π [SU(2)θ=π YM], by turning on the background fields for both the time reversal (i.e., on unorientable manifolds) and the one-form center global symmetry. We find four siblings of SU(2)θ=π YM with distinct couplings to background fields, labeled by (K1,K2)K1=0, 1 specifies Kramers singlet/doublet Wilson line and new mixed higher ’t Hooft anomalies; K2=0, 1 specifies the boson/fermionic Wilson line and a new Wess-Zumino-Witten–like counterterm. Higher anomalies indicate that to realize all higher n-global symmetries locally on n simplices, the 4d theory becomes a boundary of a 5d higher-symmetry-protected topological state (SPTs, as an invertible topological quantum field theory (iTQFT) or a cobordism invariant in math, or as a 5d higher-symmetric interacting topological superconductor in condensed matter)… Continue reading Recent Publications by Juven Wang

## Videos from the Spacetime and Quantum Mechanics Master Class Workshop

Videos from the workshop are contained in the Youtube playlist below. They can also be found here.

## Videos from the Workshop on Noncommutative Analysis, Computational Complexity, and Quantum Information

Recordings of the talks can be found in the Youtube playlist below or on our webpage. More information can be found on our webpage.