Conference on Knot Theory and its Applications to Physics and Quantum Computing

摘要：2014年10月，美国德克萨斯大学达拉斯分校将召开一场关于“结理论及其在物理和量子计算中的应用”的学术会议。打结理论是拓扑学的一个分支，它研究一个圆在三维空间中的多种放置方式——一个令人兴奋的问题是，一个表面上打结的圆是否真的打结，或者它是否看起来比实际上更复杂。目前正在使用和开发的技术已经被证明能够区分有结和无结的圆，并且在代数和拓扑学中开辟了新的挑战。结理论与物理学的联系通常涉及量子理论，本次会议的主题之一是量子计算，努力应用量子力学系统的独特特性，如纠缠，以获得大大超过当前硬件限制的计算速度。预计本次会议的演讲者将包括量子计算拓扑方面的一些领先研究人员。计划会议的一些主要议题包括：(1)结理论和量子计算之间的联系-如Temperley-Lieb重耦合，编织群和纠缠态的幺正表示，Yang-Baxter方程的幺正解，GHZ态和额外特殊的2-群，Majorana费米子的融合代数，(2)结和3-流形的不变量，包括Khovanov同调，串模，以及相关思想；(3)用结和连杆不变量求磁场和涡场的高阶不变量和更清晰的能量界。

AbstractAward: DMS 1439922, Principal Investigator: Mieczyslaw K. Dabkowski, Tobias Hagge, Viswanath RamakrishnaA conference on Knot Theory and its Applications to Physics and Quantum Computing is to be held at the University of Texas at Dallas in October 2014. Knot theory is the branch of topology that studies the many ways that a circle can be placed within three-dimensional space - a motivating question is whether an apparently knotted circle is genuinely knotted, or whether it looks more complicated than it really is. Techniques that are currently used and under development have been shown to be capable of making that distinction between knotted and unknotted circles, and are opening up new challenges in algebra as well as topology. Connections of knot theory to physics often involve quantum theory, and one of the topics of this conference is quantum computing, the effort to apply the distinctive properties of quantum mechanical systems such as entanglement to obtain computational speedups that greatly exceed the limitations of current hardware. Speakers at this conference are expected to include some of the leading researchers in topological aspects of quantum computing.Some of the main topics for the planned conference include: (1) connections between knot theory and quantum computing - such as Temperley-Lieb recoupling, unitary representations of the braid group and entangled states, unitary solutions to the Yang-Baxter equations, GHZ states and extra special 2-groups, fusion algebra of Majorana fermions, (2) invariants of knots and 3-manifolds, including Khovanov homology, skein modules, and related ideas; and (3) applications of knot and link invariants to finding higher order invariants and sharper energy bounds for energy for magnetic and vorticity fields.