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

摘要奖：DMS 1439922，主要研究者：Mieczyslaw K. Dabkowski，Tobias Hagge，Viswanath Ramakrishna关于纽结理论及其在物理学和量子计算中的应用的会议将于2014年10月在德克萨斯大学达拉斯举行。 纽结理论是拓扑学的一个分支，它研究了一个圆在三维空间中的许多放置方式--一个激发性的问题是，一个表面上打结的圆是否真的打结了，或者它看起来是否比实际上更复杂。 目前使用和正在开发的技术已被证明能够区分打结和不打结的圆，并在代数和拓扑学中开辟了新的挑战。 纽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，即应用量子力学系统的独特特性（如纠缠）来获得大大超过当前硬件限制的计算加速。 本次会议的发言者预计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）纽结理论和量子计算之间的联系-例如Temperley-Lieb再耦合，编织群和纠缠态的酉表示，Yang-Baxter方程的酉解，GHZ态和额外特殊的2-群，融合代数的马约拉纳费米子，（2）不变量的结和3-流形，包括Khovanov同源，绞链模，和相关的想法;和（3）应用结和链接不变量，以寻找更高的订单不变量和更尖锐的能量边界的能量磁场和涡度场。

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.