Conference on Lie Theory and Its Applications

李理论及其应用会议。智力价值：近年来，李群的表示理论受到了极大的关注。 这反映了围绕李理论的思想的深度及其应用的广度。 然而，表示论只是李理论所涉及的数学的一小部分。 Lie theory的思想在几何学和物理学中有影响力？Nolan Wallach等人利用不变量理论量化量子态纠缠的重要结果是他们在物理学中的最新应用之一，并促进了不变量理论的新发展。 在纯数学中，诺兰·沃勒克和他的合作者们发现了组合数学的重要应用，并为自守形式理论提供了现代数论的中心点观点，这一观点正在成为李群理论思想的主要应用。更广泛的影响：李群理论的这些最新结果表明了一个会议的潜在影响，该会议强调了李群理论对数学和物理其他领域的适用性。 我们计划开始会议有两个临时会谈，针对学生和非专家，在支持的目标，扩大参与数学科学的成员代表性不足的群体，并提供一个基础的研究会谈上最美丽和令人兴奋的工作，目前正在做的高级和初级数学家。 通过与UCSD女性数学协会分会共同举办一个或多个讲座，我们希望吸引来自UCSD研究生的相当多样化的人口成员出席，以及来自全国各地和世界各地的参与者。

Conference on Lie Theory and Its Applications. Intellectual merit: In recent years, the representation theory of Lie groups has received a great deal of attention. This is a reflection of the depth of the ideas surrounding Lie theory and the consequent breadth of its applications. Representation theory is, however, only a small part of the mathematics touched by Lie theory. Lie theoretic ideas are influential in geometry and physics?important results by Nolan Wallach and others on quantifying entanglement of quantum states using invariant theory constitute one of their newest applications in physics, and have prompted new developments in invariant theory. In pure mathematics, Nolan Wallach and his collaborators have found significant applications to combinatorics, and to the theory of automorphic forms provides a central point of view in modern number theory that is becoming a leading application of Lie theoretic ideas.Broader impact: These recent results in Lie theory demonstrate the potential impact of a conference emphasizing the applicability of Lie theory to other areas of mathematics and physics. We plan to begin the conference with two expository talks aimed at students and non-experts, in support of the goal of broadening participation in the mathematical sciences by members of under-represented groups, and to provide a foundation for research talks on the most beautiful and exciting work currently being done by both senior and junior mathematicians. By co-hosting one or more of the talks with the UCSD chapter of the Association for Women in Mathematics we expect to attract attendance from members of the quite diverse population of UCSD graduate students, in addition to participants from around the country and the world.