教育

• Ph.D.亚利桑那大学数学专业
• B.A.伯大尼路德学院数学专业
• B.A.，伯大尼路德学院，剧院

Background

上大学前, 我对人文学科很感兴趣, 我的计划是主修英语和戏剧双学位. One of the amazing things about attending a liberal arts institution is that you get to take courses in a wide sampling of fields during your first years in college, 这有时会激发你从未意识到自己拥有的兴趣! 一节通用教育的数学课(微积分I)让我看到了一个全新的世界. 我发现学习数学的内在挑战是非常刺激的, and fell in love with the beauty and sense of wonder that comes with understanding a new idea or glimpsing for the first time a new part of the mathematical landscape (incidentally, 我也喜欢在自然景观中徒步旅行).

2019年，我和丈夫都接受了为WLC服务的召唤, 上帝召唤我们大老远从法国来到这里. 我们在图森读研究生时认识的, 亚利桑那州, 然后在杰夫做博士后期间在巴黎附近待了三年. We learned the language by immersion and I finally met some of my mathematical “ancestors” who are based in the Paris area. 除了我的职业是数学教授和妻子之外，我很幸运能成为一名母亲. 我们全家都喜欢一起旅行和冒险, 在家的时候也要学会待客之道. 我们是圣. 密尔沃基的马库斯路德教会.

我喜欢信誉最好的网投平台排名教书有很多原因. Part of the mission and vision of the college is to remain faithful to the Scriptures while training students for servant leadership through the liberal arts, 这些东西 真的 告知我们每天都在做什么! I also love being at a small enough institution that I get to teach the same students at several stages of their college career, 在他们和我们在一起的时候指导他们. There is a great deal of opportunity to get to know students and tailor their education to them as individuals when the program is this size. 在类, I try to incorporate projects that give students the opportunity to think about an idea for an extended period of time, 承担起问题和解决方案的责任, 平衡个人与合作的关系, 并有效地沟通他们所理解的内容. These are skills which need to be practiced and will help prepare students for their next adventure after college, 不管是研究生院, 教学, 或者从事商业事业, 行业, 或政府. 在课堂之外，在与学生的关系中成长, I 真的 enjoy connecting them with outside opportunities like conferences and summer reSearch programs.

教学

• MAT 117 -基础统计学
• MAT 221 -微积分1
• MAT 222 -微积分II
• 常微分方程
• MAT 230 -离散数学
• MAT 421 -实分析1
• MAT 423 -复杂分析 

研究兴趣

One of the first things that intrigued me about theorem-proving in mathematics is the combination of creative and rigorous thinking which is required: creativity to try several approaches until one works, rigorous thinking to use logic and mathematical structure appropriately and to evaluate the correctness of my argument. The actual business of proving a theorem involves a cycle of these two ways of thinking: discern the problem and appropriate starting point, 考虑不同的可能方法，然后尝试一种, evaluate whether that first approach was correct or not and whether it made progress toward the desired result, then take that self-feedback and iterate the process until a correct and beautiful proof emerges. 随着时间的推移，我学到了一些数学领域的基础知识, another idea that intrigued me was the intersection of two or more of these seemingly-different areas in mathematics.

作为一名本科生，我有机会做两个研究项目. 第一个是抽象代数和计算方法的交叉. I worked with a team of peers to write computer programs that implemented already-developed theory to classify all the groups with a certain property. (在我们的抽象代数课程MAT 431中，你会学到什么是群!我的另一个研究项目是线性代数和实分析的交叉, 这个交叉点非常重要，它本身就是一个数学领域, called functional analysis (you could take a course in functional analysis during graduate school!). 在这个项目中, we studied a kind of geometry where the “points” are objects called “operators” (which are themselves generalizations of functions). 获得对问题的直觉, 我们研究了有限维的算子, 它们只是矩阵(你们会在线性代数课程中学习矩阵, 垫333). 一旦我们对运算符在特定映射下的行为有了直观的认识, then we generalized and proved the results using 技术 from analysis (you will get an introduction to the field of analysis, 我的专业, MAT 421). 长话短说, 数学专业的课程培养学生的基本思想, 技术, and rigorous thinking that opens up so many possibilities for interesting problems to solve!

My graduate work was in the intersection of analytic combinatorics (counting problems solved using analysis 技术), 离散动力系统(按一定时间间隔变化的系统), 以及可积系统(具有守恒量的系统, 比如能量守恒). My contribution is a different way of looking at certain results (elegant formulas which solve a certain counting problem, originally conjectured by physicists using the path integral formulation of quantum mechanics) and showcasing the deep mathematical structure underlying these results that seemed to just be “tricky” at first. The creative process of discovering a useful way to think about the problem included computer simulation work to visualize the time-dynamics. 严格的证明, 一旦我明白是怎么回事, included ideas that Calculus II students can understand (you’ll learn them in MAT 222) as well as properties of elliptic functions that I had to learn just to write the proofs!

I am currently interested in more broadly understanding the discrete dynamics of certain systems, 包括我毕业时的作品. A group of senior-level WLC students helped me begin investigating these systems using computer visualization. 在早期阶段, we’re looking at computer-generated pictures of the systems and comparing what happens when we change the domain of the functions, “打开”系统的一部分，这取决于它的历史, 等等....... 

我的另一个兴趣是应用数学. 这个主题本身就很美, 但正如物理学家尤金·维格纳的名言所说, mathematics is also “unreasonably effective” at explaining structures in the natural sciences, 甚至做出经验预测或指出未来的发展方向. Mathematical modeling is the process of explaining structures in the “real world” by using various tools from mathematics. A blend of creative and rigorous thinking are just as necessary for applied math as they are for theorem-proving: defining the problem, 确定假设，将问题简化得恰到好处, 找出一个数学结构，抓住问题的关键部分, 解决那个数学问题, and translating the mathematical solution back to the original problem domain are each steps in mathematical modeling that combine both modes of thinking. 

学术作品

出版物 

布朗,T., N. M. Ercolani. 2020. 统一视角下的可积映射. 可积系统与代数几何1, 剑桥大学出版社:伦敦数学学会讲义系列, 卷. 458.

林德伯格,T., N. Fieldsteel T. 伦敦,H. Tran H. Xu. 2013. 25强对称属群的分类. 休斯顿数学杂志. 39(1): 51-60.

林德伯格,T., D. Ethier,. Luttman. 2010. 一致代数与算子代数中的多项式辨识. 泛函分析年鉴. 1(1): 105-122.

选定的演讲 

统一视角下的可积映射.AMS-MAA联合数学会议, 组合结构与可积系统特别会议, 丹佛, CO; January 15, 2020.

求解递归映射枚举问题的可积动力系统方法.海报展示. Combinatorics and Interactions, Centre Internationale de Recontres Mathematiques, Marseille, France. 2017年1月10日.

通过椭圆函数的离散painlev - 1动力学.” Analysis, Dynamics, and Applications Seminar, 数学系, 亚利桑那大学. 2016年3月8日.

 组合哈密顿动力学.AMS-MAA联合数学会议, AMS可积系统专题会议, Painleve方程, 和随机矩阵, 西雅图, WA; January 6, 2016.

 随机环境中随机游走的缩放限制.” Mathematical Physics and Probability Seminar, 数学系, 亚利桑那大学. 2015年3月25日.

映射枚举与矩阵积分之间的联系.“数学科学招聘研讨会的当前思路”, 数学系, 亚利桑那大学. 2014年3月10日.

服务 

• 教务委员会
• 美国国家科学基金会审稿人
• 会议组织者SIMIODE EXPO 2022

专业的会员

• 美国数学协会
• NExT项目研究员(布朗2020年队列)