莉莎特雷诺

简要介绍

自1993年以来, 我曾在布林茅尔学院任教, 在那里我非常喜欢做研究和教学生. My mathematical research is very visually motivated: I enjoy looking at some basic shapes of space, 例如打结的线圈或圆球, and seeing how this shape can evolve under mathematical equations that have deep roots in classical physics.  我在整个课程中教授各种各样的课程, from calculus at the 100-level to graduate courses in topology at the 500-level.

我获得了博士学位.D. in 数学 in 1992 from the State University of New York at Stony Brook; Dusa McDuff was my research advisor. I pursued postdoctoral work at the Mathematical Sciences 研究 Institute in 加州大学伯克利分校, CA, 在斯坦福大学, 在巴黎亨利·庞加莱研究所的埃米尔·博雷尔中心, 法国和剑桥的艾萨克·牛顿研究所, 英格兰.  I have spent sabbaticals at the Mathematical Sciences 研究 Institute (MSRI), 加州大学伯克利分校, CA, 高级研究所(IAS), 普林斯顿大学, NJ, 以及美国数学学会(AIM), 帕洛阿尔托, CA.  I was on sabbatical for the 2022-2023 academic year and spent the fall as a 研究 Professor for the program 花同伦理论 在加州伯克利的MSRI/SLMath.

研究

我的研究兴趣是几何和拓扑学. 更具体地说, 我研究的是辛拓扑和接触拓扑, where we study many questions similar to those studied in topology except under additional constraints given by the geometry of a symplectic or contact structure. I am particularly interested in studying the flexibility and rigidity of Lagrangian submanifolds of standard symplectic spaces and of Legendrian submanifolds of contact spaces.  A motivating question is to understand the boundary between flexibility (when the Lagrangian or Legendrian submanifold behaves like their smooth counterparts) and rigidity (when the behavior of these geometric submanifolds is more restrictive). 我喜欢探索柔性和刚性现象之间的界限. 

我是这个周刊的协办人 数学协议 (Philadelphia Area (联系) 拓扑结构) seminar and of the monthly PATCH (Philadelphia Area 拓扑结构: 联系 & 双曲线)研讨会.  

多年来, I have worked on a variety of problems including the symplectic camel problem, 辛的同源性, 辛包装, Legendrian结, 和拉格朗日共轭. I have employed a variety of techniques including J-holomorphic curves, 生成函数族, 还有凸面.  下面你可以找到我的研究出版物的列表.

研究出版物

• Obstructions to Reversing Lagrangian Surgery in Lagrangian FillingsO .卡波维拉-塞尔.Legout, N.Limouzineau, M.墨菲，E.潘，Y.特拉华州的特雷纳(Traynor).，出现在J. 辛几何、 http://arxiv.org/abs/2207.13205
• 勒Legendrian环面和电缆链接道尔顿，J.埃特纳，J.特拉华州的特雷纳(Traynor).，出现在J. 辛几何、 http://arxiv.org/abs/2107.12323ArXiv
• 拉格朗日协数的构造布莱克威尔，S.乐高N. Leverson C.Limouzineau, M.Myer, Z.潘，Y.佩齐门蒂，S.， Suárez, L.S.特拉华州的特雷纳(Traynor). in  研究 Directions in in Symplectic and 联系 Geometry and 拓扑结构 (Association for Women in 数学 Series 27), 施普林格2021; http://arxiv.org/abs/2101.00031
• An Introduction to the World of Legendrian and Transverse Knots洛杉矶，特雷纳.，《推荐全球十大博彩公司排行榜》，CRC出版社，2021.
• The Relative Gromow Width of Lagrangian Cobordisms between Legendrians萨布洛夫，J. 和路易斯安那州的特雷纳.，辛几何学报，Vol . 18, No . 1, 217-250, 2020.
• The Minimal Length of a Lagrangian Cobordism between Legendrians萨布洛夫，J. 和路易斯安那州的特雷纳., 数学选集新系列，23:1419-1448,2017.
• legendrin节之间的不可定向Lagrangian协边 阿,Capovilla-Searle. 和路易斯安那州的特雷纳.，《推荐全球十大博彩公司排行榜》，第285卷，第2期. 2, 319--334. 2016; DOI 10.2140 / pjm.2016.285.319.  
• Lagrangian Cobordisms via Generating Families: Construction and Geography, 资产阶级,F.萨布洛夫，J. 和路易斯安那州的特雷纳.，几何拓扑，Vol . 15, 2439-2477, 2015.
• Obstructions to Lagrangian Cobordisms between Legendrians via Generating Families, Sabloff J. 和路易斯安那州的特雷纳., Algebraic and Geometric 拓扑结构, Vol 13, issue 5, 2733-2798, 2013.
• 手术解开了大量的Legendrian链接， B. Boranda L. 其次,年代. 燕,涉及, 第六卷，No. 3, 273-299, 2013.
• Obstructions to the Existence and Squeezing of Lagrangian Cobordisms, Sabloff J. 和路易斯安那州的特雷纳.，拓扑与分析学报，第2卷，第2期. 2, 203 - 232, 2010.
• 平面拉格朗日算子片上的偏序 艾斯曼,P.利马，美国.萨布洛夫，J.特拉华州的特雷纳(Traynor)., Journal of Fixed Point Theory and Applications, Volume 3, Number 2, 431-447, September 2008.
• 解结的Legendrian链的族不变量的生成， 约旦、J. 和路易斯安那州的特雷纳., 代数与几何拓扑，第6卷，763-807,2006.
• legendris Solid-Torus链接， L Ng,. 和路易斯安那州的特雷纳., Journal of 辛几何、 Volume 2, Number 3, 411-443, 2004.
• 生成Legendrian连杆的函数多项式洛杉矶，特雷纳.，几何与拓扑，卷. 5(2001)论文号. 23页，719- 760页.
• 环面共切束的辛填料马利，F. M.马斯特兰奇里，J. 和路易斯安那州的特雷纳.，《推荐全球十大博彩公司排行榜》第9卷第2期. 3, 2000, 435-455.
• 理性缠结的传奇式分层洛杉矶，特雷纳.，《推荐全球十大博彩公司排行榜》，第7卷第1期. 5, 1998, 659-700.
• 勒让德圆形螺旋链洛杉矶，特雷纳., Mathematical Proceedings of the Cambridge Philosophical Society, Vol 122, 1997, pp. 301 - 314.
• 辛包装结构洛杉矶，特雷纳.，《推荐全球十大博彩公司排行榜》，第42卷第1期. 2, 1995, 411 - 429.
• 通过生成函数的辛同调洛杉矶，特雷纳.，几何与泛函分析，卷. 4, No. 6, 1994, pp. 718 - 748.
• 数学杂志，卷. 72, No. 3, 1993年12月，页. 573 - 594.
• 四维辛骆驼及其相关结果McDuff, D. 和路易斯安那州的特雷纳.，辛几何，D. 萨拉蒙(ed.), London Mathematical Society Lecture Note Series, Cambridge Univ. 出版社，1993年，页. 169 - 182.

教学

我非常喜欢在布林莫尔教书. 我通过课程讲授各种课程.  最近, 我教过多元微积分, 向高等数学的过渡, 拓扑结构, 复杂的分析, 微分拓扑, 及高级会议.  自COVID爆发以来, I have started to teach many of my classes in a flipped style: I record approximately 30 minute videos for students to watch before coming to class, and then during class we work through worksheets to help the material sink in.  我所有的课堂资料都在Moodle上.

与学生一起研究

我喜欢做研究, and I truly enjoy doing research with both undergraduate and graduate students.  I have had 6 students complete their PhD under my direction; see 数学家谱. I have also supervised 8 MA theses and many undergraduate honors thesis projects. Some honors projects have been tied to my own research in symplectic and contact topology, 但我也指导过学生做结理论的项目, 博弈理论, 最优控制, 以及与计算机科学相关的几何主题.

专业服务及外展

I have held a number of leadership positions in national professional organizations: in 2000-2003, I served as Member-At-Large of the American Mathematical Society (AMS) Council, 2008-2012年, I served on the Executive Committee of the Association for Women in 数学 (AWM). 

I truly enjoy working with  young mathematicians to help them find their own way in the mathematical community. Throughout my career, I have enthusiastically organized activities around professional development.  在布林茅尔, I have organized seminars for graduate students on numerous  topics including how to effectively give a talk and how to write abstracts, 奖助金, CVs,  教学和多样性陈述.  我已经三次成为国家的导师 拓扑学学生工作坊 在佐治亚理工学院举办.  I have often been on career/advice panels for younger mathematicians during conferences. 

I have also welcomed opportunities to organize programs that promote women in mathematics: for many years, 我参与了 国际会计协会妇女与数学项目 (普林斯顿大学). 我也是一个团队的领导者 女性几何1 (在加拿大班夫)和 几何上的女性2 (墨西哥瓦哈卡). 我也是这个项目的组织者和项目负责人 辛几何与接触几何与拓扑学中的女性，于2019年7月在ICERM举行.  在布林茅尔. 

更多关于我服务的细节可以在我的 CV.

额外的利益

我喜欢花时间与我的家人:我的丈夫, 保罗·欣茨, and I have been together since our undergraduate days at Beloit College, 我们还有个儿子, 艾美特, who is starting his second year of college at Colgate University.  I enjoy a variety of outdoor activities including hiking, biking, and canoeing and kayaking.  Since the pandemic started, I have been hooked on noontime walks + audio books. On a daily basis, I enjoy doing YouTube workouts:  I am a big fan of Heather Robertson's channel.  我也喜欢烹饪和吃好吃的食物.  For many years, we have been members of a great CSA near our home: Pennypack Farm.  他们有大量的有机蔬菜可供选择, 大多数时候，时令沙拉是我的午餐选择.  我也喜欢好酒、巧克力和软冰淇淋!