REU Site: Mathematics REU at UConn

REU网站每年将有大约9名本科生参与为期10周的密集研究项目，旨在通过产生可发表的结果，会议演讲和海报来提高数学和数学金融各个领域的知识。除了研究经验，该项目还将让学生练习写作和展示他们的工作，教他们如何使用数学软件，并通过每周的系列研讨会，包括申请研究生院的研讨会，让他们接触到广泛的数学主题。学生将主要来自不授予博士学位的机构，招聘将强调数学科学领域代表性不足的群体，包括妇女、少数民族和失聪或听力障碍的人。一个主要目标是通过增加这些学生继续在这些领域进行研究生学习和/或职业的可能性，为数学和数学密集型领域的人力资源发展做出贡献。本科研究项目将涉及几个领域，包括几何和泛函分析（离散海森堡群上的泛函不等式），随机过程和遍历性（具有小随机扰动的微分和差分方程的Lyapunov指数的估计和渐近公式），分形和无序空间的分析（分形空间上的扩散过程和微分方程，包括群的极限集），概率论在数理金融中的应用。许多具体的项目涉及调查基本的例子，这些例子有望阐明理论的一些更大的部分。参与者将从事有直接应用的研究项目，例如在金融领域，或与其他科学领域有实质性联系；例如，许多分形/无序介质项目是关于可以用于模拟多孔介质和神经网络等物理结构的集上微分方程的性质，而随机项目则与数学物理中的问题密切相关。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The REU site will involve approximately 9 undergraduate students each year in intensive 10-week research projects intended to advance knowledge in various areas of mathematics and mathematical finance by producing publishable results, conference talks and posters. In addition to research experience, the program will give students practice in writing and presenting their work, teach them how to use software for mathematics and expose them to a broad range of mathematical topics through a weekly seminar series, including a workshop on applying to graduate school. Students will be drawn primarily from non-PhD granting institutions, and recruitment will emphasize under-represented groups in the mathematical sciences, including women, minorities and persons who are deaf or hard-of-hearing. A major goal is to contribute to the development of human resources in mathematics and mathematically intensive areas by increasing the likelihood that these students go on to graduate study and/or a career in these fields.Undergraduate research projects will be in several areas, including geometric and functional analysis (functional inequalities on the discrete Heisenberg group), stochastic processes and ergodicity (estimates and asymptotic formulas for Lyapunov exponents of differential and difference equations with small random perturbations), analysis on fractals and disordered spaces (diffusion processes and differential equations on fractal spaces including limit sets of groups), and applications of probability theory in mathematical finance. Many of the specific projects involve investigating basic examples that are expected to illuminate some larger part of the theory. Participants will be working on research projects that have either direct applications, e.g. in finance, or substantial connections to other areas of science; for example a number of the fractals/disordered media projects are about properties of differential equations on sets that can be used to model physical structures like porous media and neural networks, and the stochastics projects are closely linked to problems in mathematical physics.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.