REU Site: Discrete Random Structures

这一为期三年的“离散随机结构”项目将使首席研究员阿南特·戈博勒能够通过每年带领八名学生进行一系列当代和高水平的研究工作来巩固他对本科生研究的参与，每一项研究工作都旨在使参与者相信，他们可以以有意义的方式为数学领域的发展做出贡献。团队成员的问题，虽然发源于组合学、数论、图论、几何学、算法和分子生物学等领域，但将具有随机性--因此将通过使用当代概率和经典分析中的方法来寻求解决方案。参与者将在全国范围内寻找后选出，并将于夏季在东田纳西州立大学度过两个月。根据首席调查员在过去12年中的记录，可以预测，学生研究人员将平均每人研究两个问题，要么单独工作，要么以两人或两人以上的小组形式工作，并能够在其中至少一项工作上取得重大进展。学生们的发现将在国家会议上公布，例如年度AMS/MAA会议，或在精心挑选的概率/组合会议上。与以往一样，我们将尽一切努力将学生的论文提交给高水平的期刊，以便有可能发表。我们希望从广泛的学院和大学中挑选学生，并完全致力于大力招收女性、少数族裔和残疾学生。

This three-year project "Discrete Random Structures" will enable the Principal Investigator, Anant Godbole, to consolidate his involvement with undergraduate research by leading eight students each year in a series of contemporary and high-level research endeavours, each designed to convince the participants that they may contribute in a meaningful way to the development of the field of mathematics. The team-members' problems, while emanating in areas such as combinatorics; number theory; graph theory; geometry; algorithms; and molecular biology, will have a stochastic flavor -- so that solutions will be sought through the use of methods in contemporary probability and classical analysis. The participants will be selected after a nationwide search, and will spend two months at East Tennessee State University during the summer. Based on the Prinicipal Investigator's track record over the last twelve years, it can be predicted that the student researchers will each work on an average of two problems, either individually or in teams of two or more, and be able to make significant progress on at least one of these endeavors. The students' findings will be presented at national meetings such as the Annual AMS/MAA Meeting, or at a carefully selected Probability/Combinatorics conference. As in the past, every effort will be made to submit the students' papers to high-level journals for possible publication. We expect to select students from a broad range of colleges and universities, and are totally committed to the vigorous recruitment of women, minorities and disabled students.