学生研究及项目

马特奥·戈麦斯 (now a 3-2 combined plan student at Columbia University), Sherman-Fairchild Fellow; summer research 2017
导师:教授. 阿米尔Aazami

这个研究项目给了一个严谨的介绍，让我们了解当地看起来就像我们熟悉的空间, 但从全球来看，可能是弯曲的. The perfect example of this is earth: locally it looks flat, but globally it is a sphere. 事实上, our very universe itself is assumed to have this local/global property, 但作为四维空间——三维空间和一维时间——我们不能像在地球上那样“看到”这一点. 这样的空间称为流形. The key question is: how does one do calculus on manifolds? How does one study their geometry, their curvature? E.g., the shortest distance between two points on earth can no longer be a straight line, 因为地球是弯曲的, so how does one answer such questions now? 困难的任务是, given the “local/global” relationship that manifolds possess, one cannot rely solely on coordinates: one must think, 可以这么说, coordinate-independently. 事实上, everything from the ground up has to be re-formulated: differentiability, 向量, 梯度, 函数的雅可比矩阵, 等. All this needs to be understood before one can even begin to talk about geometry, 或曲率, 或重力, or the universe and Einstein’s equations.

迈克Gaiewski （现在是博士）.D. student in Applied Math at UConn), Sherman-Fairchild Fellow; summer research 2017 and 2018
导师:教授. 杰奎琳Dresch

生物系统数学建模中最重要的步骤之一是将模型的参数拟合到实验数据中. 有非常多不同的参数估计算法可用, 一个重要的问题是：在我的特定问题上应该使用什么样的参数估计方法? In an attempt to answer this question in the context of modeling gene regulation, Michael基于进化原理开发并实现了新的参数估计算法.

安德鲁Mezzi, Sherman-Fairchild Fellow; summer research 2018
导师: 教授. 吉迪恩Maschler

Andrew参与了一个项目，该项目涵盖了功能分析中的许多不同主题：无限维线性代数, 运营商, and applications of solutions to ordinary differential equations.

在夏天, 安德鲁还接触了各种互联网资源和专业工具的工作数学家, 包括arXiv, MathSciNet, LaTeX和tex相关的编辑器, as well as the MathOverflow and StackExchange websites.

艾玛Kirkman-Davis2017年夏季阅读课程
丹增高隆2017年夏季阅读课程
了雯雯沈2016年荣誉论文
导师:教授. 吉迪恩Maschler

Emma, Tenzing, and Wenwen all worked on topics in differential geometry. Their work focused on curves and surfaces, 这些的长度, intrinsic and extrinsic curvature, and the relation between curvature and topology (i.e., global geometry, the Gauss-Bonnet Theorem).

纳维德·侯赛因, Sherman-Fairchild Fellow; summer research 2016 and 2017
里根康拉德, Sherman-Fairchild Fellow; summer research 2017 and 2018
导师:教授. 杰奎琳Dresch

Predicting the location of protein binding sites within a genome is a difficult task, but is an integral part of furthering our understanding of gene regulation. Traditional methods involve PWMs (position weight matrices), 它依赖于一个潜在的假设，即TF结合位点内的每个核苷酸都独立于其他核苷酸. 最近, 已经实现的模型放宽了这一假设，包括对邻近核苷酸的依赖.e. a string of contiguous nucleotides).

Navid的项目侧重于分析原始序列数据中结合位点的频率与这些结合位点的生物信息学预测“强度”之间的相关性. 他的工作在实验设计和数学与计算机科学系Dresch小组之间的持续合作中发挥了重要作用, 德威尔生物实验室, 以及斯普拉特化学实验室.

Regan的项目专注于分析黑腹果蝇核心启动子区域结合位点的生物信息学预测，以研究潜在的核苷酸依赖性，并提高这些算法的预测能力.

洛根·毕晓普·范·霍恩，定向学习，2016春季
特奥多尔Nicola-Antoniu2016年暑期调研
导师:教授. 杰奎琳Dresch

Using raw data from microscope images in modeling gene expression levels presents the researcher with many challenges; one must be able to remove any extraneous information from the image and be able to compare images prepared and taken from different embryos on different days. 出于这个原因, Logan and Teodor’s projects focused on creating a pipeline for processing these images, including noise and background subtraction, 归一化, 空间注册, and extraction of quantitative levels of gene expression.

Trung非政府组织 (now an application developer at Morgan Stanley), honors thesis 2018
导师:教授. 迈克尔Satz

你能想象一个集合是有限的，但即使用超级计算机也无法计数吗? 构建这样一个集合的一种方法是将其定义为整数1到N的所有排列的子集. 例如, 我们难以计数的集合可能是所有这样的排列满足一些约束，包括这些整数和它们所在的位置. 取决于约束条件, the hard-to-count set may not be particularly large, 而是有N的父集! elements) may well be too large for an exhaustive check-and-count approach. 蒙特卡罗马尔可夫链方法引入随机性来估计这类复杂组合集的大小和其他特征. Trung非政府组织 applied four algorithms to one such counting problem. The algorithms were implemented in Python and tested and analyzed for performance, 收敛, 和准确性.

富兰克林·法因戈尔德 (now a project manager at Stanford University), honors thesis 2015
导师:教授. 吉迪恩Maschler

近年来, 已经有很多研究使用微分几何技术来分析大脑核磁共振成像. 富兰克林的项目重点是探索一些常用的方法，并了解如何将微分几何应用于现代医学.

First-year students in the 深入研究 course,  2014-15
导师: 教授. 纳塔莉亚斯特恩伯格

等离子电视, 等离子灯, the heat around the space shuttle and communication blackout caused by plasma, 医学上的激光治疗, 为计算机生产微芯片只是等离子体的几个应用，它已成为我们生活的重要组成部分. 学生将通过发展和研究数学模型来了解等离子体，这些模型可以解释实验并帮助获得具有某些特性的等离子体而无.  

等离子电视, 等离子灯, the heat around the space shuttle and communication blackout caused by plasma, 医学上的激光治疗, 为计算机生产微芯片只是等离子体的几个应用，它已成为我们生活的重要组成部分. 学生将通过发展和研究数学模型来了解等离子体，这些模型可以解释实验并帮助获得具有某些特性的等离子体. (导师:N.斯特恩伯格)

本课程将介绍在生物发育过程中对基因调控进行数学建模的概念. 学生将学习数学家如何与生物学家一起设计简单的实验并推导方程来模拟基因表达. 我们还将探讨一些目前在现代生物学中正在实施的计算方法, 包括生物信息学, 数据处理, 参数估计. 这一年的课程将是一个互动的经验，为学生有兴趣了解更多的数学界面, 计算机科学, 分子生物学. (导师:J.Dresch)

几何 is a branch of mathematics which closely relies on visual intuition. 像这样, parts of it are accessible even without obtaining extensive preliminary background, while still being deep and thought-provoking. 在这个研讨式的课堂上, we explore the subject from a number of different perspectives, 从而体现了它的丰富性. Among the possible topics chosen are Projective and Differential 几何, and symmetries and their relation to the mathematical concept of a group. 我们对这些选择的指导原则将是它们对直接几何直觉和想象力的可访问性. The need for prior mathematical background will be kept at a minimum level. We will also be employing computer graphics and related software for visual exploration. The main purpose is to have fun while appreciating geometry. (导师:G.Maschler)