{"id":93,"date":"2025-11-26T10:30:22","date_gmt":"2025-11-26T15:30:22","guid":{"rendered":"https:\/\/www.clarku.edu\/mathematics\/?page_id=93"},"modified":"2025-12-09T12:01:13","modified_gmt":"2025-12-09T17:01:13","slug":"student","status":"publish","type":"page","link":"https:\/\/www.clarku.edu\/mathematics\/research\/student\/","title":{"rendered":"Student research"},"content":{"rendered":"\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<p class=\"is-style-intro\">Interested in pursuing an individual research project in mathematics? We encourage you to pursue independent research under the supervision of a faculty mentor. Student research activities include:<\/p>\n\n\n\n<ul class=\"wp-block-list is-style-checkmark-list\">\n<li>Honors theses<\/li>\n\n\n\n<li>Inter- or intradisciplinary collaborative research on cutting-edge problems from a specific field of computer science<\/li>\n\n\n\n<li>Reading courses on advanced topics<\/li>\n\n\n\n<li>Qualified self-designed projects<\/li>\n<\/ul>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\"><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<h2 class=\"wp-block-heading\" id=\"h-recent-research-projects\">Recent research projects<\/h2>\n\n\n\n<div class=\"wp-block-query is-layout-flow wp-block-query-is-layout-flow\"><ul class=\"columns-2 wp-block-post-template is-layout-grid wp-container-core-post-template-is-layout-02493678 wp-block-post-template-is-layout-grid\"><li class=\"wp-block-post post-122 post type-post status-publish format-standard hentry category-student-research\">\n\n<aside class=\"wp-block-group boxout has-light-warm-gray-background-color has-background is-content-justification-left is-layout-constrained wp-container-core-group-is-layout-12dd3699 wp-block-group-is-layout-constrained\"><h3 class=\"wp-block-post-title has-small-font-size\">Differential Geometry and Brain Images<\/h3>\n\n<div class=\"entry-content wp-block-post-content is-layout-flow wp-block-post-content-is-layout-flow\">\n<p class=\"is-style-default\"><strong>Franklin Feingold<\/strong><\/p>\n\n\n<div style=\"color:inherit\" class=\"eyebrow  has-text-align-left\">Mentor: Gideon Maschler<\/div>\n\n\n\n<p class=\"has-small-font-size\">In recent years, there have been multiple studies that use techniques in differential geometry to analyze brain MRIs. Franklin\u2019s project focused on exploring some of the methods used and understanding how differential geometry can be used in modern-day medicine.<\/p>\n<\/div><\/aside>\n\n<\/li><li class=\"wp-block-post post-116 post type-post status-publish format-standard hentry category-student-research\">\n\n<aside class=\"wp-block-group boxout has-light-warm-gray-background-color has-background is-content-justification-left is-layout-constrained wp-container-core-group-is-layout-12dd3699 wp-block-group-is-layout-constrained\"><h3 class=\"wp-block-post-title has-small-font-size\">Topics in Differential Geometry<\/h3>\n\n<div class=\"entry-content wp-block-post-content is-layout-flow wp-block-post-content-is-layout-flow\">\n<p class=\"is-style-default\"><strong>Emma Kirkman-Davis, Tenzing Gurung, Wenwen Shen<\/strong><\/p>\n\n\n<div style=\"color:inherit\" class=\"eyebrow  has-text-align-left\">Mentor: Gideon Maschler<\/div>\n\n\n\n<p class=\"has-small-font-size\">Emma, Tenzing, and Wenwen all worked on topics in differential geometry. Their work focused on curves and surfaces, lengths on these, intrinsic and extrinsic curvature, and the relation between curvature and topology (i.e., global geometry, the Gauss-Bonnet Theorem).<\/p>\n<\/div><\/aside>\n\n<\/li><li class=\"wp-block-post post-120 post type-post status-publish format-standard hentry category-student-research\">\n\n<aside class=\"wp-block-group boxout has-light-warm-gray-background-color has-background is-content-justification-left is-layout-constrained wp-container-core-group-is-layout-12dd3699 wp-block-group-is-layout-constrained\"><h3 class=\"wp-block-post-title has-small-font-size\">Counting Complicated Combinatorial Sets using Markov Chain Monte-Carlo Algorithms<\/h3>\n\n<div class=\"entry-content wp-block-post-content is-layout-flow wp-block-post-content-is-layout-flow\">\n<p class=\"is-style-default\"><strong>Trung Ngo<\/strong><\/p>\n\n\n<div style=\"color:inherit\" class=\"eyebrow  has-text-align-left\">Mentor: Michael Satz<\/div>\n\n\n\n<p class=\"has-small-font-size\">Can you imagine a set that is finite but impossible to practically count even with a supercomputer? One way to build such a set is to define it as a subset all permutations of the integers 1 through N. The hard-to-count set may not be particularly large, but the parent set (which has N! elements) may well be too large for an exhaustive check-and-count approach. Monte-Carlo Markov chain methods introduce randomness to estimate the sizes and other features of such complicated combinatorial sets. Trung Ngo applied four algorithms to one such counting problem. The algorithms were implemented in Python and tested and analyzed for performance, convergence, and accuracy.<\/p>\n<\/div><\/aside>\n\n<\/li><li class=\"wp-block-post post-118 post type-post status-publish format-standard hentry category-student-research\">\n\n<aside class=\"wp-block-group boxout has-light-warm-gray-background-color has-background is-content-justification-left is-layout-constrained wp-container-core-group-is-layout-12dd3699 wp-block-group-is-layout-constrained\"><h3 class=\"wp-block-post-title has-small-font-size\">Image Processing and Drosophila Embryos<\/h3>\n\n<div class=\"entry-content wp-block-post-content is-layout-flow wp-block-post-content-is-layout-flow\">\n<p class=\"is-style-default\"><strong>Logan Bishop-Van Horn, Teodor Nicola-Antoniu<\/strong><\/p>\n\n\n<div style=\"color:inherit\" class=\"eyebrow  has-text-align-left\">Mentor: Jacqueline Dresch<\/div>\n\n\n\n<p class=\"has-small-font-size\">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. For this reason, Logan and Teodor\u2019s projects focused on creating a pipeline for processing these images, including noise and background subtraction, normalization, spatial registration, and extraction of quantitative levels of gene expression.<\/p>\n<\/div><\/aside>\n\n<\/li><li class=\"wp-block-post post-114 post type-post status-publish format-standard hentry category-student-research\">\n\n<aside class=\"wp-block-group boxout has-light-warm-gray-background-color has-background is-content-justification-left is-layout-constrained wp-container-core-group-is-layout-12dd3699 wp-block-group-is-layout-constrained\"><h3 class=\"wp-block-post-title has-small-font-size\">Topics in Functional Analysis<\/h3>\n\n<div class=\"entry-content wp-block-post-content is-layout-flow wp-block-post-content-is-layout-flow\">\n<p class=\"is-style-default\"><strong>Andrew Mezzi<\/strong><\/p>\n\n\n<div style=\"color:inherit\" class=\"eyebrow  has-text-align-left\">Mentor: Gideon Maschler<\/div>\n\n\n\n<p class=\"has-small-font-size\">Andrew worked on a project that encompassed many different topics from functional analysis: infinite-dimensional linear algebra, operators, and applications of solutions to ordinary differential equations.<\/p>\n\n\n\n<p class=\"has-small-font-size\">During the summer, Andrew was also exposed to a variety of internet resources and professional tools of the working mathematician, including the arXiv, MathSciNet, LaTeX and TeX-related editors, as well as the MathOverflow and StackExchange websites.<\/p>\n<\/div><\/aside>\n\n<\/li><li class=\"wp-block-post post-111 post type-post status-publish format-standard hentry category-student-research\">\n\n<aside class=\"wp-block-group boxout has-light-warm-gray-background-color has-background is-content-justification-left is-layout-constrained wp-container-core-group-is-layout-12dd3699 wp-block-group-is-layout-constrained\"><h3 class=\"wp-block-post-title has-small-font-size\">Designing New Evolutionary Algorithms for Parameter Estimation<\/h3>\n\n<div class=\"entry-content wp-block-post-content is-layout-flow wp-block-post-content-is-layout-flow\">\n<p class=\"is-style-default\"><strong>Mike Gaiewski<\/strong><\/p>\n\n\n<div style=\"color:inherit\" class=\"eyebrow  has-text-align-left\">Mentor: Jacqueline Dresch<\/div>\n\n\n\n<p class=\"has-small-font-size\">One of the most important steps in mathematical modeling of a biological system is fitting the parameters of your model to experimental data. There is an extremely large number of different parameter estimation algorithms available, and an important question to ask is: what parameter estimation method should be used on my particular problem? In an attempt to answer this question in the context of modeling gene regulation, Michael developed and implemented novel parameter estimation algorithms based on the principles of evolution.<\/p>\n<\/div><\/aside>\n\n<\/li><li class=\"wp-block-post post-105 post type-post status-publish format-standard hentry category-student-research\">\n\n<aside class=\"wp-block-group boxout has-light-warm-gray-background-color has-background is-content-justification-left is-layout-constrained wp-container-core-group-is-layout-12dd3699 wp-block-group-is-layout-constrained\"><h3 class=\"wp-block-post-title has-small-font-size\">Bioinformatic Analysis of Transcription Factor Binding Sites<\/h3>\n\n<div class=\"entry-content wp-block-post-content is-layout-flow wp-block-post-content-is-layout-flow\">\n<p class=\"is-style-default\"><strong>Navid Al Hossain, Regan Conrad<\/strong><\/p>\n\n\n<div style=\"color:inherit\" class=\"eyebrow  has-text-align-left\">Mentor: Jacqueline Dresch<\/div>\n\n\n\n<p class=\"has-small-font-size\">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.<\/p>\n\n\n\n<p class=\"has-small-font-size\">Navid\u2019s project focused on analyzing the correlation between the frequency of binding sites within raw sequence data and the bioinformatically predicted \u2018strength\u2019 of these binding sites. His work has been instrumental in the experimental design and continued collaboration between the Dresch group in the Mathematics and Computer Science Department, the Drewell lab in Biology, and the Spratt lab in Chemistry.<\/p>\n\n\n\n<p class=\"has-small-font-size\">Regan\u2019s project focused on analyzing bioinformatic predictions of binding sites within core promoter regions from Drosophila melanogaster to investigate potential nucleotide dependencies and improve the predictive power of these algorithms.<\/p>\n<\/div><\/aside>\n\n<\/li><li class=\"wp-block-post post-96 post type-post status-publish format-standard hentry category-student-research\">\n\n<aside class=\"wp-block-group boxout has-light-warm-gray-background-color has-background is-content-justification-left is-layout-constrained wp-container-core-group-is-layout-12dd3699 wp-block-group-is-layout-constrained\"><h3 class=\"wp-block-post-title has-small-font-size\">Our Universe as a Manifold<\/h3>\n\n<div class=\"entry-content wp-block-post-content is-layout-flow wp-block-post-content-is-layout-flow\">\n<p class=\"is-style-default\"><strong>Mateo Gomez<\/strong><\/p>\n\n\n<div style=\"color:inherit\" class=\"eyebrow  has-text-align-left\">Mentor: Amir Aazami<\/div>\n\n\n\n<p class=\"has-small-font-size\">This research project gave a rigorous introduction to understanding spaces that locally look just like our familiar space, but globally may be curved. The perfect example of this is Earth: locally it looks flat, but globally it is a sphere. In fact, our very universe itself is assumed to have this local\/global property, but being four-dimensional \u2014 three dimensions of space and one of time \u2014 we cannot \u201csee\u201d this as we can with Earth. Such spaces are called manifolds. The key question is: how does one do calculus on manifolds? How does one study their geometry, their curvature? Everything from the ground up has to be re-formulated: differentiability, vectors, the gradient, the Jacobian of a function, etc. All this needs to be understood before one can even begin to talk about geometry, or curvature, or gravity, or the universe and Einstein\u2019s equations.<\/p>\n<\/div><\/aside>\n\n<\/li><\/ul><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<h2 class=\"wp-block-heading\" id=\"h-diving-into-research\">Diving into Research<\/h2>\n\n\n\n<p>In addition to independent research projects, our department periodically provides opportunities for first-year and upper-class students to work in groups with faculty members on research projects through the course Diving into Research (MATH110, MATH 111). MATH110 Diving into Research is a year-long opportunity for first-year students to work in groups with faculty members on research projects.<\/p>\n\n\n\n<p>Recent topics have included:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Modeling re-entry communication blackout on the space shuttle caused by plasma<\/li>\n\n\n\n<li>Modeling gene regulation in a developing fruit fly embryo<\/li>\n<\/ul>\n\n\n\n<aside class=\"wp-block-group boxout has-light-yellow-background-color has-background is-content-justification-left is-layout-constrained wp-container-core-group-is-layout-12dd3699 wp-block-group-is-layout-constrained\"><div style=\"color:inherit\" class=\"eyebrow  has-text-align-left\">Please Note<\/div>\n\n\n\n<p>Groups are limited to eight students. Students earn 0.5 credits each semester, and the full year is necessary to obtain credit. May be repeated as MATH111. Neither MATH 110 nor MATH 111 count as credit towards the Math major.<\/p>\n<\/aside>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-sample-course-descriptions\">Sample course descriptions<\/h3>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>Mathematics behind Plasmas<\/summary>\n<p>Plasma televisions, plasma lights, the heat around the space shuttle and communication blackout caused by plasma, laser treatments in medicine, and production of microchips for computers are just a few applications of plasmas that became a big part of our lives. Students will learn about plasmas by developing and studying mathematical models that explain the experiments and help to obtain plasmas with certain properties.<\/p>\n\n\n\n<p><strong>Instructor: Natalia Sternberg<\/strong><\/p>\n<\/details>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>Mathematics behind Gene Regulation<\/summary>\n<p>This course will introduce the idea of mathematically modeling gene regulation in a developing organism. Students will learn how mathematicians work with biologists to design simple experiments and derive equations to model gene expression. We will also explore some of the computational approaches currently being implemented in modern biology, including bioinformatics, data processing, and parameter estimation. This one-year course will be an interactive experience for students interested in learning more about the interface of mathematics, computer science, and molecular biology.<\/p>\n\n\n\n<p><strong>Instructor: Jacqueline Dresch<\/strong><\/p>\n<\/details>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>Geometry<\/summary>\n<p>Geometry is a branch of mathematics which closely relies on visual intuition. As such, parts of it are accessible even without obtaining extensive preliminary background, while still being deep and thought-provoking. In this seminar-style class, we explore the subject from a number of different perspectives, thus demonstrating its richness. Among the possible topics chosen are Projective and Differential Geometry, and symmetries and their relation to the mathematical concept of a group. Our guiding principle for these choices will be their accessibility to direct geometric intuition and imagination. 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.<\/p>\n\n\n\n<p><strong>Instructor: Gideon Maschler<\/strong><\/p>\n<\/details>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\"><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Interested in pursuing an individual research project in mathematics? We encourage you to pursue independent research under the supervision of a faculty mentor. Student research activities include: Recent research projects Diving into Research In addition to independent research projects, our department periodically provides opportunities for first-year and upper-class students to work in groups with faculty [&hellip;]<\/p>\n","protected":false},"author":15,"featured_media":0,"parent":16,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-93","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v28.1 (Yoast SEO v28.5) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Student research | Mathematics | Clark University<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.clarku.edu\/mathematics\/research\/student\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Student research\" \/>\n<meta property=\"og:description\" content=\"Interested in pursuing an individual research project in mathematics? 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