Heegaard Floer homology and torus bundles
Heegaard Floer homology is a topological invariant i.e. it is a way of measuring topological complexity.
Read about Heegaard Floer homologyOur department has offered experiences in math research to undergraduates from all over the country for over four decades. Students are selected to participate in research projects during the summer with individual faculty mentors, investigating a wide variety of topics. The National Science Foundation supports the program via a Research Experiences for Undergraduates (REU) grant.
The REU program is ideal for students who want the opportunity to work closely with a faculty mentor on a math research project. The experience emphasizes close relationships with faculty advisors in small groups of 1-3 students.
During the admission process with we try to match each student with an appropriate project and advisor. The faculty advisor will be able to send suggestions for background reading prior to the start of the program.
The REU program unofficially begins with a reception hosted by the math department. At this event you are able meet other participants, as well as the faculty mentors.
During the first week of the program, you are given an orientation to Swain Hall Library, home to an extensive collection of math books and journals. Students are also given a tour of available computer facilities.
Throughout the eight weeks of this summer program, students meet privately with their faculty advisors several times per week. The first few weeks are dedicated to helping you understand the details of your particular project. During the middle weeks, you work full-time on the project. The last two weeks are spent preparing both a written and oral report communicating your results. All along the way, the faculty mentor provides assistance and encouragement.
REU students are given a dedicated seminar room in which to study and socialize. At least once a week, faculty mentors give accessible lectures on topics of current research interest in mathematics. A graduate student provides an introduction to the LaTeX typesetting system and serves as a consultant for preparation of the written report.
During the last week, students each give a lecture presentation about their own work. The written reports that all participants are required to complete are bound together into a single volume that is duplicated and distributed to students and faculty mentors. Although there is no requirement to do so, you are also encouraged to submit your research paper for publication.
One of the most important aspects of the REU program is student-to-student interaction. For many participants this may be the first opportunity to get to know others with comparable mathematical interest and ability. All students live together a single dormitory on campus, and are encouraged to participate in several organized social events. Each group usually develops its own unique character, often organizing some of its own activities.
If you are interested in the REU program, take some time to read the research project descriptions here. They will give you a sense of the scope of the experience.
Heegaard Floer homology is a topological invariant i.e. it is a way of measuring topological complexity.
Read about Heegaard Floer homologyFor a curve c in Rn, its convex hull is the smallest convex set containing c. There are a number of interesting questions one can ask about the relationship of a curve c to its convex hull.
Read about Convex Hulls of Closed CurvesThis project is suitable for a student with strong computational skills and a keen interest in partial differential equations from fluid dynamics.
Read about vertical averaged velocityWhen computers carry out human-level reasoning, they do it in a number of ways.
Read about Interference in Natural LanguageSuppose M is a closed manifold which can be cut open along a codimension 1 submanifold.
Read about manifolds and TQFTsHomotopy Type Theory is a new development that establishes surprising connections between logic, algebra, geometry, topology, computer science, and physics.
Read about Homotopy Type TheoryIndiana University has a large and active mathematics faculty that enjoys and supports research work with undergraduates. The breadth of mathematical interests in the department provides students in the program with a firsthand view of the richness of the field.
Students have access to a first-rate mathematics research library located next door in Swain Hall. The library subscribes to approximately 450 research periodicals many of which can be accessed on-line anywhere on campus. The mathematics librarian is experienced in conducting bibliographic instruction tailored to undergraduate mathematics students.
Students also have access to state-of-the-art computer facilities. Mathematical packages such as Maple, Mathematica, and Matlab are all readily available on a variety of platforms.
A seminar room in Rawles Hall becomes the "REU Room" in the summer and is available all day to REU students as a place to study and discuss mathematics.
During the eight weeks, particiants will
Most of our applicants have completed courses in one-variable calculus, a course in multivariable calculus, and one or more courses such as linear algebra, differential equations, and probability and statistics. Many of our applicants have completed at least one course in abstact algebra or a course in real analysis.
No, only US citizens and permanent residents are eligible.
No, only US citizens and permanent residents are eligible.
No, only students who have not received their undergraduate degree are eligible.
Yes--send them to Mandie McCarty, amm3308@indiana.edu
Per NSF guidelines: Undergraduate student participants supported with NSF funds in either REU Supplements or REU Sites must be citizens or permanent residents of the United States or its possessions. An undergraduate student is a student who is enrolled in a degree program (part-time or full-time) leading to a baccalaureate or associate degree. Students who are transferring from one college or university to another and are enrolled at neither institution during the intervening summer may participate. High school graduates who have been accepted at an undergraduate institution but who have not yet started their undergraduate study are also eligible to participate. Students who have received their bachelor's degrees and are no longer enrolled as undergraduates are generally not eligible to participate.
Formally, no. However, our program is competitive, and most of our applicants have GPAs in excess of 3.5 on a 4.0 scale.
The National Science Foundation maintains a comprehensive list of REU sites.
Be sure to read the Frequently Asked Questions and Application page carefully.
Letters of recommendation may be emailed to Mandie McCarty, amm3308@indiana.edu.
If you have further questions, you may send an email to
Chris Connell, Director
Indiana University Mathematics REU program
connell@indiana.edu