# Stanford Undergraduate Research Institute in Mathematics

## 2019 Information

**Application: **The application for Summer 2019 is now closed.

**Program Dates:** 10 Weeks: Monday, June 24 through Friday, August 30, 2019

**Eligibility:**

- Current Stanford undergraduate students.
- Students receiving support during the Summer must be enrolled in undergraduate studies for both the preceding Spring quarter and the following Fall quarter.

**Financial Support:** Participants receive a $7500 stipend for 10 weeks of full time research.

**Contact:** surim_program@stanford.edu

### Program Goals

At SURIM, students will be exposed to questions that are of interest in current mathematics, as well as the research and exploration aspects that accompany such questions. With their mentor’s assistance, students will study the prerequisite materials to understand their program’s topic and will then participate in exploration of their questions about the subject. *See below for examples of project topics from previous years.*

The emphasis will be on self-discovery of examples and properties. In addition to learning new mathematics and gaining experience in mathematical research, students will practice presenting research in a seminar environment, learn to typeset mathematical research results using LaTeX, use various software packages to explore mathematics, and have valuable interactions with mathematics faculty and graduate students.

### Program Format

Most students will be divided into groups depending on their mathematical interest and background. Each of these groups will work closely with graduate students. Other students may want to work one-on-one with a faculty member, and should have some idea of their project at the time they apply.

### A Typical Week

SURIM is a full-time program for 10 weeks.

There will be a couple of formal meetings with mentors each week. At the start, the mentors will lay out the beginning of the project, and the groups will decide how best to begin. Each group will prepare presentations to the entire institute each week, giving status reports to their peers working on different problems. Remember: Communicating difficult ideas is essential to doing and teaching mathematics!

Much of the week will be spent working individually and in groups, and in informal discussions with mentors.

There will be roughly two additional events per week. Some will be introductions to research tools (from writing with LaTeX to the use of various software packages). Others will be lectures from researchers in academia and industry on what research is actually about—how it is done, how to do it, and what it is like. The SURIM group will also have access to various classrooms during the summer.

*To get a better idea of SURIM’s week-to-week structure, and for examples of faculty talks, click here to see the 2018 calendar.*

### Examples of Project Topics from Previous Years

*Zeros of modular forms and theta series from Brandt matrices*(Number Theory, Group Project 2017)*The Erdős–Ginzburg–Ziv constant for finite abelian groups*(Combinatorics, Group Project 2017)*Bernoulli convolutions of random variables*(Probability, Group Project 2017)*Schubert calculus on the Grasmannian*(Algebraic Geometry, Individual Project 2017)*Persistent homology of molecular rotation projections*(Applied Topology, Individual Project 2017)*Mapping class groups and Lefschetz fibrations*(Topology and Geometry, Group Project 2016)*The congruent number problem*(Number Theory, Group Project 2016)*The cohomology of toric varieties*(Algebraic Geometry, Group Project 2016)*Front propagation in reaction-diffusion equations*(Applied Mathematics, Group Project 2015)*The cap set problem*(Combinatorics, Individual Project 2016)*The topology of random spaces*(Topology and Geometry, Group Project 2015)