# Mathematics

The Department of Mathematics offers superior MS and PhD programs. Our students consistently land spots in top PhD programs, join cutting-edge research labs, and find dynamic jobs in thriving companies.

Below, you’ll find video interviews with grad students and basic info on the program. For more details and to apply, visit the department page and BYU Graduate Studies.

## Research Areas

### Algebraic Geometry

#### Algebraic Geometry

Students in this area use both algebraic and geometric methods to study curves, surfaces, and higher-dimensional objects and their connections to other fields, such as mathematical physics.##### Areas of Emphasis

Algebraic curves, algebraic surfaces, and moduli spaces

##### Associated Faculty

Tyler JarvisWilliam E. Lang### Combinatorics and Matrix Theory

#### Combinatorics and Matrix Theory

Combinatorics is an area of discrete mathematics devoted to counting and arranging finite configurations, which often assist the analysis of algorithms and of finite (but very large and complex) physical structures.##### Areas of Emphasis

Discrete math

##### Associated Faculty

Rodney W. Forcade### Matrix Theory

#### Matrix Theory

Matrix theory is the study of two-dimensional arrays of real or complex numbers. Matrices may describe multivariate linear phenomena, or systems of equations in math, physics, chemistry, engineering, economics, computer science, and cryptography.##### Areas of Emphasis

Combinational matrix theory and graph theory

##### Associated Faculty

Wayne Barrett### Differential Equations and Dynamical Systems

#### Differential Equations and Dynamical Systems

Kening Lu, just one of the faculty members in this area, is an internationally recognized expert in infinite-dimensional dynamical systems because of his groundbreaking work on the theory of superconductivity. His recent focus has been on modifying the theory of dynamical systems so as to incorporate random effects in meaningful ways.##### Areas of Emphasis

Celestial mechanics, nonlinear partial differential equations, smooth maps on manifolds, and stochastic differential equations

##### Associated Faculty

Lennard BakkerTodd FisherChristopher P. GrantKenneth KuttlerKening LuTiancheng Ouyang### Geometric Topology and Geometric Group Theory

#### Geometric Topology and Geometric Group Theory

There are many talented and knowledgable faculty in this area, and Jessica Purcell is one of them. She was recently awarded the prestigious Sloan Research Fellowship for her substantial contributions to the field. Purcell is one of the 20 mathematicians to receive the award this year.##### Areas of Emphasis

3D manifolds, discrete conformal mapping, geometric function theory, geometric group theory, hyperbolic geometry, knot theory, low-dimensional topology, minimal surfaces, and wild topology

##### Associated Faculty

James W. CannonGregory ConnorMichael DorffDenise HalversonStephen HumphriesJessica PurcellEric SwensonDavid G. Wright### Mathematical Biology

#### Mathematical Biology

Mathematical biology research in the department focuses on physiology. Current research deals with cell motion and cell-extracellular interactions as they relate to wound healing and pattern formation in developmental processes.##### Areas of Emphasis

Dynamical systems, functional analysis, partial differential equations, and scientific computation

##### Associated Faculty

John Dallon### Numerical Analysis and Applied Mathematics

#### Numerical Analysis and Applied Mathematics

This group focuses on the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).##### Areas of Emphasis

Asymptotic methods, classical and quantum optics, wave scattering, operations research, and decision theory

##### Associated Faculty

Shue-Sum ChowScott GlasgowJeff HumpherysVianey Villamizar### Operations Research

#### Operations Research

Students in operations research study the mathematics of business management. Applications include the management of manufacturing, distribution, retailing and pricing of consumer products; the scheduling of airplane flights worldwide; quantitative analysis of financial instruments and investments; etc.##### Areas of Emphasis

Computing and information technologies; decision analysis; environment, energy, and natural resources; financial engineering; inventory theory; manufacturing; service sciences; and supply chain management

##### Associated Faculty

Robert Roundy

### Meet Amanda: Profile

Hometown: Salt Lake City, Utah

Undergraduate Degree: mathematics, University of Utah ’02

Research Area: algebraic geometry

Likes: running, reading, movies, yoga, zumba

**What are you researching?**

We are working on finding out more about the FJRW structure associated to various kinds of singularities. In particular, we are working on proving that this structure matches another structure (called the B-side structure) built around the transpose of the singularity.

**What have you discovered?**

We have discovered that for a type of singularity, called a “chain” the two structures match at the level of Frobenius algebra.

**What kind of equipment do you have access to?**

For our research project, we do most of our computing using mathematical software called Sage. We have access to a department server and a great computer lab where we can run the code we’re writing and store the latest version of our work there.

**What does your future look like?**

I have an eighteen-month-old son, so after my PhD, I will take some time off to take care of my family. When my children are older I would love to work at a university where I can mentor other students, work on research, and teach my favorite math classes!

**How do you like Provo?**

Provo has a really nice feel. There are great restaurants, live music on the weekends, and tons of activities put on by the university and the city of Provo. Best of all, the mountains are so close and so beautiful. There are a lot of great things to enjoy here!

**What do you like about BYU?**

What I love most about BYU is the people. Every faculty member and every graduate student will do anything in their power to help you succeed. There is a great support network here, full of people who really care about your success in the mathematics program as well as in your life.

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