Undergraduate Student Research Awards (USRA) Award Recipients

 

Undergraduate Student Research Awards (USRA) NSERC Award Holders

The Natural Sciences and Engineering Research Council of Canada (NSERC) subsidizes student researchers to support eligible professors in specific research projects. These undergraduates get hands-on research experience in an academic setting, preparing them for graduate research or careers.

2019 NSERC Award Holders

Suemin Lee Dr Paul Tupper Extinction of Variant Spellings
Vincent Nguyen Dr Razvan Fetecau Math Models of Crime in Metro Vancouver
Tabriz Popatia Dr Jonathan Jedwab Combinatorial Problems Arising in Digital Communications
Danielle Rogers Dr Matt Devos Representing Graphs
Khalil Shivji Dr Michael Monagan The Dixon Matrix and Computing its Determinant
YingDong Sun Dr Michael Monagan The Dixon Matrix and Computing its Determinant

Suemin Lee: Extinction of Variant Spellings

Many words English words have multiple spellings, for example "humor" and "humour". Historically this was even more common before English spelling was largely standardized. In this project students will use Google Ngram viewer to examine the prevalence of different spellings versus time, and in particular examine the extinction of spellings. Models for the dynamics of spelling prevalence will be fit to the data and assessed. 

 

Requirements: Dynamical systems or statistics

Vincent Nguyen: Math Models of Crime in Metro Vancouver

This is a joint project with Prof. Patricia Brantingham from the SFU School of Criminology. The goal is to develop mathematical models to understand and predict crime patterns in Metro Vancouver. A significant amount of crime data is available from the Vancouver Police Department, so there is an opportunity to test the models against real data. The modelling will likely involve differential equations, both theoretical and numerical.  

 

Possible topics for a project include: 

 

* Impact of clustering of bars/pubs in entertainment areas

* Metro stations as hot spot generators

* The impact of road type of crime clusters (like the peaking at intersections along major arteries)

* The time flow of different crime types through the court system in BC based on the seriousness and/ or the complexity of the legal case

* How number and timing of appearances changes in courts depending on the size and location of provincial courts

 

Students are expected to have taken and performed well in MATH 310 and MACM 316. No previous background in Criminology is required.

Tabriz Popatia: Combinatorial Problems Arising in Digital Communications

The project will involve the study of combinatorial problems arising in digital communications.  See http://people.math.sfu.ca/~jed/research.html for background on the general area of research, and http://people.math.sfu.ca/~jed/students.html for examples of previous USRA projects.

Requirements: Students should have completed MACM 201 (Discrete Mathematics II), and preferably have some programming experience. However, the most important attributes are enthusiasm, persistence, and a willingness to learn new skills.

Danilelle Rogers: Representing Graphs

Graphs are ubiquitous as models for real world networks and data, and an important real-world problem is to find “nice” ways of drawing or representing graphs that help to illuminate their structure.  In this project we will be utilizing some concepts from linear algebra and algebraic graph theory to represent graphs in 3 dimensional space.  Then we will be using a 3D printer to actually print and realize these graphs! 

This project has a mixture of theory and computing and will have up to 3 USRA students in addition to some graduate student involvement.  I will give a series of lectures on the subject to provide background and students will use Maple and some other computing software to work with graphs. 

Khalil Shivji: The Dixon Matrix and Computing its Determinant

Given a system of n polynomial equations in n unknowns x1, x2, ..., xn, the determinant of the Dixon matrix is a polynomial in x1 where the variables x2, ..., xn have been eliminated.  We are interested in
polynomial systems of equations which also involve one or more parameters corresponding to physical constants like lengths and masses. In this case the Dixon matrix will be a matrix of polynomials
in x1 and the parameters.

The project is firstly, to study how to construct the the Dixon matrix, secondly, to investigate why it often has a block structure, and thirdly, to investigate how to compute it's determinant. Computing determinants of matrices of polynomials is an interesting problem. We aim to develop a fast method that interpolates the parameters in the determinant from monic images in x1.

The project is suitable for one or two students.

Requirements: Students must have taken a course in linear algebra and also a first course in either abstract algebra or number theory (MATH 340 or MATH 342 at SFU) where you have seen modular arithmetic. Also, students must have taken a second programming course in either C or C++ or Java or Python.  We will use Maple and C for computational experiments.  No prior knowledge of Maple is required.

Yiongdong Sun: The Dixon Matrix and Computing its Determinant

Given a system of n polynomial equations in n unknowns x1, x2, ..., xn, the determinant of the Dixon matrix is a polynomial in x1 where the variables x2, ..., xn have been eliminated.  We are interested in
polynomial systems of equations which also involve one or more parameters corresponding to physical constants like lengths and masses. In this case the Dixon matrix will be a matrix of polynomials
in x1 and the parameters.

The project is firstly, to study how to construct the the Dixon matrix, secondly, to investigate why it often has a block structure, and thirdly, to investigate how to compute it's determinant. Computing determinants of matrices of polynomials is an interesting problem. We aim to develop a fast method that interpolates the parameters in the determinant from monic images in x1.

The project is suitable for one or two students.

Requirements: Students must have taken a course in linear algebra and also a first course in either abstract algebra or number theory (MATH 340 or MATH 342 at SFU) where you have seen modular arithmetic. Also, students must have taken a second programming course in either C or C++ or Java or Python.  We will use Maple and C for computational experiments.  No prior knowledge of Maple is required.

2018 NSERC Award Holders

RECIPIENT SUPERBVISOR PROJECT
Wes Chorney
Dr Nathan Ilten
Tangent Cones in Truncated Power Series Rings
Evgueni Filatov Dr Nils Bruin
Computational arithmetic geometry: Twists of the Burkhardt Quartic
Einar Gabbassov           
Dr Ben Adcock
Deep Learning Techniques for Inverse Problems in Imaging
Ryan Konno
Dr Nilima Nigam
The role of architecture and regionalization of tissue in muscle mechanics
Ryan Mehregan
Dr Michael Monagan
Counting and Generating Irreducible polynomials and solving…
Megan Monkman
Dr Nilima Nigam The role of architecture and regionalization of tissue in muscle mechanics
Cassidy Tam
Dr Nilima Nigam The role of architecture and regionalization of tissue in muscle mechanics

Wes Chorney: Tangent Cones in Truncated Power Series Rings

Given an ideal I ⊂ C[x1, . . . , xn], its tangent cone is the ideal generated by inf for all f ∈ I, where inf is the lowest degree part of f. Seen geometrically, the tangent cone cuts out limits of secant lines between 0 and p, as p approaches 0 in the variety V (I) defined by the ideal I — hence the name. There are essentially two algorithms (due to Mora and Lazard) which can be used to calculated the tangent cone of an ideal. They can be seen as relatives of Buchberger’s algorithm, which calculates a Gr¨obner basis for an ideal. The key difference is that the “term order” underlying the tangent cone is not well-ordered. The goal of this project is to adapt the known algorithms to quickly calculate the tangent cone up to a fixed degree d for ideals of the form I + hx1, . . . , xni d . This has important applications in deformation theory and the lifting of syzygies. In addition to theoretical work, the student will be expected to implement their algorithm in the computer algebra system Macaulay2. In carrying out this project, the student will be exposed to a variety of ideas from algebraic geometry and commutative algebra.

Evgueni Filatov: Computational arithmetic geometry: Twists of the Burkhardt Quartic

Recent work [*] has exhibited a very explicit correspondence between a certain quartic threefold and sextic polynomials with very particular properties. It also found that the two classical models of this quartic do NOT define the same variety over Q. There is a very interesting connection with a so-called "field of definition obstruction" here that can be examined computationally.

Prerequisites: a reasonably algebra knowledge; preferably also algebraic geometry; willingness to use computational tools to explore mathematical problems. The exact research topic can changed depending on the interests and skills of the qualifying candidate.

[*] Nils Bruin, Brett Nasserden, Arithmetic aspects of the Burkhardt quartic threefold, ArXiv preprint arXiv:1705.09006, (2017)

Einar Gabbassov: Deep Learning Techniques for Inverse Problems in Imaging

In the last few years, deep neural networks have outperformed state-of-the-art methods in challenging computer-vision tasks such as classification and segmentation. More recently, they have also shown promising results when applied to inverse problems in computer imaging such as deblurring, denoising, super-resolution, and the efficient reconstruction of medical images from linear measurements (e.g., Magnetic Resonance Imaging and Computer Tomography). 

Instead of fixing a statistical prior (such as the sparsity of the image) to regularize the inverse problem, these new approaches seek to learn the reconstruction algorithm itself by taking advantage of a preliminary learning phase where the neural network is optimized based on a large dataset of training examples.

In this project, we will explore these new techniques and compare them with classical tools for inverse regularization, with the aim of understanding how to fully exploit their potential for inverse problems in computer imaging. 

Requirements: Candidates should have a strong mathematical background.  Analysis, linear algebra, numerical analysis and Matlab experience are essential.  Previous knowledge of optimization and image processing are beneficial, but not strictly necessary.

Ryan Konno: The role of architecture and regionalization of tissue in muscle mechanics

The study of movement in mammals has a long history, but somewhat surprisingly, one of the most popular mathematical models of muscle mechanics continues to be an 80-year-old description of a 1-D muscle fibre due to Hill. In this project, the student will be involved in an ongoing project to develop a fully 3-D mathematical model for muscle. Concretely, the student will learn about a new nonlinear elasticity model for muscle; design computational experiments, and run these on an existing mathematical software. We are particularly interested in understanding the role of muscle density and connective tissues in locomotion. We would also like to examine what happens during Parkinson's disease. The work will be joint with Professor James Wakeling in the BPK department, and a nice opportunity to explore mathematical applications in physiology.

Ryan Mehregan: Counting and Generating Irreducible polynomials and solving…

 

We are looking for a student, either a mathematics major or a computing major who likes algebra and programming, to work on one or both of the following projects.

1: We would like to count the number of and find algorithms for generating irreducible polynomials of certain forms. For example, for a given degree d, how many irreducible trinomials are there of the form x^d + a x + b over a finite field of size q? If we need one such polynomial, what's the best way to get one?

2: The main step to factoring a multivariate polynomial uses Hensel lifting which must solve several polynomial diophantine equations. These are equations of the form  

  sigma1 A1 + sigma2 A2 + ... + sigman An = C

where the A1, A2, ..., An and C are given polynomials and we want to solve for the simgas.  We are developing algorithms based on polynomial evaluation and interpolation which can be parallelized.

Requirements: Students should have taken a first course in either algebra or number theory (MATH 340 or MATH 342 at SFU) and have some programming experience  in either C or C++ or Python. We will use Maple and C and Cilk C (a parallel version of C)  for experiments.  No parallel programming knowledge is needed.

Megan Monkman: The role of architecture and regionalization of tissue in muscle mechanics

The study of movement in mammals has a long history, but somewhat surprisingly, one of the most popular mathematical models of muscle mechanics continues to be an 80-year-old description of a 1-D muscle fibre due to Hill. In this project, the student will be involved in an ongoing project to develop a fully 3-D mathematical model for muscle. Concretely, the student will learn about a new nonlinear elasticity model for muscle; design computational experiments, and run these on an existing mathematical software. We are particularly interested in understanding the role of muscle density and connective tissues in locomotion. We would also like to examine what happens during Parkinson's disease. The work will be joint with Professor James Wakeling in the BPK department, and a nice opportunity to explore mathematical applications in physiology.

Cassidy Tam: The role of architecture and regionalization of tissue in muscle mechanics

The study of movement in mammals has a long history, but somewhat surprisingly, one of the most popular mathematical models of muscle mechanics continues to be an 80-year-old description of a 1-D muscle fibre due to Hill. In this project, the student will be involved in an ongoing project to develop a fully 3-D mathematical model for muscle. Concretely, the student will learn about a new nonlinear elasticity model for muscle; design computational experiments, and run these on an existing mathematical software. We are particularly interested in understanding the role of muscle density and connective tissues in locomotion. We would also like to examine what happens during Parkinson's disease. The work will be joint with Professor James Wakeling in the BPK department, and a nice opportunity to explore mathematical applications in physiology.

2018 KEY Big Data NSERC Award Holders

RECIPIENT SUPERVISOR PROJECT
Robyn Hearn             
Dr Michael Monagan      
Counting and Generating Irreducible Polynomials and Solving Polynomial Diophantine              Equations

Robyn Hearn: Counting and Generating Irreducible Polynomials and Solving Polynomial Diophantine Equations

We are looking for a student, either a mathematics major or a computing major who likes algebra and programming, to work on one or both of the following projects.

1: We would like to count the number of and find algorithms for generating irreducible polynomials of certain forms. For example, for a given degree d, how many irreducible trinomials are there of the form x^d + a x + b over a finite field of size q? If we need one such polynomial, what's the best way to get one?

2: The main step to factoring a multivariate polynomial uses Hensel lifting which must solve several polynomial diophantine equations. These are equations of the form  

  sigma1 A1 + sigma2 A2 + ... + sigman An = C

where the A1, A2, ..., An and C are given polynomials and we want to solve for the simgas.  We are developing algorithms based on polynomial evaluation and interpolation which can be parallelized.

Requirements: Students should have taken a first course in either algebra or number theory (MATH 340 or MATH 342 at SFU) and have some programming experience  in either C or C++ or Python. We will use Maple and C and Cilk C (a parallel version of C)  for experiments.  No parallel programming knowledge is needed.

2017 NSERC Award Holders

RECIPIENT

SUPERVISOR

PROJECT

FILATOV, Eugene

Dr Marni Mishna

Random Generation of Maps

Mark Forteza

Dr Cedric Chauve

Graph-theoretic Methods for Improving Clustering Genes in Families

Gabriel Henderson  

Dr Michael Monagan     

Sparse Polynomial Interpolation

Matthew Lynn

Dr Paul Tupper

Tight Spans for Metric Structures

Matthew King-Roskamp

Drs Adcock & Brugiapaglia

Optimal Sampling Strategies for Compressive Imaging

Maksym Neyra-Nesterenko

Dr Paul Tupper

Tight Spans for Metric Structures

2016 NSERC Award Holders

RECIPIENT

SUPERVISOR

PROJECT

Michael Bartram

Dr Nathan Ilten

Linear Subspaces of Special Hypersurfaces

Wes Chorney
Dr Karen Yeats
The c_2 Invariant of Graphs w/ Recursive Structure

Jesse Elliot  

Dr Michael Monagan

Analysis of Algorithms and Computing with Polynomials

Sean La

Dr Cedric Chauve

Math and Comp Epidemiology

Matthew Lynn

Dr Karen Yeats

Examples Satisfying Higher Renormalization Group Equations

Charlotte Trainor

Drs Ilten and Mishna

Classification of Almost-Toric Fano Manifolds

William Yolland

Dr Jonathan Jedwab

Combinatorial Problems Arising in Digital Communication

2015 NSERC Award Holders

RECIPIENT

SUPERVISOR

PROJECT

Kelvin Chan

Dr Veselin Jungic

Generalizations of van der Waerden's Theorem and the Large Sets Conjecture

Darshan Crout

Drs Fetecau & Wittenberg

Opinion Dynamics

Matthew King-Roscamp

Dr Ben Adcock

Approximating High-Dimensional Functions with Compressed Sensing

Conor McCoid

Dr Manfred Trummer

High-Order Methods for Differential Equations

Gregory Maxedon

Dr Karen Yeats

A Graph Theoretic Understanding of an Algebro-Geometric Condition

Charlotte Trainer

Dr Jonathan Jedwab

Combinatorial Problems Arising in Digital Communications

Charles Turo

Dr Nathan Ilten

Degenerations to Stanley-Reisner Schemes

Undergraduate Student Research Awards (USRA) VPR Award Holders

SFU’s Vice-President Research (VPR) funds awards for undergraduates working on a major research project with an eligible university professor. For 16 weeks these students are engaged in full-time research, preparing them to succeed in graduate programs and research environments beyond their undergraduate degree.

2019 VPR Award Holders

Hyukho Kwon Dr Imin Chen The LWE Problem
Taku Marwendo Dr Amarpreet Rattan Results in Lattice Path Enumeration
Reuben Rauch Drs Manfred Trummer and JF Williams High-Order Numerical Methods for Differential Equations
Samantha Zimmerman Drs Sandy Rutherford and Tamon Stephen Optimizing Delivery of Health care to Vulnerable People in Vancouver
Zhe Zu Dr Paul Tupper Fraisse Limit…

Hyukhi Kwon: The LWE Problem

The LWE (learning with errors) problem involves finding a vector s, given that s lies on a list of hyperplanes known only up to some error. The objective of this project is study and give an independent exposition of a result of Regev [1] which shows that if there exists an efficient algorithm that solves LWE, then there exist an efficient quantum algorithm that approximates the decision version of the shortest vector problem.  This hardness result, and later variants such as RLWE, are often used to motivate approaches to post-quantum cryptography and homomorphic encryption.

[1] On Lattices, Learning with Errors, Random Linear Codes, and Cryptography, Oded Regev, Journal of the ACM 56(6), article 34, 2009.

Taku Marwendo: Results in Lattice Path Enumeration

The idea of counting lattice paths in the plane subject to constraints is a fairly old problem, yet continues to be a fruitful area of modern mathematical research.  In the case of exact enumerative results, the goal is to find and solve a problem by learning about the past results and seeing what kind of results and constraints can be modified to find new, interesting, tractable and/or applicable results.

Requirements: The student would be expected to read some background literature in this area and, together with the adviser, would hone in on a particular problem.  MACM 201 and a third year algebra course is essential.

Reuben Rauch: High-Order Numerical Methods for Differential Equations

This project investigates spectral methods and radial basis function methods for solving differential equations with a focus on introducing adaptivity. The initial focus will be on singularly perturbed boundary value problems. To numerically resolve boundary layers we will look at various transformation techniques, and we will try to find the optimal parameters in those transformations via an adaptive process. We will also explore the application of spectral methods for differential-difference equations (equations with a delay).

The other issue to be addressed is the treatment of boundary conditions. In particular, we will investigate the use of rectangular differentiation matrices in standard spectral and radial basis function methods. This approach allows for a more systematic treatment of boundary conditions.

Samantha Zimmerman: Optimizing Delivery of Health care to Vulnerable People in Vancouver

This project will combine data analysis and operations research to improve the delivery of health care services to vulnerable people in Vancouver, many of whom have mental health and substance use issues. Data on patient visits, staffing, services offered, and opening hours at a community health centre will be analysed. This data will be linked to emergency department visits at inner-city hospitals. Vancouver Community Health Services at Vancouver Coastal Health will provide data and expert advice for the project.

Key questions to be addressed are:

1. What are the optimal health centre service delivery hours for scheduled and walk-in patients to minimize emergency department visits resulting from gaps in primary care?

2. What are the optimal medical staff schedules to minimize wait times for walk-in patients, subject to staffing, budgetary, and booked patient constraints?

These questions will be addressed using a hybrid optimization approach, which combines integer linear programming with simulation-based optimization. The focus of the research will be on developing a heuristic hybrid optimization approach, which is able to deal with a large number of constraints and multiple objectives. The ultimate goal is a computationally efficient algorithm that is implemented on real data for the community health centre.

Requirements: This project is well-suited to a student interested in operations research, applied optimization, and simulation modelling. Familiarity with integer linear programming, simulation, and Python are important. Good communication skills are essential, because the student will be expected to participate in meetings and consultations at Vancouver Community Health Services.

 

Zhe Xu: Fraisse Limit…

Fraisse limit (if it exists) is a metric space that contains all members of the class as subspaces and has some other homogeneity properties.

2018 VPR Award Holders

RECIPIENT SUPERVISOR
PROJECT
Randy Bergman
Dr Ben Adcock
Deep Learning Techniques for Inverse Problems in Imaging
Marius Ticu Dr Imin Chen
The LWE Problem
Rihan Yao
Drs Adcock & Brugiapaglia
Stochastic collocation methods for uncertainty quantification of physical model
Samantha    Zimmerman
Drs Sandy Rutherford &  Williams
Mathematical Modelling of HIV Testing, Treatment, and Care

Randy Bergman: Deep Learning Techniques for Inverse Problems in Imaging

In the last few years, deep neural networks have outperformed state-of-the-art methods in challenging computer-vision tasks such as classification and segmentation. More recently, they have also shown promising results when applied to inverse problems in computer imaging such as deblurring, denoising, super-resolution, and the efficient reconstruction of medical images from linear measurements (e.g., Magnetic Resonance Imaging and Computer Tomography). 

Instead of fixing a statistical prior (such as the sparsity of the image) to regularize the inverse problem, these new approaches seek to learn the reconstruction algorithm itself by taking advantage of a preliminary learning phase where the neural network is optimized based on a large dataset of training examples.

In this project, we will explore these new techniques and compare them with classical tools for inverse regularization, with the aim of understanding how to fully exploit their potential for inverse problems in computer imaging. 

Requirements: Candidates should have a strong mathematical background.  Analysis, linear algebra, numerical analysis and Matlab experience are essential.  Previous knowledge of optimization and image processing are beneficial, but not strictly necessary.

Marius Ticu: The LWE Problem

The LWE (learning with errors) problem involves finding a vector s, given that s lies on a list of hyperplanes known only up to some error.

 

The objective of this project is to study and give an independent exposition of a result of Regev [1] which shows that if there exists an efficient algorithm that solves LWE, then there exist an efficient quantum algorithm that approximates the decision version of the shortest vector problem.  This hardness result, and later variants such as RLWE, are often used to motivate approaches to post-quantum cryptography and homomorphic encryption.

 

[1] On Lattices, Learning with Errors, Random Linear Codes, and Cryptography, Oded Regev, Journal of the ACM 56(6), article 34, 2009.

Rihan Yao: Stochastic collocation methods for uncertainty quantification of physical model

Uncertainty is ubiquitous in science and engineering.  Uncertainty quantification is the process of deriving quantitative characterizations of uncertainties in both computational models and real-world applications.  One of the most common problems in UQ focuses on determining the parameter dependence of solutions of parametrized systems of PDEs.  Although this can be recast as the problem of approximating a high-dimensional function from sampled data, a major challenge lies with the fact that the amount of data is often small, since gathering data is time-consuming.  Efficient uncertainty quantification requires techniques from not only approximation theory, but also numerical analysis, statistics, and sparse recovery.

This project will investigate a recent class of techniques for high-dimensional approximation based on sparse approximation.  Its focus will firstly be on the improvement of these techniques, through, for instance, the design of novel adaptive sampling procedures, and the development of learning procedures to reduce the dimensionality.  It will also consider their application to parametric PDEs.

Requirements: Analysis, numerical analysis, linear algebra and Matlab experience are essential.  Optimization is beneficial but not mandatory.

Samantha Zimmerman: Mathematical Modelling of HIV Testing, Treatment, and Care

This project will combine mathematical modelling of the HIV epidemic in Vancouver with operations research analysis of HIV testing, engagement in care, and retention in care. The models are defined as systems of ordinary differential equations.  Data for the project has been provided by Vancouver Coastal Health and the BC Centre for Excellence in HIV/AIDS. Key questions to be addressed are:

1.      What are the optimal allocations of resources across treatment programs to minimize HIV incidence, morbidity, and mortality?

2.      What are the optimal allocations of public health resources between treatment and testing programs to minimize HIV incidence, morbidity, and mortality?

 

These questions can be framed as “black box” optimization problems, in which the objective function is obtained by numerically solving the ordinary equation models. However, these optimization problems are computationally challenging, because the objective function is nonconvex and high-dimensional. The focus of this research will be on developing parallelized code for solving these problems using metaheuristic optimization methods. The computations will be done on Compute Canada’s high-performance computing cluster at SFU.

Requirements: This project is well-suited for a student interested in operations research and applied optimization. Experience with Matlab and familiarity with concepts from differential dynamical systems, especially in the context of diseases models would be useful.

2017 VPR Award Holders

RECIPIENT SUPERVISOR PROJECTS
AOKI, Yusuke Dr Paul Tupper
Gronov-Hausdorff Distances for Diversities
FEIJOO, Claudio                         
Dr David Muraki                                                                              Computation of Fluid Models for Atmospheric Science
MONKMAN, Megan
Dr Marni Mishna Random Generation of Maps
SUTTON, Hannah
Dr Nilima Nigam
Optimizing the Lowest "Sloshing" Eigenvalues

2016 VPR Award Holders

RECIPIENT

SUPERVISOR

PROJECT

Anya (Casie) Bao

Dr Ben Adcock

Solving a PDE in 100 Dimensions

Kelvin Chan

Dr Luis Goddyn

3-D Rendering and Printing of Combinatorially Described Graph Embeddings

Wes Chorney

Dr Karen Yeats

The c_2 Invariant of Graphs w/ Recursive Structure

Matthew King-Roskamp

Dr Petr Lisonek

Set Partitions in Vector Spaces

Maksym Neyra-Nesterenko

Dr Karen Yeats

Examples Satisfying Higher Renormalization Group Equations

Ningxin Wei

Dr Weiran Sun

Boundary Layer Models for Kinetic Equations

Alexander (Sasha) Zotine

Dr Nils Bruin

Computation of Monodromy and Period Matrices of Complete Riemann Surfaces

2015 VPR Award Holders

RECIPIENT

SUPERVISOR

PROJECT

Adriano Arce

Dr Michael Monagan

 

Reid Constable      

Dr Paul Tupper

Classification of Four-Point Diversities

Laura Gutierrez Funderburk

Dr Luis Goddyn

Computer Exploration of Thrackable Graphs

Hao Zhuang

Dr Michael Monagan

Algorithms for Computing with Polynomials

Alexander Zotine

Dr Nathan Ilten

Determinantal Complexity of Cubic Polynomials

Undergraduate Student Research Awards (USRA): Charles Allard USRA

The Charles Allard USRA funds awards for undergraduates working on a major research project with an eligible university professor. This award is rotated between science faculties with one department offering the award each year. For 16 weeks these students are engaged in full-time research, preparing them to succeed in graduate programs and research environments beyond their undergraduate degree.

2018 Charles Allard USRA Holders

RECIPIENT SUPERVISOR PROJECT
Matthew Lynn           Dr Paul Tupper       
Gromov-Hausdorff Distance for Metric Stuctures

Undergraduate Student Research Awards (USRA): Departmental USRA

The Department of Math funds awards for undergraduates working on a major research project with an eligible university professor. For 16 weeks these students are engaged in full-time research, preparing them to succeed in graduate programs and research environments beyond their undergraduate degree.

2019 Departmental USRA Holders

Federico Firoozi                 
Dr Amarpreet Rattan                                
Results in Lattice Path Enumeration                             
     

Federico Firoozi: Results in Lattice Path Enumeration

The idea of counting lattice paths in the plane subject to constraints is a fairly old problem, yet continues to be a fruitful area of modern mathematical research.  In the case of exact enumerative results, the goal is to find and solve a problem by learning about the past results and seeing what kind of results and constraints can be modified to find new, interesting, tractable and/or applicable results.

Requirements: The student would be expected to read some background literature in this area and, together with the adviser, would hone in on a particular problem.  MACM 201 and a third year algebra course is essential.