On Tuesday, August 15th, the Math Department hosted their Annual Symposium on Mathematics & Computation event. At the event, several prizes were handed out to honour some exceptional research work by our Math Students.

## Symposium on Mathematics & Computation Poster Prizes

**Graduate Winners**

## Adam DYCK - Winner

**Supervisor: **J Jedwab, Mathematics

**Title: ***The Realisability of γ-Graphs*

**Undergraduate Winners**

## Joseph LUCERO - Winner

**Supervisor:** L Chindelevitch, Computing Science

**Title:*** Inferring Maximum Likelihood Phylogenies from MIRU-VNTR Data*

## Aniket MANE - Runner Up

**Supervisor:** C Chauve, Mathematics

**Title: ***A tractable variant of the Single Cut or Join distance with duplicated genes*

## Matthew KING-ROSKAMP - Runner Up

**Supervisor:** B Adcock, Mathematics

**Title: ***Optimal Sampling Strategies for Compressive Imaging*

## Undergraduate Research Prizes for 2016

## Anyi (Casie) BAO (Supervisor B Adcock)

Anyi’s (Casie’s) research project involved the development and analysis of a novel compressed sensing algorithm for correcting for corrupted measurements in the field of Uncertainty Quantification. This is a well-known, but challenging issue that had not been addressed previously by the community. Beside the development of the algorithm, a significant part of Casie’s work was devoted to its theoretical analysis. She was able to show that in some cases, a constant fraction of the measurements can be corrupted, but that the algorithm can account for this with surprisingly little deterioration in recovery error. Casie presented this work at the 2017 SIAM Computational Science & Engineering conference, and - in collaboration with her supervisor and researchers from the University of Utah and Sandia National Labs – she developed it into a journal paper which is currently under review. The core mathematical content of the paper is predominantly Casie’s work.

## Charlotte TRAINOR (Supervisors N Ilten & M Mishna)

Charlotte carried out the research project "Classification of Fano divisorial polytopes" during the summer of 2016 as part of an NSERC USRA. She has turned the results of this research into an excellent honours thesis she can be proud of, as well as a forthcoming research article coauthored with Professors Ilten and Mishna.

The fundamental objects Charlotte was investigating are "divisorial polytopes", a quasi-combinatorial object generalizing the notion of lattice polytopes. These objects have relevance in algebraic geometry, as they correspond to an extremely useful class of geometric objects known as complexity-one T-varieties. It is an important open problem to understand all complexity-one T-varieties with the special property of being ``Fano'', that is, having positive Ricci curvature. Charlotte's research sheds light on this problem: she establishes some important and previously unknown bounds on the structure that such Fano complexity-one T-varieties possess. Furthermore, her work establishes a foundation for an approach towards effectively classifying all such varieties. As such, it is an important contribution at the interface of algebraic geometry and combinatorics.

Throughout the research and writing process, Charlotte demonstrated the ability to work independently, and generate interesting ideas of her own. Her excellence in writing and presentation is reflected in her receipt of first prize in the 2016 poster competition at SFU's Symposium on Mathematics and Computation. Likewise, her penchant for learning and hard work led her to win a Governor General's Silver Medal in 2017, an award given annually to only two undergraduates at SFU.

## William YOLLAND (supervisor J Jedwab)

William’s project was to determine whether or not there is a difference set in a specific nonabelian group of order 256. This was the final piece of information needed to complete a five-year international collaboration whose goal was to settle the existence question for all 56,092 groups of order 256. William knew at the outset that the existence question for the final group could in principle be resolved by computer, but the search size of 2^{64} was computationally infeasible. William devised a series of ingenious numerical experiments to constrain the search space, and thereby succeeded in producing an example of a difference set in the required group. He then developed a novel recursive construction that completely explains the existence of a difference set in this final group, using sequences with special correlation properties. As a direct result of his work, an international workshop will take place in 2018 to discuss the completion of the collaboration and its implications. The leaders of the collaboration are also preparing a monograph in which William’s new method will play a crucial role.