# Computer Science

## PIMS-SFU 20th Anniversary Celebration: Nataša Pržulj - Data Driven Medicine

The Pacific Institute for the Mathematical Sciences (PIMS) was founded in 1996, and Simon Fraser University is a founding member. The members of PIMS now include all the major Canadian research universities west of Ontario, as well as universities in Washington and Oregon. Please join us to celebrate 20 years of productive collaboration, with a lecture by SFU alumna and professor at UCL Nataša Pržulj on Data Driven Medicine followed by a reception.

We are faced with a flood of molecular and clinical data. Various biomolecules interact in a cell to perform biological function, forming large, complex systems. Large amounts of patient-specific datasets are available, providing complementary information on the same disease type. The challenge is how to model and mine these complex data systems to answer fundamental questions, gain new insight into diseases and improve therapeutics. Just as computational approaches for analyzing genetic sequence data have revolutionized biological and medical understanding, the expectation is that analyses of networked “omics” and clinical data will have similar ground-breaking impacts. However, dealing with these data is nontrivial, since many questions we ask about them fall into the category of computationally intractable problems, necessitating the development of heuristic methods for finding approximate solutions.

We develop methods for extracting new biomedical knowledge from the wiring patterns of large networked biomedical data, linking network wiring patterns with function and translating the information hidden in the wiring patterns into everyday language. We introduce a versatile data fusion (integration) framework that can effectively integrate somatic mutation data, molecular interactions and drug chemical data to address three key challenges in cancer research: stratification of patients into groups having different clinical outcomes, prediction of driver genes whose mutations trigger the onset and development of cancers, and re-purposing of drugs for treating particular cancer patient groups. Our new methods stem from network science approaches coupled with graph-regularised non-negative matrix tri-factorization, a machine learning technique for co-clustering heterogeneous datasets.

## Sparsity, Complexity and Practicality in Symbolic Computation

Modern symbolic computation systems provide an expressive language for describing mathematical objects. For example, we can easily enter equations such as

into a computer algebra system. However, to determine the factorization

with traditional methods would incur huge expression swell and high complexity. Indeed, many problems related to this one are provably intractable under various reasonable assumptions, or are suspected to be so. Nonetheless, recent work has yielded exciting new algorithms for computing with sparse mathematical expressions. In this talk, we will attempt to navigate this hazardous computational terrain of sparse algebraic computation. We will discuss new algorithms for sparse polynomial root finding and functional decomposition. We will also look at the "inverse" problem of interpolating or reconstructing sparse mathematical functions from a small number of sample points. Computations over both traditional" exact and symbolic domains, such as the integers and finite fields, as well as approximate (floating point) data, will be considered.

## Foundational Methods in Computer Science

## The Mathematics of Lattice-based Cryptography

TBA

## High dimensional expanders and Ramanujan complexes

Expander graphs have played, in the last few decades, an important role in computer science, and in the last decade, also in pure mathematics. In recent years a theory of "high-dimensional expanders" is starting to emerge - i.e., simplical complexes which generalize various properties of expander graphs. This has some geometric motivations (led by Gromov) and combinatorial ones (started by Linial and Meshulam). The talk will survey the various directions of research and their applications, as well as potential applications in math and CS. Some of these lead to questions about buildings and representation theory of p-adic groups.

We will survey the work of a number of people. The works of the speaker in this direction are with various subsets of { S. Evra, K. Golubev, T. Kaufman, D. Kazhdan , R. Meshulam, S. Mozes }

## High Dimensional Expanders and Ramanujan Complexes

Expander graphs have played, in the last few decades, an important role in computer science, and in the last decade, also in pure mathematics. In recent years a theory of "high-dimensional expanders" is starting to emerge - i.e., simplical complexes which generalize various properties of expander graphs. This has some geometric motivations (led by Gromov) and combinatorial ones (started by Linial and Meshulam). The talk will survey the various directions of research and their applications, as well as potential applications in math and CS. Some of these lead to questions about buildings and representation theory of p-adic groups.

We will survey the work of a number of people. The works of the speaker in this direction are with various subsets of { S. Evra, K. Golubev, T. Kaufman, D. Kazhdan , R. Meshulam, S. Mozes }

## Sparse - Dense Phenomena

The dichotomy between sparse and dense structures is one of the profound, yet fuzzy, features of contemporary mathematics and computer science. We present a framework for this phenomenon, which equivalently defines sparsity and density of structures in many different yet equivalent forms, including effective decomposition properties. This has several applications to model theory, algorithm design and, more recently, to structural limits.

## Cryptography: Secrets and Lies, Knowledge and Trust

## How Does Google Google?

**Abstract:**We all Google. You may even have found this talk by Googling. What you may not know is that behind the Google's and other search engines is beautiful and elegant mathematics. In this talk, I will try to explain the workings of page ranking and search engines using only rusty calculus.

**Bio:**Dr. Margot Gerritsen is the Director of the Institute for Computational and Mathematical Engineering at Stanford University. She is also the chair of the SIAM Activity group in Geoscience, the co-director and founder of the Stanford Center of Excellence for Computational Algorithms in Digital Stewardship, and the director of Stanford Yacht Research. She has been appointed to several prestigious positions, including Magne Espedal Professorship at Bergen University, Aldo Leopold Fellow, Faculty Research Fellow at the Clayman Institute and she is also a Stanford Fellow. She is the editor of the Journal of Small Craft Technology and an associate editor of Transport in Porous Media. We are delighted to have Dr. Gerritsen participate in the Mathematics of Planet Earth series.

## How Does Google Google? The Math Behind the Internet

An alternative version of this lecture presented at the University of Calgary is also available.