# Mathematics

## Theory Reduction, Algebraic Number Theory, and the Complex Plane

## Counting Problems for Elliptic Curves over a Fixed Finite Field

## Managing Patients with Chronic Conditions

## Automorphism groups in algebraic geometry

## Efficient Compression of SIDH Public Keys

## Prison Guard’s Dilemma: Optimal Inmate Assignment by Multi-Objective MILO

## Distinguished models of intermediate Jacobians

## 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.

## Jacobian versus Infrastructure in Real Hyperelliptic Curves

Hyperelliptic curves of low genus are good candidates for curve-based cryptography. Hyperelliptic curves comes in two models: imaginary and real. The existence of two points at inﬁnity in real models makes them more complicated than their imaginary counterparts. However, real models are more general than the other model, every imaginary hyperelliptic curve can be transformed into a real curve over the same base ﬁeld Fq , while the reverse process requires a larger base ﬁeld.

Real hyperelliptic curves have not received as much attention by the cryptographic community as imaginary models, but more recent research has shown them to be suitable for cryptography. Real models admit two structures, the Jacobian (a ﬁnite abelian group) and the infrastructure (almost group just fails associativity). In this talk, we explain these two structures and compare their arithmetic based on some recent research. We show that the Jacobian makes a better performance in the real model. We also conﬁrm our claim with some numerical evidence for genus 2 and 3 hyperelliptic curves.

For more information on this event, please see the event webpage