# Seminars, Colloquia, and Special Events

A list of upcoming and past events

## Dr Quan Long

**Depart****ment of Mathematics and Statistics
Colloquium Series 2020-2021**

**Opening Lecture**

**Thusday September 17**

**Dr Quan Long
Department of Biochemistry & Molecular Biology
Cumming School of Medicine
University of Calgary**

**kTWAS: Integrating Kernel Machine with Feature Selections for Genotype-Phenotype Association Mapping**

The power of genotype-phenotype association mapping studies increases greatly when contributions from multiple variants in a focal region are meaningfully aggregated. Currently, there are two popular categories of variant aggregation methods. Transcriptome-wide association studies (TWAS) represent a category of emerging methods that select variants based on their effect on gene expressions, providing pretrained linear combinations of variants for downstream association mapping. In contrast, kernel methods such as SKAT model genotypic and phenotypic variance using various kernel functions that capture genetic similarity between subjects, allowing non-linear effects to be included. From the perspective of machine learning, these two methods cover two complementary aspects of feature engineering: feature selection/pruning, and feature modeling. Thus far, no thorough comparison has been made between these categories, and no methods exist which incorporate the advantages of TWAS and kernel-based methods. In this work we developed a novel method called kTWAS that applies TWAS-like feature selection to a SKAT-like kernel association test, combining the strengths of both approaches. Through extensive simulations, we demonstrate that kTWAS has higher power than TWAS and multiple SKAT-based protocols, and we identify novel disease-associated genes in WTCCC genotyping array data and MSSNG (Autism) sequence data. The source code for kTWAS and our simulations are available in our GitHub repository (https://github.com/theLongLab/kTWAS)

## Dr. Renate Scheidler

**Depart****ment of Mathematics and Statistics
Colloquium Series 2020-2021**

**Thursday September 24**

**Dr Renate Scheidler
Department of Mathematics and Statistics**

**Faculty of Science**

**University of Calgary**

Is it possible to arrange the integers 1, 2, … , n in a circle such that any two adjacent entries sum to a square? Cube? Fibonacci number? What if the word sum is changed to difference? Or the square, cube, Fibonacci number restriction is replaced by some other permissible finite set of values? If such arrangements are possible, how many are there? Are there infinitely many? Richard Guy loved these types of questions which live at the interface between number theory and combinatorics and sound like simple brain teasers, but for which coming up with proofs is frequently extremely difficult if not outright impossible.

Our protagonist in this talk is an (a,b)-difference necklace, which is a circular arrangement of the first n non-negative integers such that the absolute difference of any two neighbours takes on one of two possible values (a,b). We prove that such arrangements almost always exist for sufficiently large n, and provide explicit recurrence relations for the cases (a,b) = (1,2), (1,3), (2,4) and (1,4). Using the transfer matrix method from graph theory, we then prove that for any pair (a,b) – and in fact for any finite set of two or more difference values – the number of such arrangements satisfies a linear recurrence relation with fixed integer coefficients.

This talk is accessible to a general audience; all “proofs” are by picture. No knowledge of number theory or graph theory is required. This work began in summer 2017 as an NSERC USRA project undertaken by Ethan White, now a PhD candidate at UBC, and jointly supervised by Richard Guy and the speaker.

## Celebrating Richard Guy

A series of events taking place October 1-4, 2020 which will celebrate the life of Emeritus professor and mathematician Dr. Richard Guy.

A series of events on October 1-4, 2020 which celebrates the life of Emeritus professor and mathematician Dr. Richard Guy. He was an inspirational teacher, colleague, philanthropist, mountaineer, and treasured friend who will be greatly missed and fondly remembered.

**Speaker: **Dr. Terence Tao, Professor and The James and Carol Collins Chair in the College of Letters and Sciences Mathematics, UCLA

Speaker bio and full lecture abstract

**Title: ***The notorious Collatz conjecture*

**Date: **Thursday, October 1, 2020

**Time: **5:00 – 6:15 p.m. (MST)

**Location: **Online

Celebrating the living legacy of the mathematics of Richard Guy

Join us for a one-day conference in honour of Richard Guy and his contribution to mathematical research. There will be two parallel sessions, geared towards combinatorics and number theory, respectively. Each session will feature three talks throughout the day.

Session details will be posted here closer to the event.

**Date:** Friday, October 2, 2020

**Time:** 9:00 a.m. – 3:30 p.m. (MST)

**Location:** Online

Special Lecture: The Life and Numbers of Richard Guy (1916 – 2020)

**Speaker:** Dr. Hugh Williams, Professor Emeritus, University of Calgary

Speaker bio and full lecture abstract

**Title:** *The Life and Numbers of Richard Guy (1916 - 2020)*

**Date:** Friday, October 2, 2020

**Time:** 4:00 – 5:15 p.m. (MST)

**Location:** Online

Mathematical Play in honour of Richard Guy: A day of recreational math for high school students

Richard Guy was an enthusiastic participant in recreational mathematics. We would like to invite you to propagate his love of doing math for fun by joining us to solve mathematical puzzles, problems and challenges! Problems from a special issue of Crux Mathematicorum dedicated to Richard Guy will be distributed on Saturday morning by email to registered participants. Mathematicians will be available via Zoom in drop in sessions to discuss the problems with students, and to offer additional hourly challenges. Participants are invited to post their solutions on a discussion board, and notable contributions by students will be recognized during the closing ceremonies session. Organized by Dr. Bill Sands and Dr. Lauren DeDieu.

Session details will be posted here closer to the event.

**Date:** Saturday, October 3, 2020

**Drop-in problem sessions: **10 a.m. – 3 p.m. (MST)

**Closing Ceremony: **4:00 – 5:00 p.m. (MST)

**Location: **Online

“Peace is a disarming concept”: a celebration of the life of Richard Guy

You’re invited to join Richard and Louise’s family and their many friends to raise a cup of hot chocolate together and celebrate the impact their lives have had beyond the world of mathematics. We have spent time celebrating Richard’s passion for mathematics and sharing this passion with others. It’s now time for family, friends, and colleagues to share their memories of Richard and reflect on the impact he has made to the community and in their lives.

**Date: **Sunday, October 4, 2020

**Time: **1:00 – 2:30 p.m. (MST)

**Location:** Online

## Dr. Wilten Nicola

**Depart****ment of Mathematics and Statistics
Colloquium Series 2020-2021**

**Thursday October 8th 2020**

**Dr Wilten Nicola
Cell Biology and Anatomy
Hotchkiss Brain Institute
University of Calgary**

Populations of neurons display an extraordinary diversity in the behaviors they affect and display. Both numerical and analytical techniques have recently emerged that allow us to create networks of model neurons that display behaviors of similar complexity. Here we demonstrate the direct applicability of one such technique, the FORCE method, to spiking neural networks. FORCE training relies on the reservoir computing framework and allows for rapid online training of spiking networks to perform arbitrary dynamics. We train these networks to mimic dynamical systems, classify inputs, and store and replay discrete sequences that correspond to the notes of a song. Finally, the analysis of synaptic weights after training leads to offline analytical and non-unique solutions for the synaptic weights.

## Dr. Thierry Chekouo

**Statistics and Actuarial Science**

**Department of Mathematics and Statistics
Faculty of Science
University of Calgary**

**Colloquium Series 2020-2021
Thursday October 15th 2020**

In cancer radiomics, textural features evaluated from image intensity-derived gray-level co-occurrence matrices (GLCMs) have been studied to evaluate gray-level spatial dependence within the regions of interest in the brain. Most of these analysis work with summary statistics (or texture-based features) constructed using the GLCM entries, and potentially overlook other structural properties in the GLCM. In our proposed Bayesian framework, we treat each GLCM as a realization of a two-dimensional stochastic functional process observed with error at discrete time points. The latent process is then combined with the outcome model to evaluate the prediction performance. We use simulation studies to assess the performance of our method and apply it to data collected from individuals with lower grade gliomas. We found our approach to outperform competing methods that use only summary statistics to predict isocitrate dehydrogenase (IDH) mutation status.

## Dr. Ashok Krishnamurthy

**Mount Royal University**

**Department of Mathematics and Statistics Adjunct Faculty
University of Calgary**

**Colloquium Series 2020-2021
Thursday October 22th 2020**

The global coronavirus pandemic (COVID-19) reached Lagos, Nigeria on February 27, 2020. Since then, COVID-19 infections have been reported in the majority of Nigerian states. We present a spatial Susceptible-Exposed-Infectious-Recovered-Dead (SEIRD) compartmental model of epidemiology to capture the transmission dynamics of the spread of COVID-19 and provide insight that would support public health officials towards informed, data-driven decision making.

Data assimilation is a general category of statistical tracking techniques that incorporate and adapt to real-time data as they arrive by sequential statistical estimation. Data assimilation applied to the SEIRD model receives daily aggregated epidemiological data from the Nigeria Centre for Disease Control (NCDC) and uses this data to perform corrections to the current state vector of the epidemic. In other words, it enhances the operation of the SEIRD model by periodically executing a Bayesian correction to the state vector, in a way that is, at least arguably, statistically optimal. We observe that the prediction improves as data is assimilated over time. It is essential to understand what future epidemic trends will be, as well as the effectiveness and potential impact of government disease intervention measures. Predictions for disease prevalence with and without mitigation efforts are presented via spatiotemporal disease maps.

## Dr. Thomas Bitoun

**Assistant Professor
Department of Mathematics and Statistics
Faculty of Science
University of Calgary**

**Colloquium Series 2020-2021
Thursday October 29th 2020**

The theory of D-modules studies linear partial differential equations using the tools of ring theory and homological algebra of the ring D of differential operators. Originally motivated by questions of analysis, it has had considerable applications in other fields of mathematics. After introducing some basics of the theory, we will review some of the speaker's results in local cohomology and the b-function. This serves as a motivation for the study of more general commutative subalgebras of the ring of differential operators in positive characteristic, which we will conclude with.

## Geoffrey Mark Vooys

**Eric Milner Graduate Scholarship Colloquium**

**Friday October 30th 2020**

Department of Mathematics and statistics

Faculty of Science

University of Calgary

A fundamental concept in algebra and geometry is the notion of symmetry of an object or some base space. It can frequently happen in nature that two distinct objects can have related symmetries that move them around (such as a circle having quarter rotations and a square having quarter rotations too). Equivariance os the study of moving two objects that have common symmetries acting upon them and seeing which functions respect these symmetries, as well as how these symmetries can be used to capture important geometric information. In this talk, I will explain precisely what I mean by symmetries acting upon objects, and use this to describe what it means to be equivariant more generally. After this I will give a brief (but gentle) description of what it means to be a sheaf, and finally explore how these sheafy techniques and farming metaphors can help us study geometry, representation theory, and algebra.

## Dr. Jinniao Qiu

**Assistant Professor
Department of Mathematics and Statistics
Faculty of Science
University of Calgary**

**Colloquium Series 2020-2021
Thursday November 5th 2020**

**Stochastic Black-Scholes Equation under Rough Volatility and Computations with Deep Learning-Based Methods**

Rough volatility is a new paradigm in finance. We shall talk about the option pricing problems for rough volatility models. As the framework is non-Markovian, the value function for a European option is not deterministic; rather, it is random and satisfies a backward stochastic partial differential equation (BSPDE) or so-called stochastic Black-Scholes equation. The well-posedness of such kind of BSPDEs and associated Feynman-Kac representations will be discussed. These BSPDEs are also used to approximate American option prices. Moreover, a deep learning-based method will be investigated for the numerical approximations to such BSPDEs and associated non-Markovian pricing problems. Examples will be presented for both European and American options.

*This talk is based on joint work with Dr. Christian Bayer from the Weierstrass Institute (Berlin, Germany) and the graduate student Yao Yao from the University of Calgary.*

## Dr. Hua Shen

**Assistant Professor
Department of Mathematics and Statistics
Statistics and Actuarial Science
Faculty of Science
University of Calgary**

**Colloquium Series 2020-2021
Thursday November 19th 2020**

Clinical prediction models are important in clinical practice for the identification of patients at risk of developing an adverse outcome to initiate preventive measures. An appropriate variable selection is fundamental in the development of a prediction model. It determines the set of variables providing the best fit for the model to make accurate predictions and is often considered one of the most difficult aspects of model building. However, variables are often measured with error in medical research. While it is well known that errors in the measurement of covariates introduce bias and imprecision in the quantification of exposure-outcome relationship, it remains under-studied to what extent misclassification in response causes in variable selection and prediction modeling. We investigate how misclassification affect the performance of variable selection when traditional techniques are used. We provide a general framework to deal with variable selection in the presence of misclassification in the response variable and absence of validation data. The key steps of a maximum likelihood estimation method are outline and performance of the proposed method is investigated in simulation studies showing convincing results.

## Dr. Dang Khoa Nguyen

**Assistant Professor
Canada Research Chair in Number Theory and Arithmetic Geometry**

**Department of Mathematics and Statistics**

Faculty of Science

University of Calgary

Faculty of Science

University of Calgary

**Colloquium Series 2020-2021
Thursday November 26th 2020**

\textbf{Transcendental Series of Reciprocals of Fibonacci Numbers} by Dang-Khoa Nguyen (University of Calgary)

\medskip

Let $F_1=1$, $F_2=1$, and $F_n=F_{n-1}+F_{n-2}$ for $n\geq 3$ be the Fibonacci sequence. Motivated by

the identity

$\displaystyle\sum_{k=0}^{\infty}\frac{1}{F_{2^k}}=\frac{7-\sqrt{5}}{2}$, Erd{\"o}s and Graham asked whether $\displaystyle\sum_{k=1}^{\infty}\frac{1}{F_{n_k}}$ is irrational for

any sequence of positive integers $n_1,n_2,\ldots$

with $\displaystyle\frac{n_{k+1}}{n_k}\geq c>1$. We resolve the transcendence counterpart of their question: as a special case of our main theorem, we have that $\displaystyle\sum_{k=1}^{\infty}\frac{1}{F_{n_k}}$ is transcendental when

$\displaystyle\frac{n_{k+1}}{n_k}\geq c>2$.

The bound $c>2$ is best possible thanks to the identity at the beginning.

I will start from scratch: no knowledge of algebraic/transcendental numbers or diophantine approximation is required. A large part of this talk is accessible to those who know what a convergent series means

## Dr. Qingrun Zhang

**Assistant Professor
Department of Mathematics and Statistics
Faculty of Science
University of Calgary**

**Colloquium Series 2020-2021
Thursday December 3rd 2020**

L_{1}-norm regularization is a widely used method in regression applications where shrinkage is afforded in addition to variable selection. In the field of bioinformatics where is the norm rather than the exception, this has tended to the LASSO being applied to a multitude of datasets in both prediction and association studies. However, of note is that the LASSO can be inconsistent in its selection of variables especially in the presence of highly correlated variables. Since this is once more a norm in omics data, the use of obtaining a consensus gene set based on multiple LASSO runs in a bootstrap-like fashion is investigated. In multiple RNA-Seq datasets (The Cancer Genome Atlas, TCGA), biologically valid signatures are recovered, and the gene sets are validated as predictive in independent testing datasets of similar cancers. Furthermore, a co-expression-based pathway enrichment method finds pathways that have been previously experimentally identified as associated with the respective cancers. An overview of the field of biomarker identification, gene expression analysis and RNA-Seq techniques will also be introduced at the beginning of the presentation.

## Dr. Ha Tran

Assistant Professor

Department of Mathematical and Physical Sciences

Concordia University

Adjunct Assistant Professor,

Department of Mathematics and Statistics

University of Calgary

Colloquium Series 2020-2021

Thursday January 28 2021

Ideal lattices form a powerful tool not only for computational number theory but also for cryptography and coding theory, thanks to their underlying structures that enable a variety of useful constructions. In this talk, we will first discuss ideal lattices and their application in computational number theory such as computing important invariants of a number field (the class number, the class group and the unit group). Then we will discuss an application of ideal lattices in cryptography: constructing cryptosystems that are conjectured to be secure under attacks by quantum computers. An application of ideal lattices in coding theory - minimizing the value of the inverse norm sums - will be presented after that.

## Dr. Matthew Greenberg

Associate Professor

Department of Mathematics and Statistics

Faculty of Science

University of Calgary

Colloquium Series 2020-2021

Thursday February 25th 2021

Machine learning has been an active field of research since the mid 20th century. Over the last decade, however, it’s mindshare has exploded in academia and in industry, often crossing over into popular and political arenas. This explosion was catalyzed by advances in computing (GPUs) and data engineering (massive, curated data sets) catching up to an already mature theory, leading to the latter’s rapid validation. Investment by industry and government followed, leading to a virtuous cycle of theoretical advancement, software and hardware development, and compelling applications. In fleshing out this story, I’ll attempt to balance articulation of the powerful, high-level paradigms that powered machine learning’s rise and fuel optimism for its future with providing enough technical, low-level detail to satisfy a mathematically sophisticated audience.