**Upcoming colloquiums**

**Vijay Ganesh - University of Waterloo - October 29th**

3:30 p.m. talk

**Machine Learning and Logic Solvers: The Next Frontier**** **

Over the last two decades, software engineering has witnessed a silent

revolution in the form of Boolean SAT solvers. These solvers are now

integral to many analysis, synthesis, verification, and testing

approaches. This is largely due to a dramatic improvement in the

scalability of these solvers vis-a-vis large real-world formulas. What

is surprising is that the Boolean satisfiability problem is

NP-complete, believed to be intractable in general, and yet these

solvers easily solve instances containing millions of variables and

clauses in them. How can that be?

In my talk, I will address this question of why SAT solvers are so

efficient through the lens of machine learning as well as ideas from

(parameterized) proof complexity. I will argue that SAT solvers are

best viewed as proof systems, composed of prediction engines that

optimize some metric correlated with solver running time. These

prediction engines can be built using ML techniques, whose aim is to

structure solver proofs in an optimal way. Thus, two major paradigms

of AI, namely machine learning and logical deduction, are brought

together in a principled way to design efficient SAT solvers. A result

of my research is the MapleSAT solver, that has been the winner of

several recent international SAT competitions, and is now widely used

in industry and academia.

Please email compmath@uwaterloo.ca for Zoom link

**Past colloquiums**

**Eldad Haber - University fo British Columbia - October 1st **^{ }

^{ }

3:30 p.m. talk

**A Computational Mathematics View of Deep Learning with Applications **SLIDES

In this talk we discuss neural networks from the point of view of continuous dynamical systems namely, ODEs and PDEs. We show a strong link that suggests how one can view deep learning as a system of differential equations, which, in turn allows us to develop new network architectures. In the second part of the talk we discuss how deep learning can impact scientific computing by developing new integration techniques that can impact problems such as protein folding and molecular dynamics.

Please email compmath@uwaterloo.ca for Zoom link

**Bartosz Protas- McMaster University - February 27th **^{ }

^{ }

Professor – Department of Mathematics and Statistics

DC 1304

3:00 p.m. refreshments | 3:30 p.m. talk

**Searching for Singularities in Navier-Stokes Flows Using Variational Optimization Methods**

In the presentation we will discuss our research program focused on a systematic search for the most singular behaviors possible in viscous incompressible flows. These events are characterized by extremal growth of various quantities, such as the enstrophy, which control the regularity of the solution. They are therefore intimately related to the question of singularity formation in the 3D Navier-Stokes system, known as the hydrodynamic blowup problem, which remains one of the most important open problems in mathematical fluid mechanics. We demonstrate how new insights concerning such questions can be obtained by formulating them as variational PDE optimization problems which can be solved computationally using suitable discrete gradient flows. More specifically, such an optimization formulation allows one to identify "extreme" initial data which, subject to certain constraints, leads to the most singular flow evolution. In offering a systematic approach to finding flow solutions which may saturate known estimates, the proposed paradigm provides a bridge between rigorous mathematical analysis and scientific computation. In particular, it makes it possible to determine whether or not certain mathematical estimates are "sharp", in the sense that they can be realized by actual vector fields, or if these estimates may still be improved. In the presentation we will review a number of results concerning 2D and 3D flows characterized by the maximum possible growth of different Sobolev norms of the solutions. Even when extreme initial data is used, highresolution computations for the 3D Navier-Stokes system reveals no tendency or singularity formation in finite time.

**Henry Lam - Columbia University - February 11th **^{ }

^{ }

Associate Professor – Department of Industrial Engineering and Operations Research

MC 6460

3:15 p.m. refreshments | 3:30 p.m. talk

**Efficient Uncertainty Quantification in Simulation Analysis**

Simulation-based prediction, for instance in discrete-event analysis and machine learning, often incurs errors from both Monte Carlo computation and calibration noise from data. These errors, if overlooked, can result in incorrect inference and underestimation of risks that degrade decision-making. We present several methods to efficiently quantify these errors, by injecting subsampling, distributionally robust optimization, and random perturbation respectively into simulation runs. We explain the statistical mechanisms of these approaches and why they help resolve each of the discussed challenges faced by existing methods. This is joint work with Huajie Qian (Columbia).

**Ricardo Fukasawa - University of Waterloo - January 13th **^{ }

^{ }

Associate Professor, Combinatorics and Optimization

MC 6460

2:15 p.m. refreshments | 2:30 p.m. talk

**Solving the Vehicle Routing Problem**

The vehicle routing problem (VRP) consists of finding the most efficient way to route a fleet of vehicles that depart from a common depot in order to serve a set of customers. Each customer has a given demand and the total demand carried by each vehicle cannot exceed its capacity. is The VRP is a well-studied classical combinatorial optimization problem proposed in 1959, and the techniques developed for solving it have been used to solve practical optimization problems in logistics and other application areas for years.

In this talk, we will discuss the VRP and different approaches to get optimal solutions to it. The approaches are based on integer programming formulations for the problem, each of which has its own advantages and drawbacks. We will review a few of these and discuss the main ideas behind them and how those can be extended to consider variants of the problem.

**Andrew Sutherland - Massachusetts Institute of Technology - November 7th ^{ }**

Principal Research Scientist, Department of Mathematics

M3 3103

3:15 p.m. refreshments | 3:30 p.m. talk

**Sum of Three Cubes**

In 1953 the British mathematician Louis Mordell famously asked if one can write the number 3 as a sum of three cubes in any way other than the obvious two solutions 1^3+1^3+1^3 and 4^3+4^3 -5^3. Over the next sixty-six years many mathematicians attempted to answer Mordell's question, and while they failed to find any new solutions for 3, they were eventually able to determine all positive integers k ≤ 100 that can be expressed as a sum of three cubes, except for k = 42.

In this talk I will present joint work with Andrew Booker that used Charity Engine's crowd-sourced compute grid to affirmatively answer Mordell's question:

569936821221962380720^3 - 569936821113563493509^3 -472715493453327032^3 = 3;

as well as settling the case k = 42. I will also discuss a conjecture of Heath-Brown that predicts the existence of infinitely many more solutions and explains why they are so difficult to find.

**Lin Wang - University of Jinan - October 28th ^{ }**

Associate Professor, Shandong Provincial Key Laboratory of Network Based Intelligent Computing

DC 1304

2:45 p.m. refreshments | 3:00 p.m. talk

**Evolutionary Computation and Evolving Reverse Engineering-based Scientific ****Modeling**Modeling enables scientists to compare observations with theory, extract physical parameters, and predict the behaviors of system. Currently, for modeling many systems, traditional first-principle methods are not satisfactory in comparison with the observations. For example, current models of cement material fall short of explaining its hydration process. The evolving reverse engineering-based scientific modeling brings hope for discovering knowledge, and distilling natural laws. In this talk, we will introduce evolutionary computation and some theoretical contributions. Then, we will exhibit some real-world examples of evolving reverse modeling.

**Anita Layton - University of Waterloo - September 24th ^{ }**

Associate Dean, Research and International, Mathematics

Professor of Applied Mathematics, Pharmacy, and Biology

Chair, Research Equity, Diversity, and Inclusion Council

MC 5479

2:20 p.m. refreshments | 2:30 p.m. talk

**Mathematical Models and Their Applications in Diabetes, Hypertension, and Autism**

Computational modelling can be used to reveal insights into the mechanisms of new drugs and to develop new diagnostic tools. Here I will discuss three major diseases: diabetes, hypertension, and autism. I will talk about how we construct models to simulate new diabetes drugs, to understand sex differences in hypertension, and to develop a new approach for diagnosing autism in children.

**Leland McInnes - Tutte Institute - March 21 ^{st }**

Research Mathematician and Data Scientist at Tutte Institute for Mathematics and Computing

**Unsupervised Learning**

Topological Data Analysis is a relatively new field of research that seeks to bring powerful tools from algebraic topology to bear on practical problems in data science (where statistics has been the more traditional toolset). This talk, by Dr. Leland McInnes from the Tutte Institute for Mathematics and Computing, will begin by using topological methods to construct a new approach to dimension reduction, and then build out the theory to provide new approaches to clustering and anomaly detection. Our goal is to provide a unified topological approach to unsupervised learning.

**Tim Merlis - McGill University - Febuary 25 ^{th }**

Associate Professor in Atmospheric and Oceanic Sciences at McGill University

Canadian Research Chair (Tier 2) in Atmospheric and Climate Dynamics.

Member of the McGill Space Institute

**Monday 25th February, 2019**

3:30pm in MC 5417

refreshments at 3:15pm

#### High-resolution climate simulations to understand how global warming affects hurricanes

In the last decade, global climate models have achieved sufficiently high resolution that they can simulate hurricanes, one of the most destructive forms of extreme weather. This new capability has been deployed to assess how human-caused global warming affects hurricanes. In this seminar, I will provide an overview of the technique and highlight results of my research that use simplified boundary conditions to *understand *the sensitivities of hurricanes to climate change.