CMS is organizing three-hour mini-courses to add more value to meetings and make them attractive for students and researchers to attend.

The mini-courses will be held on Friday, June 3 and include topics suitable for any interested parties. **You don’t have to be registered for the meeting in order to register for mini courses. **

**Registration fees for the mini-courses are as follows. **

| |

Student/ Postdocs (members) | $50 |

Student/ Postdocs (non-members) | $75 |

CMS Members | $100 |

CMS Non-Members | $150 |

RBC Sponsored Closing the Gap (Black, Indigenous, female-identifying, LGBTQ+, or person with disabilities; must be 15-29 years of age) – CMS student member ***Canadian citizens and permanent residents only | $25 |

### Geometry of Black Hole Mergers

##### Friday, June 3, 2022 | 9:00 - 12:00 NDT

**Presenter:** Ivan Booth, Memorial University

Black holes are astrophysical objects. They play a central role in many of the most dramatic astrophysical processes in our universe including supernova, active galactic nuclei and black hole mergers. In dramatic developments in the last few years, new observational techniques have not only “listened” to the gravitational waves emitted during a black hole merger (LIGO, VIRGO) but also actually taken a horizon-scale X-ray picture of the 2.4 billion solar mass black hole at the centre of M87 (the Event Horizon Telescope).

Black holes are also geometrical objects. As solutions of Einstein’s equations, black hole spacetimes are four-dimensional manifolds with Lorentzian-signature metrics. The horizon of a black hole boundary at an “instant in time” is then a Riemannian signature, two-dimensional, closed manifold. Geometrically, these two-dimensional boundaries are very closely related to minimal surfaces from classical differential geometry (even being identical in some special cases) and so they can be studied and classified with many of the same mathematical tools.

This series of lectures will begin with a review of geodesics and minimal surfaces in Riemannian geometry, including the information contained in their Jacobi/stability operators. We will then consider the closely related marginally outer trapped surfaces (MOTS) of general relativity, which feature prominently in mathematical and numerical relativity studies of black holes and see how they relate to the better known apparent and event horizons. Finally, using these tools along with both numerical and exact examples, we will see what a study of MOTS can tell us about the intricacies of black hole mergers. In particular we will address the problem as to how, during merger of a pair of black holes, two apparent horizons can become one.

### Introduction to arithmetics in function fields

##### Friday, June 3, 2022 | 9:00 - 12:00 NDT

**Presenter:** Matilde Lalin, Université de Montréal

### Modes of Motion by a Coronavirus

##### Friday, June 3, 2022 | 13:00 - 16:00 NDT

**Presenter:** Goong Chen, Texas A&M University;

**Organizer:** Jie Xiao, Memorial University

In this mini-course, we study coronavirus from a structural molecular biology point of view, with certain emphasis on how the mechanical motions of the coronavirus may play in the invasion process of healthy cells.

We first give a brief introduction and survey of the biological properties of a coronavirus concerning how it moves and how it invades healthy cells. We then proceed to build our model by continuum mechanics in lieu of an atom-by-atom model. A spherical shell with many spikes mimicking the shape of coronavirus has been chosen as the elasto-plastic continuum. We then analyze its eigenmodes of vibration by Modal Analysis. We have found the six degree of freedom rigid body modes and several thousands more nontrivial modes, some peculiar ones of which can play important roles in the invasion process. Related problems are also posed.

Many animation videos from supercomputer computations and simulations will be shown to illustrate the motions of a coronavirus.

### Introduction to non-Archimedean Analysis

##### Friday, June 3, 2022 | 13:00 - 16:00 NDT

**Presenter:** Khodr Shamseddine, University of Manitoba

In this mini-course, I will first review basic properties of ultrametric spaces, valued fields and ordered fields as well as the connection between these different mathematical objects. In particular, I will present elements of the algebraic, topological and metric structures of non-Archimedean valued fields which are different from what we know for the Archimedean fields of real and complex numbers. As examples of non-Archimedean valued fields, I will introduce the *p*-adic fields as well as the so-called general Hahn fields and Levi-Civita fields, and I will present a summary of their key properties.

Then, I will focus on two special Levi-Civita fields: R and its complex counterpart C. Among all the non-Archimedean fields surveyed in the first part of the course, R and C are unique from a pure mathematical point of view as well as from a computational point of view. I will give a brief summary of my research group’s work on R and C, and show one computational application.

Basic knowledge of Analysis, Algebra and Topology at the undergraduate level will be assumed.

### An invitation to high-dimensional approximation: from sparse polynomials to deep learning

##### Friday, June 3, 2022 | 13:00 - 16:00 NDT

**Presenter:** Simone Brugiapaglia, Concordia University

Although this mini-course will be mostly focused on theoretical aspects, we will also illustrate numerical examples. We will assume at least some familiarity with the basics of real and complex analysis, approximation theory, numerical analysis, and probability.