**Schedule and Program **

You can download the conference booklet containing the abstracts of sutdent talks, detailed schedules of the event and many more useful informations here.

You can download the general schedule of the event here.

If you wish to give a talk or present a poster at the CUMC, please make sure to send us the title and abstract of your presentation along with the presentation type (talk or poster) before July 8 at cumc@cms.math.ca.

The format of the talk is a 20-25 minutes presentation with 5 minutes for questions. You will have access to a projector for slides and a whiteboard.

The poster session will be a one hour activity on Saturday, July 16. You will need to stand next to your poster to present it and answer questions from other students.

You may present in English or French, and we invite you to write your slides in the other language if you can. If you have specific needs or restrictions (e.g., if you wish to present in teams or if you will be absent on some days), please let us know in your email.

**Keynote lectures**

**Linan Chen**

### McGill University

**Title:** Infinite Dimensional Randomness: from Brownian motion to Gaussian Random Field

**Abstract:** In this talk, we will discuss how to "host" randomness in an infinite dimensional space, and how the randomness will in return "configure" the hosting space. From random paths to random surfaces, to random fields, the journey gives us a (extremely incomplete) glimpse into the world of random geometry.

**Maxime Fortier-Bourque** **(Slides)**

### Université de Montréal

**Title:** From sphere packings to extremal problems on surfaces

**Abstract:** What proportion of space can be occupied by congruent balls that do not overlap? Under the same hypotheses, how many balls can be tangent to a central ball? These two classical questions have a fascinating history leading up to very recent developments. We know the exact answer to the first question only in dimensions 1, 2, 3, 8, and 24. The answer to the second question is known in the same dimensions as well as in dimension 4. In most cases, the best known upper bounds are obtained through analysis rather than geometry, via a method called "linear programming" developed by Delsarte. This method can be applied in a variety of situations such as for error-correcting codes and in graph theory. I will discuss four problems concerning hyperbolic surfaces where this method yields the best upper bounds known to date apart from a few exceptions.

**Guy Lacroix** **(Slides)**

### Université Laval

**Title:** Science économique = f(mathématiques, statistiques, informatique, psychologie,…, données), _{i}>0, f_{ii}>0

**Abstract:** La science économique est une science sociale. Elle s’intéresse aux comportements individuels et à leurs interactions dans un environnement complexe, changeant et aléatoire. Les comportements humains sont eux-mêmes complexes, changeants et aléatoires. Dans un tel environnement, la production de biens et services et leur distribution entre les individus sont pratiquement toujours largement assurées par un système de marché. Or, ce système engendre des inégalités et des externalités négatives qui doivent être corrigées par des politiques publiques. Quels sont les fondements de ces politiques, et comment s’assurer qu’elles atteignent leurs objectifs?

La présentation abordera les fondements psychologiques de la théorie du comportement et évoquera les emprunts aux mathématiques pour lui donner une assise formelle et rigoureuse. Par ailleurs, certains aspects du comportement humain soulèvent des problèmes statistiques particuliers qui ont donné lieu à de nombreuses innovations à l’aide de la théorie statistique. Enfin, l’avènement de bases de données administratives a permis aux économistes d’apporter des contributions importantes aux méthodes d’apprentissage automatique, notamment dans l’analyse causale.

Le design et l’évaluation des politiques publiques sont fondés sur l’idée que celles-ci ont des effets causals sur les comportements, et donc sont prévisibles. Je tâcherai de montrer comment les économistes s’y prennent pour valider la théorie économique et mesurer l’effet causal des politiques publiques.

**Kumar Murty**

### University of Toronto

**Title:** x^{n} + x + a

**Abstract:** This family of polynomials has many nice properties. In particular, we will discuss their irreducibility, their discriminants, and their Galois groups, and why they are relevant in coding theory and in cryptography. There are many interesting open problems about the prime divisors of the discriminants. I will describe joint work with Shuyang Shen on some of these questions in which we explore consequences of the ABC conjecture.

**Monica Nevins** **(Slides)**

### University of Ottawa

**Title:** New Frontiers in Mathematical Cryptography

**Abstract:** Public-key cryptography ensures the security of communications and is utterly essential to our modern world. It reposes on the hardness of solving certain mathematical problems. As we collectively learn more, and as we build more viable quantum computers, this set of problems has to evolve. In this talk, we’ll share some of the present and future of mathematical cryptography, and explore the (undergraduate!) mathematical underpinnings of the algorithms at its new frontiers.

**William Ross** **(Slides)**

### University of Richmond

**Title:** Defying Gravity: functions and break your intuition

**Abstract:** We often have a misconception of what constitutes a continuous or a differentiable function. We are often taught that a continuous function is "one you can draw without lifting your pencil" and that a differentiable function is "one that you can draw without making any sharp corners". Though these rudimentary definitions serve us well is developing our intuition, they do not serve us well when we apply the proper definition of continuous and differentiable. This talk will survey intuition breaking functions such as Dirichlet’s nowhere continuous function, Thomae’s function that is continuous only on the irrational numbers, Conway’s function that satisfies the intermediate value property but is nowhere continuous, Cantor’s devil’s staircase function that is continuous and increasing but its derivative is zero almost everywhere, Weierstrass’ nowhere differentiable function, and so on. Moreover, I will also discuss how these types of intuition defying functions are everywhere and, despite the fact they are difficult to create, are extremely common. I’ll also discuss the fact that though Riemann’s name is on everything, he is not as smart as you think he is. The only requirement for this talk is calculus and the willingness to expand your mind.