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The Montreal Math Circle is an enrichment program that offers an occasion for students interested in mathematics to solve challenging problems at their grade level. The circle aims at bringing pleasure and confidence in children while doing mathematics. The problems during each meeting will be centered around a specific topic. The instructor is bilingual and will accommodate students from both English and French instruction schools. For more information, please feel free to send an email at email@example.com.<br/><br/>The event will take place on Sundays.
In 2019, The New Yorker ran a short piece entitled "The Men Who Still Love Fight Club" referencing the enduring legacy of the 1996 novel by Chuck Palahniuk and its 1999 film adaptation by David Fincher. Focused primarily on American society, the article fails to mention Fight Club's appeal to many in Europe and elsewhere who have also been attracted by its aggressive masculinism and critique of consumer lifestyles.
The problem of finding rational or integer solutions to polynomial equations is one of the oldest problems in mathematics and is one of the key driving forces in the development of Number Theory. In the last 15 years new methods were developed that can sometimes effectively solve this problem. These methods attempt to find the solutions inside the larger set of solutions of the same equation in the field of p-adic numbers as the vanishing set of some computable function. When these methods work they give the rational solutions to arbitrarily large p-adic precision, which usually suffices to rigorously recover the full set of solutions. I will survey the new methods, originating from the work of Kim and from the more recent work of Lawrence and Venkatesh. I will then explain my work with Muller and Srinivasan that uses a p-adic version of the notion of norms on line bundles and associated heights, as used for example in arithmetic dynamics, to give a new approach to some Kim type results.
The notion of a Bowley optimum (or Stackelberg equilibrium) has gained recent popularity as an equilibrium concept in reinsurance markets, but it assumes a monopolistic structure on the supply side. This is in contrast to reinsurance markets in which equilibrium pricing arises through strategic price competition between reinsurers. In this talk, I will discuss both market structures and argue that the notion of a Subgame Perfect Nash Equilibrium (SPNE) is the appropriate solution concept in the latter market setting. I will provide a characterization of equilibrium reinsurance contracts in each case, under fairly general assumptions about the preferences of market participants. Finally, I will discuss the Pareto-efficiency of equilibria and whether efficient allocations can be decentralized in each market structure. Specifically, Bowley-optimal contracts lead to Pareto-efficient allocations, but they make the insurer indifferent with the status quo. Moreover, only those Pareto-efficient contracts that make the insurer indifferent between suffering the loss and entering into the reinsurance contract are Bowley optimal. This is indicative of the limitations of Bowley optimality as an equilibrium concept. In the second market structure, equilibrium contracts induced by an SPNE result in Pareto-efficient allocations. Additionally, under mild conditions, the insurer realizes a strict welfare gain, which addresses the shortcomings of the Bowley setting and thereby ultimately reflects the benefit to the insurer of competition on the supply side.
- Peter Dietsch (University of Victoria)
- Pablo Gilabert (Concordia University)
- Jan Kandiyali (Durham University)
- Martin O’Neill (University of York)
- Avia Pasternak (University of Toronto)
- Sabine Tsuruda (Queen’s University)
- Åsbjørn Melkevik (Queen’s University)
- Louis-Philippe Hodgson (York University)
- Will Roberts (McGill University)
- Eleni Schirmer (Concordia University)
- Sylvie Loriaux (Université Laval)
- Denise Celentano (Université de Montréal)
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