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Jan

24

2020

We shall consider a stochastic model, which is used to analyze competitive population dynamics. This cyclic and non-transitive model is based on the well-known rock-paper-scissors game. It can be viewed as the stochastic analog of the Lotka-Volterra deterministic model for predator-prey interactions. It has been observed that in order to maintain species richness it is essential for the system to be nonhierarchical in nature. One of the central goals of ecology is to figure out strategies that help to maintain biodiversity or species richness in the long term.

Jan

24

2020

Ada, a modern math student, joins forces with Sir Isaac Newton in a buddy comedy for the ages! Archimedes, Robert Hooke, Gottfried Leibniz, Lâ€™Hopital and Riemann are part of the action. Musical parodies that span genres introduce and illuminate concepts of limits, integration and differentiation. Hilarious, catchy songs deliver powerful mnemonic content proven to get stuck in studentsâ€™ heads, bringing the instantaneous rate of change and the area under the curve vividly alive with an unforgettable soundtrack.

Jan

27

2020

Motivated by the study of the five Platonic solids, we trace the geometric ideas of points, lines, polygons, polyhedra and higher-dimensional polytopes, and the parallel combinatorial ideas of abstract polytopes and maniplexes.

Hidden agenda: I want to talk about symmetry as it applies to each of these ideas.

Jan

27

2020

Jan

28

2020

Unitary Shimura varieties are moduli spaces of abelian

varieties with extra structure. Rapoport-Zink spaces (moduli spaces of

p-divisible groups with extra structure) are key tools in studying the

supersingular loci of these Shimura varieties. In this talk, we'll

discuss the geometry of the GL(4) Rapoport-Zink space. As an

application, we'll also discuss the geometry of the supersingular loci

of some particular unitary Shimura varieties.