Abstract.In this talk we will look at various examples of classification problems in symplectic linear algebra: conjugacy classes in the symplectic group and its Lie algebra, linear lagrangian relations up to conjugation, tuples of (co)isotropic subspaces. I will explain how many such problems can be encoded using the theory of symplectic poset representations, and will discuss some general results of this theory. Finally, I will recast this discussion from a broader category-theoretic perspective.

Talk slides:

]]>However, there are some people who have put out some good work on this, from the perspective of an organic farmer/permaculturist – https://www.youtube.com/watch?v=VIBIO1vywP4 – from the younger generation, to the perspective of an evolutionary biologist – https://www.youtube.com/watch?v=nOMLdefHGA8 – from the older generation.

The trouble is that people like this, who get away from the accepted narrative, get shut down in quick order. So there’s that difficulty, and that’s only addressed by universities recapturing their original role as places where free thought and debate can take place.

]]>**Systems as wiring diagram algebras**

Abstract.We will start by describing the monoidal category of labeled boxes and wiring diagrams and its induced operad. Various kinds of systems such as discrete and continuous dynamical systems have been expressed as algebras for that operad, namely lax monoidal functors into the category of categories. A major advantage of this approach is that systems can be composed to form a system of the same kind, completely determined by the specific way the composite systems are interconnected (‘wired’ together). We will then introduce a generalized system, called amachine, again as a wiring diagram algebra. On the one hand, this abstract concept is all-inclusive in the sense that discrete and continuous dynamical systems are sub-algebras; on the other hand, we can specify succinct categorical conditions for totality and/or determinism of systems that also adhere to the algebraic description.

Her talk will be based on this paper:

• Patrick Schultz, David I. Spivak and Christina Vasilakopoulou, Dynamical systems and sheaves.

but she will focus more on the algebraic description (and conditions for deterministic/total systems) rather than the sheaf theoretic aspect of the input types. This work builds on earlier papers such as these:

• David I. Spivak, The operad of wiring diagrams: formalizing a graphical language for databases, recursion, and plug-and-play circuits.

• Dmitry Vagner, David I. Spivak and Eugene Lerman, Algebras of open dynamical systems on the operad of wiring diagrams.

]]>**Social contagion modeled on random networks**

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Abstract. A social contagion may manifest as a cultural trend, a spreading opinion or idea or belief. In this talk, we explore a simple model of social contagion on a random network. We also look at the effect that network connectivity, edge distribution, and heterogeneity has on the diffusion of a contagion.

• Mathematics in the 21st century.

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]]>Here is Jade’s abstract:

Fong, Spivak and Tuyéras have found a categorical framework in which gradient descent algorithms can be constructed in a compositional way. To explain this, we first give a brief introduction to backprogation and gradient descent. We then describe their monoidal category

Learn, where the morphisms are given by abstract learning algorithms. Finally, we show how gradient descent can be realized as a monoidal functor fromPara, the category of Euclidean spaces with differentiable parameterized functions between them, toLearn.

Her talk will be based on this paper:

• Brendan Fong, David I. Spivak and Rémy Tuyéras, Backprop as functor: a compositional perspective on supervised learning.

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