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Inside Every Calculus Is A Little Algebra Waiting To Get Out

YOW! 2020 Melbourne

Because of deep learning, there has been a surge in interest in automatic differentiation, especially from the functional programming community. As a result, there are many recent papers that look at automatic differentiation from a Category Theory perspective. However, Category Theorists have already been looking at differentiation and calculus in general since the late ’60s in the context of Synthetic Differential Geometry, but it seems that this work is largely ignored by those interested in AD. In this talk, we will provide a gentle introduction to the ideas behind SDG, by relating them to dual numbers, and show how it provides a simple axiomatic and purely algebraic approach to (automatic) differentiation and integration. And no worries if you suffer from arithmophobia, there will be plenty of Kotlin code that turns the math into something fun you can play with for real.

Erik Meijer

Director of Engineering

Facebook

Netherlands

Erik is a Dutch computer scientist and entrepreneur. He received his Ph.D. from Nijmegen University in 1992 and has contrubted to both academic institutions and major technology corporations.Erik's research has included the areas of functional programming (particularly Haskell) compiler implementation, parsing, programming language design, XML, and foreign function interfaces. He has worked as an associate professor at Utrecht University, adjunct professor at the Oregon Graduate Institute, part-time professor of Cloud Programming within the Software Engineering Research Group at Delft University of Technology, and Honorary Professor of Programming Language Design at the School of Computer Science of the University of Nottingham, associated with the Functional Programming Laboratory.From 2000 to early 2013 Erik was a software architect for Microsoft where he headed the Cloud Programmability Team. His work at Microsoft included C#, Visual Basic, LINQ, Volta, and the reactive programming framework (Reactive Extensions) for .NET.  He founded Applied Duality Inc. in 2013 and since 2015 has been a Director of Engineering at Facebook.