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• November 18:
• (Re)imagining mathematics in a world of reasoning machines

In the coming decades, developments in automated reasoning will likely transform the way that research mathematics is conceptualized and carried out. I will discuss some ways we might think about this. The talk will *not* be about current or potential abilities of computers to do mathematics – rather I will look at topics such as the history of automation and mathematics, and related philosophical questions.

• November 19:
• Racah-Wigner coefficients

In the 1940s Giulio Racah and Eugene Wigner studied a numerical invariant attached to a tetrahedron with half-integer side lengths, in relation to the quantum theory of angular momentum. The resulting invariants, often called 6j symbols, have many beautiful properties; they reflect intricate features of the geometry of tetrahedra, and, as shown by Regge, they have many unexpected symmetries. Later, they surfaced in different fields, including quantum topology and the theory of orthogonal polynomials.

I will explain some of this history, and take another look at the mathematics. My eventual goal is to explain how the 6j symbols and Regge symmetries are related to the duality in the sense of Langlands, but no knowledge of this is assumed. Joint work with Griffin Wang (IAS).

Speaker Bio: Akshay Venkatesh was born in India and grew up in Australia, where he did his undergraduate studies. He then completed a PhD at Princeton University in 2002. Since 2018, he has been a faculty member at the Institute for Advanced Study. Venkatesh’s research interests are in number theory, as well as various related fields. Most recently he has worked on surprising parallels between number theory and certain mathematical structures arising in quantum field theory.

About the Ahlfors Lecture Series: The Ahlfors Lecture Series is presented by the Harvard University Math Department in memory of our distinguished colleague, Professor Lars Ahlfors.