Seminars Sorted by Series

One way to define a matroid is via its base polytope.  From this point of view, some matroid invariants easily have geometric interpretations: e.g., the number of bases is the number of vertices of the polytope.  It turns out that most interesting...

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Torus-orbit closures in Grassmannians or flag varieties are closely related to matroid theory. I will review some known properties of these torus-orbit closures, with an emphasis on some open problems which are related to Schubert calculus.

The Borel-Weil-Bott theorem gives a method for constructing the irreducible representations of a connected compact Lie group on cohomology spaces associated to line bundles on flag varieties.  In this lecture, we review the necessary background from...

I’ll describe a circle of ideas that links Schubert polynomials with representation theory, via some configuration spaces studied by Magyar (and which include Schubert’s famous space of complete triangles). Most of the geometric connections were...

I’ll describe a circle of ideas that links Schubert polynomials with representation theory, via some configuration spaces studied by Magyar (and which include Schubert’s famous space of complete triangles). Most of the geometric connections were...

There is a bijection between solutions of the Kadomtsev-Petiashvili (KP) hierarchy and points on an infinite Grassmannian, now often simply referred to as "the Sato Grassmannian". This connection is made via the Plücker coordinates, the expansion...

We discuss some equivariant compactifications of linear subspaces, controlled by the combinatorics of polymatroids. Open problems of interest to the Schubert calculus community will be emphasized. Joint with Colin Crowley & Botong Wang.

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In 1984, Ryan showed that any smooth Schubert variety in type A is an iterated fiber-bundle of Grassmannian varieties. Later, Haiman calculated the generating function for the number of smooth permutations (equivalently smooth Schubert varieties) of...

Knot Theory and Machine Learning

Andras Juhasz, University of Oxford

The signature of a knot K in the 3-sphere is a classical  invariant that gives a lower bound on the genera of compact oriented surfaces in the 4-ball with boundary K. We say...

Geordie Williamson, University of Sydney

Combinatorial Invariance: a Case Study of Pure Math / Machine  Learning Interaction

The combinatorial invariance conjecture is a fascinating conjecture in Representation Theory. Basically it says that...

Alex Davies, University of Cambridge

What is Machine Learning Good For?

Machine learning has seen remarkable success in many areas in the past decade, but this inevitably leads to hype that obscures what it can and cannot do. In this talk we will...

Alhussein Fawzi, EPFL

AlphaZero and Matrix Multiplication

Marc Lackenby, University of Oxford

The Signature and Natural Slope of Hyperbolic Knots

Andras Juhasz has explained in his talk how machine learning was used to discover a previously unknown relationship between invariants in knot theory. This...

Andras Juhasz
Alex Davies
Marc Lackenby
Alhussein Fawzi
Geordie Williamson

Fireside Chat

In December last year, a cover article of Nature described a collaboration between a team from DeepMind and several top mathematicians showing how tools from...

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In this talk, I will define the Ruelle invariant of a measure preserving flow equipped with a symplectic cocycle. This is a natural dynamical quantity that measures a spacetime averaged rotation of the cocycle along the flow. I will then discuss the...