Affine Grassmannian slices are varieties which appear naturally in

geometric representation theory. Their quantisations are given by truncated

shifted Yangians. I will describe a recent result which gives an equivalence of

categories between modules for truncated shifted Yangians and modules for

Khovanov-Lauda-Rouquier-Webster algebras. We use this theorem to a) resolve a

conjecture describing the highest weights of truncated shifted Yangians, and b)

prove the so-called "symplectic duality" between affine Grassmannian slices and

Nakajima quiver varieties in the simply-laced cases. The latter result provides

a link between two very different geometric models for representations of

semisimple Lie algebras. This is joint work with Kamnitzer, Tingley, Webster,

and Weekes.

### About Pure mathematics seminars

We present regular seminars on a range of pure mathematics interests. Students, staff and visitors to UQ are welcome to attend, and to suggest speakers and topics.

Seminars are usually held on Tuesdays from 3pm to 3.50pm.

Talks comprise 45 minutes of speaking time plus five minutes for questions and discussion.

#### Information for speakers

Researchers in all pure mathematics fields attend our seminars, so please aim your presentation at a general mathematical audience.

Contact us

To volunteer to talk or to suggest a speaker, email Ole Warnaar.