Abstracts

Week of April 6, 2025

April 7, 2025
Geometry, Symmetry and Physics Representations of Simple Affine Vertex Algebras and Affine Springer Fibres 4:30pm -
KT 801

I will explain some results and conjectures relating the representation theory of simple affine vertex algebras to the geometry of homogeneous elliptic affine Springer fibres associated with the Langlands dual affine Lie algebra. I will also explain generalizations of this relation to chiral algebras associated with an n-punctured Riemann surface of genus g, constructed by T. Arakawa, and the geometry of the Hitchin moduli space on the same Riemann surface. 
April 8, 2025
Quantum Topology and Field Theory Fukaya-Seidel category of One-Forms and the Algebra of the Infrared 5:15pm -
KT 221

The Fukaya-Seidel category is classically defined in terms of a Kähler manifold X equipped with a holomorphic function W, with the relevant data encoded in the exact one-form dW. However, a natural generalization suggests itself: to replace dW with an arbitrary closed (but not necessarily exact) holomorphic one-form α on X. This more general version arises in many constructions in low-dimensional topology. In this talk, I will explore how the framework of the algebra of the infrared provides a means to understand this extension and illuminates the structure of the resulting category. 
April 10, 2025
Analysis TBA 4:00pm -
Geometry, Symmetry and Physics Geometry of Coulomb Branches 4:30pm -
KT 801

I’ll report recent progress on understanding the geometry of Coulomb branches of 3D N = 4 supersymmetric gauge theories, in particular on results relating Coulomb branches with different gauge groups.
April 11, 2025
Friday Morning Seminar TBA 10:00am -
KT 801

A relaxed-pace seminar on impromptu subjects related to the interests of the audience. Everyone is welcome. The subjects are geometry, probability, combinatorics, dynamics, and more!
Geometry, Symmetry and Physics Projectivity of the Moduli of Branchvarieties 4:00pm -
KT 801

It is a fact of life that the moduli of (reduced) equidimensional subvarieties of projective space is often not complete. In 2010, Alexeev and Knutson introduced a compactification called the moduli of branchvarieties. This is a proper Deligne–Mumford stack parameterizing equidimensional varieties equipped with a finite morphism to projective space. In principle, this is a great parameter space to carry out GIT constructions of moduli of varieties. However, there is one main caveat to this: Alexeev and Knutson left as an open problem whether their proper DM stack is projective. In this talk, I will explain a proof of projectivity obtained in joint work with Dan Halpern-Leistner, Trevor Jones, and Ritvik Ramkumar.
Geometry, Symmetry and Physics Projectivity of the moduli of branchvarieties 4:00pm -
KT801

It is a fact of life that the moduli of (reduced) equidimensional subvarieties of projective space is often not complete. In 2010, Alexeev and Knutson introduced a compactification called the moduli of branchvarieties. This is a proper Deligne-Mumford stack parameterizing equidimensional varieties equipped with a finite morphism to projective space. In principle, this is a great parameter space to carry out GIT constructions of moduli of varieties. However, there is one main caveat to this: Alexeev and Knutson left as an open problem whether their proper DM stack is projective. In this talk, I will explain a proof of projectivity obtained in joint work with Dan Halpern-Leistner, Trevor Jones and Ritvik Ramkumar.