Upcoming talks

Non-invertible symmetries along 4d RG flows

Luigi Tizzano, ULB, Brussels

Tuesday 5 December 2023, 14:00-15:30

I will present novel examples of RG flows that preserve a non-invertible duality symmetry, with a primary focus on N=1 quadratic superpotential deformations of N=4 SYM. A famous theory that can be obtained in this way is N = 1* SYM, where all adjoint chiral multiplets possess a finite mass term. This IR theory exhibits a a rich structure of vacua that I will describe. Through this analysis, I will elucidate the physics underlying spontaneous duality symmetry breaking which occurs in the degenerate gapped vacua. Finally, I will briefly comment on various generalizations of these ideas for RG flows resulting in gapless IR theories.

Recent talks

An unobstructedness result for the coisotropic deformation problem

Stephane Geudens (UCL)

Tuesday 28 November 2023, 14:00-15:30

I will talk about deformations of coisotropic submanifolds in symplectic geometry. Unlike the deformation problem of Lagrangian submanifolds, the coisotropic deformation problem is generally obstructed, meaning that there may exist first order deformations which are not tangent to any path of deformations. I will review this fact and explain why the coisotropic deformation problem becomes unobstructed if one additionally keeps the diffeomorphism type of the characteristic foliation fixed.

Non-perturbative partition functions for supersymmetric QFT's

Lotte Hollands, Heriot-Watt University

Tuesday 21 November 2023, 14:00-15:30

In the intro to this seminar I will introduce the concept of a spectral network, we will work through a simple example together, and I will motivate why spectral networks are so important in the context of 4d N=2 supersymmetric field theories. In the main talk I will explain how to build a new kind of N=2 partition function starting from a spectral network. Compared to the well-known Nekrasov partition function, this new partition function depends (in a locally constant way) on an additional phase, and can be defined regardless of whether the N=2 theory has a Lagrangian definition. Jumps have an interpretation in terms of 4d BPS states, and the Nekrasov partition function is recovered from a special type of spectral network. When lifted to 5d, this partition function is now known as the non-perturbative topological string partition function.

B-brane Transport in K_{G(2,N)} GLSMs

Lucy Smith, Tsinghua University

Thursday 16 November 2023, 13:00-14:00
Watson LTC

A class of gauged linear sigma models is used to study the category of branes possessing N=2_B supersymmetry that can be transported across phases of the Kahler moduli space. The focus is models with a canonical line bundle over G(2,N) - theories with non-abelian gauge symmetry that have Grassmannian target space geometries, thus potentially leading to equivalences of derived categories of Grassmannians and matrix factorisations of gauged Landau-Ginzburg models. This talk will detail the transportation of a selection of branes across phases of the moduli space, from viewing the lay of the land of the moduli space, to moulding branes into the right form, to then transporting them across phase boundaries and back in monodromy loops. The main result is a prescription for constructing a general monodromy action to apply to branes in K_{G(2,N)} models, which are Fourier-Mukai transformations on the respective derived category.

Quotients for linear algebraic group actions via Geometric Invariant Theory

Eloise Hamilton, University of Cambridge

Tuesday 14 November 2023, 14:00-15:30

Given a linear algebraic group acting on a variety, finding a suitable quotient in the category of varieties is typically a non-trivial task. Geometric Invariant Theory (GIT) is a powerful theory for constructing such quotients, provided the group is reductive. When the group is unipotent (in particular non-reductive), the theory of locally nilpotent deviations can be used instead to construct quotients under suitable assumptions. After reviewing the reductive and unipotent approaches, I will explain how they can be combined into a so-called Non Reductive GIT which enables the construction of quotients for possibly non-reductive group actions. Finally (and time permitting) I will list some applications to the construction and study of old and new moduli spaces.

The tropical geometry of orbifolds

Robert Crumplin, Cambridge

Tuesday 31 October 2023, 14:00-15:30

I will introduce and study the tropicalisation of orbifolds and logarithmic orbifolds. These will be spaces built from integral tori, encoding the interactions of logarithmic and orbifold contact orders. Using these new tools, I will show a tropical lifting theorem for twisted stable maps, namely, given a graph mapping to a real torus (with some additional data), there is a genuine geometric twisted map to an orbifold which tropicalises to the starting data.

Predictions in Open FJRW Theory Using Mirror Symmetry and Wall-Crossing

Rob Maher, University of Birmingham

Tuesday 17 October 2023, 14:00-15:30

FJRW theory is an enumerative curve count for Landau-Ginzburg models. Analogous to Gromov-Witten theory for Calabi-Yau or Fano varieties, there is a mirror to FJRW theory that has become known as Saito-Givental theory. In this talk, I will motivate Saito-Givental theory as a twisted topological quantum field theory, as well as describing closed r-spin intersection numbers as the simplest example of FJRW theory. I will then explain closed Saito-Givental theory as a cohomological field theory by providing explicit formulas for the flat coordinates of the Frobenius manifold associated to any simple or elliptic singularity. This is an extension of work done by Noumi-Yamada. Finally, based on recent work of Gross-Kelly-Tessler, I will construct Saito-Givental theory for open invariants by describing a Lie group of wall-crossing transformations in rank 2, in addition to describing modularity properties in the elliptic case.

Mock modular forms as Z-invariants

Ioana Coman, IPMU

Tuesday 10 October 2023, 14:00-15:30

A new family of topological 3-manifold invariants has been proposed recently, with the property that they are q-series with integrality properties that allow categorification. They have a mathematical definition based on the data which specifies the associated 3-manifold, though this is of limited applicability and restricted to cases which satisfy a certain negativity condition. Aside from their relevance in topology, these invariants have proven to be of broad interest through a web of relations. Physically, they capture the partition functions of certain 3-dimensional SQFTs, while from a number theory perspective they provide examples of holomorphic quantum modular forms. Here I will discuss an underlying hidden symmetry of these invariants and how considerations of modularity can be leveraged to predict what these should be for manifolds not covered by their original definition, as well as the wider implications of these results.

Elliptic Log Symplectic Brackets on Projective Bundles

Mykola Matviichuk, Imperial College London

Tuesday 3 October 2023, 16:00-17:30

I will present a novel approach to constructing holomorphic log symplectic Poisson brackets that have a geometric connection to elliptic curves. This method relies on the deformation theory and involves combinatorics of graphs with decorations. I will demonstrate its effectiveness by creating new examples, as far as my knowledge extends, on complex projective bundles over a polydisc. Additionally, I will revisit and rediscover the Feigin-Odesski log symplectic brackets on projective spaces.