Combining the conjectures of Schanuel and Zilber-Pink
Pila, J
Rendiconti Lincei. Matematica e Applicazioni
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Tue, 16 Jun 2026
15:30
15:30
L4
Wall-crossing Package via Non-Abelian Localization
Ivan Karpov
(MIT)
Abstract
Recent and seminal work of Dominic Joyce and his coauthors has produced a new (and, indeed, the first) wall-crossing machinery in the context of certain quasi-smooth moduli stacks of abelian categories: quiver representations, sheaves on Fano threefolds, and so forth.
Henry Liu has later explained how its K-theoretic version should look like.
Most importantly, perhaps, this machinery defines reasonable virtual fundamental classes for moduli stacks that may contain strictly semistable objects.
Unfortunately, these results do not, without further modification, apply to stacks of objects in derived categories (as opposed to abelian ones) since they require certain additional data.
This data, the so-called 'framing functor', plays an important rôle in the original constructions, and is unavailable in the derived case.
I shall try to explain a modest extension of Joyce-Liu’s K-theoretic Monster Wall-Crossing Formalism which, in most cases, makes it possible to dispense with this additional data, and clarifies the relation to motivic wall-crossing.
Our proof of this extension is very different from Joyce’s own, and is based instead on Halpern-Leistner’s Non-Abelian Localization (NAL) Theorem, and on the use of Blanc's topological K-theory.
The applications include carrying out the Feyzbakhsh–Thomas programme for Fano threefolds with even canonical class, and proving (simultaneously with R. Anderson and D. Joyce, though under stricter assumptions on the underlying variety) rationality and functional equations for generating functions of Pandharipande–Thomas invariants.
Time permitting, I shall also try to sketch a very short proof of the wall-crossing formula for Calabi–Yau 4-folds (conjectured by Joyce and later investigated by Bojko) which follows the NAL strategy and uses the so-called Drinfeld–Gaitsgory degeneration. This argument explains also the relation between the NAL story and the hyperbolic localization package.
Everything is joint with M. Moreira, and is partly in progress.
Neural systems in general - and the human brain in particular - are organised as networks of interconnected components. Across a range of spatial scales from single cells to macroscopic areas, biological neural networks are neither perfectly ordered nor perfectly random.
Thu, 12 Mar 2026
12:45
12:45
L6
An obstruction to realizing anomalous symmetries in 1+1d lattice models
Rajath Radhakrishnan
Abstract
Realizing quantum field theories on lattice models is important for several reasons, ranging from enabling non-perturbative studies of field theories to quantum simulations. However, it is well known that not all quantum field theories can be realized on a lattice (for example, Nielsen-Ninomiya theorem).
In this talk, I will consider a very special aspect of this problem. Given a symmetry described by a group G with a specific choice of ’t Hooft anomaly, can it be realized in a quantum spin system, i.e., a lattice model whose Hilbert space is a tensor product of finite-dimensional Hilbert spaces associated with each site? I will describe an explicit constraint which shows that certain anomalous symmetries cannot be realized in such lattice models.
This talk is based on https://arxiv.org/pdf/2602.13948 (also, https://arxiv.org/pdf/2401.02533 and https://arxiv.org/pdf/1409.5436).
Further Information
Please submit papers to discuss and topic suggestions here: https://sites.google.com/view/math-phys-oxford/journal-club
Thu, 05 Mar 2026
12:45
12:45
L6
"Filtering" CFTs at large N
Marta Bucca
Abstract
The map between large-N conformal field theories and semiclassical gravity has been one of the defining achievements of holography. However, the large N holographic dictionary remains incomplete. One of its most notable criticisms, is the failure to address the factorization problem, where the appearance of Euclidean wormholes in the gravitational path integral, lacks a clear interpretation on the large N CFT side. A related challenge is the possibility of erratic N dependence in CFT observables, behaviour with no evident semiclassical gravitational counterpart. In arXiv:2512.13807, a solution is proposed in the form of a large N filter that removes the erratic N dependence of CFT quantities and provides a boundary explanation of wormhole contributions.
In this talk, I will briefly review the factorization problem and illustrate the proposed large N filter resolution. Time permitting, I will also outline some of the Lorentzian spacetime structures that can emerge when working within the framework of such a large N filter, such as the appearance of baby universes and black holes interiors.
In this talk, I will briefly review the factorization problem and illustrate the proposed large N filter resolution. Time permitting, I will also outline some of the Lorentzian spacetime structures that can emerge when working within the framework of such a large N filter, such as the appearance of baby universes and black holes interiors.
Further Information
Please submit papers to discuss and topic suggestions here: https://sites.google.com/view/math-phys-oxford/journal-club
Thu, 26 Feb 2026
12:45
12:45
L6
Are Generalised Symmetries Symmetries?
Thomas Bartsch
Abstract
Traditionally, a symmetry of a quantum system refers to a transformation that preserves transition probabilities between physical states. In recent years, this notion has been expanded to so-called generalised symmetries, which correspond to (possibly non-invertible) topological defects in quantum field theory. At first sight, it is not obvious how the above two notions of symmetry are related. In this talk, I will review the notion of generalised symmetries and discuss how they relate to (and depart from) the traditional notion of symmetry.
Further Information
Please submit papers to discuss and topic suggestions here: https://sites.google.com/view/math-phys-oxford/journal-club
Thu, 19 Feb 2026
12:45
12:45
L6
Setting the stage for flat space holography
Emil Have
Abstract
Flat space holography, if there really is such a thing, is intimately related to Carrollian geometry. I will give an introduction to Carrollian geometry, and discuss how many Carrollian spaces of interest arise as homogeneous spaces of the Poincaré group. Finally, I will discuss the construction of Cartan geometries modelled on these spaces.
Further Information
Please submit papers to discuss and topic suggestions here: https://sites.google.com/view/math-phys-oxford/journal-club
Thu, 12 Feb 2026
13:00
13:00
L6
Non-conformal Dp-brane holography
Alice Lüscher
Abstract
The canonical example of AdS/CFT relates N=4 SYM in 4d to supergravity on AdS5 x S5 by considering a stack of D3-branes. A natural question then emerges: what about considering other Dp-branes? The worldvolume theory is again SYM but is not conformal anymore, while the supergravity dual is now only conformally AdS. Despite these differences, some control remains, and some inspiration from the p=3 case can be sought. In this talk, I will review this setup and discuss the recent results of [2503.18770] and [2503.14685] regarding the computation of correlation functions.
Further Information
Please submit papers to discuss and topic suggestions here: https://sites.google.com/view/math-phys-oxford/journal-club
Thu, 05 Feb 2026
12:45
12:45
L6
Puzzles for babies
Boris Post
Abstract
For this JC, I will review the recently much debated puzzles that arise in holographic systems with baby universes. After describing the original set-up of Antonini-Sasieta-Swingle, I will explain the paradox raised by Antonini-Rath, which suggests the existence of a single CFT state that can have two distinct holographic descriptions in the bulk: one with a closed baby universe and one without. I will discuss various proposed resolutions of this puzzle, which may (or may not) require us to rethink the holographic dictionary in AdS/CFT.
Further Information
Please submit papers to discuss and topic suggestions here: https://sites.google.com/view/math-phys-oxford/journal-club