Tue, 11 Mar 2025
13:00
13:00
L5
Topological Quantum Dark Matter via Standard Model's Global Gravitational Anomaly Cancellation
Juven Wang
(LIMS)
Abstract
In this talk, we propose that topological order can replace sterile neutrinos as dark matter candidates
to cancel the Standard Model’s global gravitational anomalies. Standard Model (SM) with 15 Weyl fermions per family
(lacking the 16th, the sterile right-handed neutrino νR) suffers from mixed gauge-gravitational anomalies tied to baryon number plus or minus
lepton number B±L symmetry. Including νR per family can cancel these anomalies, but when B±L
symmetry is preserved as discrete finite subgroups rather than a continuous U(1), the perturbative
local anomalies become nonperturbative global anomalies. We systematically enumerate
these gauge-gravitational global anomalies involving discrete B ± L that are enhanced from the
fermion parity ZF2 to ZF2N , with N = 2, 3, 4, 6, 9, etc. The discreteness of B ± L is constrained by
multi-fermion deformations beyond-the-SM and the family number Nf . Unlike the free quadratic
νR Majorana mass gap preserving the minimal ZF2 , we explore novel scenarios canceling (B ± L)-gravitational anomalies
symmetry is preserved as discrete finite subgroups rather than a continuous U(1), the perturbative
local anomalies become nonperturbative global anomalies. We systematically enumerate
these gauge-gravitational global anomalies involving discrete B ± L that are enhanced from the
fermion parity ZF2 to ZF2N , with N = 2, 3, 4, 6, 9, etc. The discreteness of B ± L is constrained by
multi-fermion deformations beyond-the-SM and the family number Nf . Unlike the free quadratic
νR Majorana mass gap preserving the minimal ZF2 , we explore novel scenarios canceling (B ± L)-gravitational anomalies
while preserving the ZF2N discrete symmetries, featuring 4-dimensional interacting gapped topological orders
or gapless sectors (e.g., conformal field theories). We propose symmetric anomalous sectors as
quantum dark matter to cancel SM’s global anomalies. We find the uniqueness
of the family number at Nf = 3, such that when the representation of ZF2N from the faithful B + L
for baryons at N = Nf = 3 is extended to the faithful Q + NcL for quarks at N = NcNf = 9, this
symmetry extension ZNc=3 → ZNcNf =9 → ZNf =3 matches with the topological order dark matter
construction. Key implications include: (1) a 5th force mediating between SM and dark matter via
discrete B±L gauge fields, (2) dark matter as topological order quantum matter with gapped anyon
excitations at ends of extended defects, and (3) Ultra Unification and topological leptogenesis.
of the family number at Nf = 3, such that when the representation of ZF2N from the faithful B + L
for baryons at N = Nf = 3 is extended to the faithful Q + NcL for quarks at N = NcNf = 9, this
symmetry extension ZNc=3 → ZNcNf =9 → ZNf =3 matches with the topological order dark matter
construction. Key implications include: (1) a 5th force mediating between SM and dark matter via
discrete B±L gauge fields, (2) dark matter as topological order quantum matter with gapped anyon
excitations at ends of extended defects, and (3) Ultra Unification and topological leptogenesis.
The community mile is a mass event, open to all abilities and ages from six and above. The course (1 mile long) will start on St Aldate’s and proceed down the High Street, crossing Magdalen Bridge before finishing on Iffley Road, where bespoke finisher medals will be presented.
From 9 am on Monday 5th May.
In this case study we survey the historical development of $\mathrm{Lip}(\gamma)$ functions, beginning with the work of Hassler Whitney from the 1930s and ending with some of the recent properties established by Terry Lyons and Andrew McLeod that are particul
Tue, 11 Mar 2025
12:00
12:00
C4
Non-commutative derived geometry
Federico Bambozzi
(University of Padova)
Abstract
I will describe a non-commutative version of the Zariski topology and explain how to use it to produce a functorial spectrum for all derived rings. If time permits I will give some examples and show how a weak form of Gelfand duality for non-commutative rings can be deduced from this. This work is in collaboration with Simone Murro and Matteo Capoferri.
Mon, 26 May 2025
14:15
14:15
L5
Towards a gauge-theoretic approximation of codimension-three area
Alessandro Pigati
(Bocconi University)
Abstract
In the last three decades, a fruitful way to approximate the area functional in low codimension is to interpret submanifolds as the nodal sets of maps (or sections of vector bundles), critical for suitable physical energies or well-known lagrangians from gauge theory. Inspired by the situation in codimension two, where the abelian Higgs model has provided a successful framework, we look at the non-abelian SU(2) model as a natural candidate in codimension three. In this talk we will survey the new key difficulties and some recent partial results, including a joint work with D. Parise and D. Stern and another result by Y. Li.
Low complexity among principal fully irreducible elements of Out(F3)
Andrew, N
Hillen, P
Lyman, R
Pfaff, C
Algebraic and Geometric Topology
Homology growth of polynomially growing mapping tori
Andrew, N
Guerch, Y
Hughes, S
Kudlinska, M
Groups, Geometry, and Dynamics
The impact of confinement on deformable porous structures in flow
Finney, S
https://www.bristol.ac.uk/people/person/Matthew-Hennessy-6236a14f-01dc-40ed-bc9f-20bc40ce1666/