Low-rank approximation of parameter-dependent matrices via CUR decomposition
Park, T
Nakatsukasa, Y
SIAM Journal on Scientific Computing
Fri, 28 Feb 2025
09:00 -
Wed, 31 Dec 2025
00:00
Mezzanine
Kathleen Hyndman - Nature+Maths=Art
Further Information
The Mathematical Institute is delighted to be hosting a major exhibition of artist Kathleen Hyndman's mathematically inspired work.
The exhibition of drawings and paintings illustrate Hyndman’s desire to see nature and the world around her in mathematical sequences and geometrical patterns. Golden Section proportions and angles, prime numbers as well as Fibonacci numbers and eccentric constructions are all used to create works achieving a calm and balanced unity.
Born in Essex, Hyndman trained at Kingston-upon-Thames School of Art and exhibited widely in the UK and abroad, including MOMA Oxford and the Hayward Annual in London. As well as a full time artist, she was also a teacher and mother of two. She lived and had her studio in Kingston Bagpuize in Oxfordshire and had exhibitions at Zuleika Gallery in Woodstock until her death in 2022.
The exhibition is curated by Zuleika Gallery and Professor Martin Kemp FBA, and will run until the end of the year.
Bottom from left: Hot Breeze, 1994; Heat, 1976; Exit (a seventeen sided work), 1993; Straight Line Rotation, White on Black. Forest, 1986
Below: film of the exhibition by Evan Nedyalkov
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.