Seminars in the next week

Feb 28 (Wed)

11:00 zoom A&CRomain Ruzziconi (Oxford): *Carrollian amplitudes in flat space holography*

Carrollian holography aims to express gravity in asymptotically flat space-time in terms of a dual Carrollian CFT living at null infinity. In this talk, I will review some aspects of Carrollian holography and argue that this approach is naturally related to the AdS/CFT correspondence via a flat limit procedure. I will then introduce the notion of Carrollian amplitude, which allows to encode massless scattering amplitudes into boundary correlators, and explain its connection to celestial amplitudes. Finally, I will present recent results concerning Carrollian OPEs and deduce how soft symmetries act at null infinity. This talk will be mainly based on https://arxiv.org/abs/2312.10138.

**Venue:** zoom

Zoom: https://durhamuniversity.zoom.us/j/97074859719?pwd=N3Q4RDJDdkRFU3dIaXVIdUhNRk82Zz09

Feb 29 (Thu)

13:00 MCS2068 G&TLaura Wakelin (Imperial): *Non-characterising slopes for satellite knots*

A slope p/q is non-characterising for a knot K in the
3-sphere if there exists a different knot K' in the 3-sphere such that
Dehn surgery of slope p/q on each of K and K' produces
orientation-preserving homeomorphic 3-manifolds. In this talk, we will
explore 3 different approaches to constructing non-characterising slopes
for satellite knots. For the |p|=1 case, I'll describe how to use JSJ
decompositions to find suitable satellite knots of hyperbolic type
(joint work with Patricia Sorya). For the |q|=1 case, I'll discuss how
to use RBG links to address certain knots concordant to satellites of
(2,k)-torus knots (joint work with Charles Stine). Finally, for the
general p/q case, I'll explain how the Montesinos trick could
potentially be used to show that every p/q can be realised as a
non-characterising slope for some pair of satellite knots (joint work
with Kyle Hayden and Lisa Piccirillo).

**Venue:** MCS2068

Mar 01 (Fri)

13:00 MCS0001 HEPMFelipe Diaz-Jaramillo (Humboldt University): *Gauge Independent Kinematic Algebra of Self-Dual Yang-Mills*

The double copy is a remarkable relation between Yang-Mills theory and gravity. In Yang-Mills theory, scattering amplitudes contain information about color in the form of elements of a Lie algebra, and information about kinematics encoded in so-called kinematic numerators. The double copy states that, provided that certain algebraic conditions are fulfilled, exchanging the color information by kinematic information in Yang-Mills amplitudes leads to amplitudes in gravity. The algebraic considerations put color and kinematics on the same footing, suggesting that there is an algebra underlying the kinematics of Yang-Mills, similar to how color is encoded in a Lie algebra. The first explicit realization of a kinematic algebra was the Lie algebra of area-preserving diffeomorphisms in the self-dual sector of Yang-Mills theory after imposing a light-cone gauge condition. In this talk, using a framework based on homotopy algebras, I will show that there exists a larger kinematic algebra in the self-dual sector of Yang-Mills which does not rely on any choice of gauge and contains enough information to construct self-dual gravity.

**Venue:** MCS0001

Mar 04 (Mon)

13:00 MCS0001 PureFernando Galaz-Garcia (Durham): *tba*

tba

**Venue:** MCS0001

Mar 05 (Tue)

15:00 MCS3070 APDEDenis Patterson (Durham): *Spatial models of forest-savanna bistability*

Empirical studies suggest that for vast tracts of land in the tropics, closed-canopy forests and savanna are alternative stable states, a proposition with far-reaching implications in the context of ongoing climate change. Consequently, numerous mathematical models, both spatially implicit and explicit, have been proposed to capture the mechanistic basis of this bistability and quantify the stability of these ecosystems. I will present analysis of a spatially extended version of the Staver-Levinforest-savanna model and highlight some open mathematical problems related to the dynamics generated by these nonlocal PDEs. On a homogeneous domain, relevant to smaller spatial scales, we uncover various types of pattern-forming bifurcations in the presence of resource limitation. On larger (continental) spatial scales, heterogeneity plays a significant role in determining observed vegetative cover. Incorporating domain heterogeneity is a pressing mathematical challenge and leads to interesting phenomena such as front-pinning, complex waves of invasion, and extensive multi-stability.

**Venue:** MCS3070

Click on title to see abstract.

Upcoming Events

These events are hosted in and/or organised by members of the Department (follow links for details):

Mar 21--22 [tba] KineticNet

Mar 25--28 [MCS0001] LMS Regional Meeting & Continued Fractions and SL_2 Tilings

Upcoming Seminars by Series

(Click on series to expand.)
Usual Venue: zoom

Contact: arthur.lipstein@durham.ac.uk

Feb 28 11:00 Romain Ruzziconi (Oxford): *Carrollian amplitudes in flat space holography*

Carrollian holography aims to express gravity in asymptotically flat space-time in terms of a dual Carrollian CFT living at null infinity. In this talk, I will review some aspects of Carrollian holography and argue that this approach is naturally related to the AdS/CFT correspondence via a flat limit procedure. I will then introduce the notion of Carrollian amplitude, which allows to encode massless scattering amplitudes into boundary correlators, and explain its connection to celestial amplitudes. Finally, I will present recent results concerning Carrollian OPEs and deduce how soft symmetries act at null infinity. This talk will be mainly based on https://arxiv.org/abs/2312.10138.

**Venue:** zoom

Usual Venue: MCS3070

Contact: alpar.r.meszaros@durham.ac.uk

Mar 05 15:00 Denis Patterson (Durham): *Spatial models of forest-savanna bistability*

Empirical studies suggest that for vast tracts of land in the tropics, closed-canopy forests and savanna are alternative stable states, a proposition with far-reaching implications in the context of ongoing climate change. Consequently, numerous mathematical models, both spatially implicit and explicit, have been proposed to capture the mechanistic basis of this bistability and quantify the stability of these ecosystems. I will present analysis of a spatially extended version of the Staver-Levinforest-savanna model and highlight some open mathematical problems related to the dynamics generated by these nonlocal PDEs. On a homogeneous domain, relevant to smaller spatial scales, we uncover various types of pattern-forming bifurcations in the presence of resource limitation. On larger (continental) spatial scales, heterogeneity plays a significant role in determining observed vegetative cover. Incorporating domain heterogeneity is a pressing mathematical challenge and leads to interesting phenomena such as front-pinning, complex waves of invasion, and extensive multi-stability.

**Venue:** MCS3070

Mar 12 15:00 Jakub Skrzeczkowski (Oxford): *Several derivations of the degenerate Cahn-Hilliard equation via singular limits*

The degenerate Cahn-Hilliard equation, originally introduced in material science, is nowadays used in several different fields, including biology (tumor growth, cell-cell adhesion) and fluid dynamics (high-friction limit in the Euler-Korteweg equation). In this talk, we discuss several derivations of this equation: via hydrodynamic limit from the Vlasov equation (arXiv:2208.01026, arXiv: 2306.06486), from the nonlocal equation and related interacting particle system in the spirit of Giacomin-Lebowitz work (arXiv:2208.08955, arXiv:2303.11929), and most recently, from the Euler-Korteweg equation (arXiv:2305.01348). In most of these cases, fully rigorous solutions are available only in the case of torus and so, we will stress fundamental difficulties related to the presence of physical boundaries. This is a joint work with C. Elbar, B. Perthame (Paris), J. A. Carrillo (Oxford), M. Mason (Milan), A. Świerczewska-Gwiazda, and P. Gwiazda (Warsaw).

**Venue:** MCS3070

Usual Venue: MCS2052

Contact: andrew.krause@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time or during industrial actions).

Usual Venue: MCS2068

Contact: alexander.mangerel@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time or during industrial actions).

Usual Venue: OC218

Contact: mohamed.anber@durham.ac.uk

For more information, see HERE.

Mar 21 14:00 Vitor Cardoso: *TBA*

**Venue:** OC218

Usual Venue: MCS0001

Contact: inaki.garcia-etxebarria@durham.ac.uk,sunil.chhita@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time or during industrial actions).

Usual Venue: MCS3052

Contact: andrew.krause@durham.ac.uk

Usual Venue: MCS3070

Contact: gabriel.fuhrmann@durham.ac.uk

Usual Venue: MCS2068

Contact: martin.p.kerin@durham.ac.uk

Recordings of past seminars can be found HERE.

Feb 29 13:00 Laura Wakelin (Imperial): *Non-characterising slopes for satellite knots*

A slope p/q is non-characterising for a knot K in the
3-sphere if there exists a different knot K' in the 3-sphere such that
Dehn surgery of slope p/q on each of K and K' produces
orientation-preserving homeomorphic 3-manifolds. In this talk, we will
explore 3 different approaches to constructing non-characterising slopes
for satellite knots. For the |p|=1 case, I'll describe how to use JSJ
decompositions to find suitable satellite knots of hyperbolic type
(joint work with Patricia Sorya). For the |q|=1 case, I'll discuss how
to use RBG links to address certain knots concordant to satellites of
(2,k)-torus knots (joint work with Charles Stine). Finally, for the
general p/q case, I'll explain how the Montesinos trick could
potentially be used to show that every p/q can be realised as a
non-characterising slope for some pair of satellite knots (joint work
with Kyle Hayden and Lisa Piccirillo).

**Venue:** MCS2068

Mar 07 13:00 Subhankar Dey (Durham): *Essential surfaces in link exteriors and link Floer homology*

Knot/link Floer homology is a link invariant package,
introduced independently by Ozsvath-Szabo and Rasmussen, has been shown
to be quite useful to solve a number of questions in low dimensional
topology in the last two decades. Although it is not a complete
invariant of knots/links, a number of knots and links have been shown to
be detected by this toolbox. The center of most of these results have
been careful examination of certain essential surfaces in the knot/link
exteriors and observing that operations on those surfaces can be kept
track by the link/knot Floer homology of those knots/links. In this
mostly self-contained talk, we will be talking about those results and
some new ones. This is based on joint work with Fraser Binns, some of
which is ongoing.

**Venue:** MCS2068

Mar 14 13:00 Anthea Monod (Imperial): *TBA*

**Venue:** MCS3070

Apr 25 13:00 Luc Vranken (KU Leuven): *Homogeneous 6 dimensional nearly Kaehler manifolds and their
submanifolds*

We present a survey of how the curvature tensor of all known
homogeneous 6 dimensional nearly Kähler spaces (both in the definite and
in the pseudo Riemannian case) can be expressed in an invariant way
using the induced geometric structures on the 6 dimensional nearly
Kähler space.

As an application we show how this can be used to study special classes of submanifolds in these spaces. In the latter case we will in particular focus on totally geodesic Lagrangian submanifolds and equivariant Lagrangian immersions.

**Venue:** MCS2068

May 09 13:00 Andrey Lazarev (Lancaster): *TBA*

**Venue:** MCS2068

May 16 13:00 Asma Hassannezhad (Bristol): *TBA*

**Venue:** MCS2068

Usual Venue: MCS3070

Contact: andrea.grigoletto@durham.ac.uk,nakarin.lohitsiri@durham.ac.uk

Usual Venue: MCS0001

Contact: silvia.nagy@durham.ac.uk,ana.retore@durham.ac.uk

Mar 01 13:00 Felipe Diaz-Jaramillo (Humboldt University): *Gauge Independent Kinematic Algebra of Self-Dual Yang-Mills*

The double copy is a remarkable relation between Yang-Mills theory and gravity. In Yang-Mills theory, scattering amplitudes contain information about color in the form of elements of a Lie algebra, and information about kinematics encoded in so-called kinematic numerators. The double copy states that, provided that certain algebraic conditions are fulfilled, exchanging the color information by kinematic information in Yang-Mills amplitudes leads to amplitudes in gravity. The algebraic considerations put color and kinematics on the same footing, suggesting that there is an algebra underlying the kinematics of Yang-Mills, similar to how color is encoded in a Lie algebra. The first explicit realization of a kinematic algebra was the Lie algebra of area-preserving diffeomorphisms in the self-dual sector of Yang-Mills theory after imposing a light-cone gauge condition. In this talk, using a framework based on homotopy algebras, I will show that there exists a larger kinematic algebra in the self-dual sector of Yang-Mills which does not rely on any choice of gauge and contains enough information to construct self-dual gravity.

**Venue:** MCS0001

Mar 08 13:00 Shai Chester (Imperial College London): *Bootstrapping N = 4 SYM for all N and coupling*

We combine supersymmetric localization with the numerical conformal bootstrap to bound the scaling dimension and OPE coefficient of the lowest-dimension operator in N = 4 SU( N) super-Yang-Mills theory for a wide range of N and Yang-Mills couplings g. We find that our bounds are approximately saturated by weak coupling results at small g. Furthermore, at large N our bounds interpolate between integrability results for the Konishi operator at small g and strong-coupling results, including the first few stringy corrections, for the lowest-dimension double-trace operator at large g. In particular, our scaling dimension bounds describe the level splitting between the single- and double-trace operators at intermediate coupling.

**Venue:** MCS0001

Mar 15 13:00 Valentina Forini (Humboldt University): *TBA*

TBA

**Venue:** MCS0001

Usual Venue: MCS2068

Contact: kohei.suzuki@durham.ac.uk

Mar 08 13:00 Vladislav Vysotskiy (Sussex): *Persistence of AR(1) sequences with Rademacher innovations and linear mod 1 transforms*

We study the probability that an autoregressive Markov chain X_{n+1} = a X_n + Y_{n+1}, where 0 < a < 1 is a constant, stays non-negative for a long time. We find the exact asymptotics of this probability and the weak limit of X_n conditioned to stay non-negative, assuming that the i.i.d. innovations Y_n take only two values +1, -1 and a <= 2/3. This limiting distribution is quasi-stationary. The limiting distribution has no atoms and is singular with respect to the Lebesgue measure when 1/2 < a <= 2/3, except for the case a = 2/3 and P(Y_n=1)=1/2, where it is uniform on the interval [0,3]. This is similar to the properties of Bernoulli convolutions.

It turns out that for the +1, -1 innovations there is a close connection between X_n killed at exiting [0, \infty) and the classical dynamical system defined by the piecewise linear mapping x -> ( x/a + 1/2) mod 1. Namely, the trajectory of this system started at X_n deterministically recovers the values of the killed chain in reversed time! We use this property to construct a suitable Banach space, where the transition operator of the killed chain has the compactness properties that let us apply a conventional argument of Perron--Frobenius type. The difficulty in finding such space stems from discreteness of the innovations.

**Venue:** MCS2068

Mar 15 13:00 Edward Crane (Bristol): *Markov lumpings, intertwinings, and couplings*

For a Markov process X in discrete or continuous time, taking values in a state space A, and a function F from A to another space B, the process (F(X_t)) is in general not a Markov process. But in some interesting cases (F(X_t)) does have the Markov property, in which case F is said to be a weak lumping of X. In the first part of the talk, I will discuss what is known about weak lumpings in general, and some stronger properties called strong lumping and exact lumping, which account for most examples of weak lumpings in the probability literature. In the second part of the talk, I will describe our results about the problem of coupling two given homogeneous discrete time Markov chains so that the coupled process is also a homogeneous Markov chain, subject to given constraints on the set of allowed coupled states and allowed transitions of the coupled chain. The connection with the first half of the talk is that the projection maps to the marginal processes must both be weak lumpings. I will aim to make the talk accessible to any undergraduates who have learned about Markov chains and the basics of queueing theory and renewal processes.

**Venue:** MCS2068

Usual Venue: MCS0001

Contact: raphael.zentner@durham.ac.uk

Mar 04 13:00 Fernando Galaz-Garcia (Durham): *tba*

tba

**Venue:** MCS0001

Mar 11 13:00 Michel Boileau (Aix-Marseille): *tba*

tba

**Venue:** MCS0001

Apr 22 13:00 Abigail Ward (Cambridge): *tba*

tba

**Venue:** MCS0001

Usual Venue: MCS3070

Contact: irving.d.calderon-camacho@durham.ac.uk,joe.thomas@durham.ac.uk

Usual Venue: MCS2068

Contact: hyeyoung.maeng@durham.ac.uk,andrew.iskauskas@durham.ac.uk

Contact: adam.stone2@durham.ac.uk