Seminars in Mathematical Sciences

Seminars in the next week
Jan 18 (Tue)

13:00

Jan 19 (Wed)

16:00 Paul Heslop: Superblocks and applications in quantum gravity

I will summarise work done obtaining certain superblocks in various supersymmetric theories - in particular focussing on further explorations of new relations with the mathematical literature on symmetric polynomials and CMS systems. Then (if time) focussing on N=4 SYM I will outline some applications of their use in bootstrapping quantum gravity on AdS space via AdS/CFT.
Jan 20 (Thu)

13:00 Jesús Núñez-Zimbrón: Harmonic functions on spaces with Ricci curvature bounded below

The so-called spaces with the Riemannian curvature-dimension conditions (RCD spaces) are metric measure spaces which are not necessarily smooth but admit a notion of “Ricci curvature bounded below and dimension bounded above”. These spaces arise naturally as Gromov-Hausdorff limits of Riemannian manifolds with these conditions and, in contrast to manifolds, RCD spaces typically have topological or metric singularities. Nevertheless a considerable amount of Riemannian geometry can be recovered for these spaces. In this talk I will present recent work joint with Guido De Philippis, in which we show that the gradients of harmonic functions vanish at certain singular points of the space. I will mention two applications of this result which are new on smooth manifolds: there does not exist an a priori estimate on the modulus of continuity of the gradient of harmonic functions depending only on lower bounds of the sectional curvature and there is no a priori Calderón-Zygmund inequality for the Laplacian with bounds depending only on the sectional curvature.

14:00 Alessandro Torrielli: Integrable scattering of massless particles and the AdS/CFT correspondence

After a brief introduction to some of the impact which integrable methods and the Bethe ansatz have had on the study of the AdS/CFT correspondence in string theory, we will focus on the axiomatic approach to S-matrix theory in 1+1 dimensions. We will highlight the issues that arise when the particles are massless, and how this is in fact connected to Zamolodchikov's way of describing two-dimensional conformal field theories by means of integrability techniques. We will then mention how the axiomatic approach extends to form-factors, which are the gate to access the n-point functions of the theory. If time permits, we will briefly depict how this finds a contemporary application in the area of the AdS_3/CFT_2 correspondence.

Venue: (unless stated above) OC218

Jan 21 (Fri)
In this talk we develop the theory of a metric, which we call the $\nu$-based Wasserstein metric and denote by $W_\nu$, on the set of probability measures $\mathcal P(X)$ on a domain $X \subseteq \mathbb{R}^m$. This metric is based on a slight refinement of the notion of generalized geodesics with respect to a base measure $\nu$ and is relevant in particular for the case when $\nu$ is singular with respect to $m$-dimensional Lebesgue measure; it is also closely related to the concept of linearized optimal transport. The $\nu$-based Wasserstein metric is defined in terms of an iterated variational problem involving optimal transport to $\nu$; we also characterize it in terms of integrations of classical Wasserstein distance between the conditional probabilities when measures are disintegrated with respect to optimal transport to $\nu$, and through limits of certain multi-marginal optimal transport problems. As we vary the base measure $\nu$, the $\nu$-based Wasserstein metric interpolates between the usual quadratic Wasserstein distance (obtained when $\nu$ is a Dirac mass) and a metric associated with the uniquely defined generalized geodesics obtained when $\nu$ is sufficiently regular (eg, absolutely continuous with respect to Lebesgue). When $\nu$ concentrates on a lower dimensional submanifold of $\mathbb{R}^m$, we prove that the variational problem in the definition of the $\nu$-based Wasserstein distance has a unique solution. We establish geodesic convexity of the usual class of functionals, and of the set of source measures $\mu$ such that optimal transport between $\mu$ and $\nu$ satisfies a strengthening of the generalized nestedness condition introduced in McCann&Pass 2020. If time permitted we also present an applications of the ideas introduced: we also use the multi-marginal formulation to characterize solutions to the multi-marginal problem by an ordinary differential equation, yielding a new numerical method for it.

13:00 Costis Papageorgakis: Towards Solving CFTs with Artificial Intelligence

I will introduce a novel numerical approach for solving the conformal-bootstrap equations with Reinforcement Learning. I will apply this to the case of two-dimensional CFTs, successfully identifying well-known theories like the 2D Ising model and the 2D CFT of a compact scalar, but the method can be used to study arbitrary (unitary or non-unitary) CFTs in any spacetime dimension.
Jan 24 (Mon)

00:00 Clare Wallace: TBC

TBC

Venue: (unless stated above) MCS2068

13:00 Graeme Wilkin: Morse theory, old and new

Morse theory is an old subject with a long history of spectacular applications to different problems in geometry, topology and analysis. I will review some of this history due to the work of such luminaries as Morse, Bott, Milnor and Smale, before moving on to more modern applications of Atiyah & Bott, Kirwan and Witten. If time permits, I will talk about more recent work of my own which applies a number of these ideas to singular spaces.

Venue: (unless stated above) MCS0001

Jan 25 (Tue)

13:00

Topology has become a much-discussed part of current research in solid-state magnetism, providing an organising principle to classify field theories, and their ground states and excitations, that are now regularly realized in magnetic materials. Examples include topological excitations such as skyrmions which exist in the spin textures of an expanding range of magnetic systems, and one-dimensional spin-chain systems, where topological considerations are key in understanding their properties. Central to this story is the role of the sine-Gordon model, which was important in motivating Skyrme's work and also in understanding the properties of spin chains using field theories. From this starting point, I will review some of the states that we might expect to realize in magnetic materials, and provide two sets of examples of where and how these have been found. Firstly, I will present examples spin chains and ladders formed of molecular building blocks, where the versatility of carbon chemistry allows access to spin Luttinger liquids, and sine-Gordon and Haldane chains. Secondly I shall discuss materials that host magnetic skyrmions and related excitations, along with the prospects for finding still more of these in the future.

13:05

The theory of unlikely intersections makes predictions about how endomorphism algebras vary in families of abelian varieties. I will explain some of these predictions and outline methods used to prove results of this type using reduction theory of arithmetic groups.

Venue: (unless stated above) MCS3070

Click on title to see abstract (and venue, if in person). Zoom links, if available, are given for today's seminars only.

Upcoming Seminars by Series
(Click on series to expand.)
• Amplitudes and Correlators

Contact: arthur.lipstein@durham.ac.uk

Jan 19 16:00 Paul Heslop: Superblocks and applications in quantum gravity

I will summarise work done obtaining certain superblocks in various supersymmetric theories - in particular focussing on further explorations of new relations with the mathematical literature on symmetric polynomials and CMS systems. Then (if time) focussing on N=4 SYM I will outline some applications of their use in bootstrapping quantum gravity on AdS space via AdS/CFT.
• Analysis and PDE Seminar

Jan 21 13:00

In this talk we develop the theory of a metric, which we call the $\nu$-based Wasserstein metric and denote by $W_\nu$, on the set of probability measures $\mathcal P(X)$ on a domain $X \subseteq \mathbb{R}^m$. This metric is based on a slight refinement of the notion of generalized geodesics with respect to a base measure $\nu$ and is relevant in particular for the case when $\nu$ is singular with respect to $m$-dimensional Lebesgue measure; it is also closely related to the concept of linearized optimal transport. The $\nu$-based Wasserstein metric is defined in terms of an iterated variational problem involving optimal transport to $\nu$; we also characterize it in terms of integrations of classical Wasserstein distance between the conditional probabilities when measures are disintegrated with respect to optimal transport to $\nu$, and through limits of certain multi-marginal optimal transport problems. As we vary the base measure $\nu$, the $\nu$-based Wasserstein metric interpolates between the usual quadratic Wasserstein distance (obtained when $\nu$ is a Dirac mass) and a metric associated with the uniquely defined generalized geodesics obtained when $\nu$ is sufficiently regular (eg, absolutely continuous with respect to Lebesgue). When $\nu$ concentrates on a lower dimensional submanifold of $\mathbb{R}^m$, we prove that the variational problem in the definition of the $\nu$-based Wasserstein distance has a unique solution. We establish geodesic convexity of the usual class of functionals, and of the set of source measures $\mu$ such that optimal transport between $\mu$ and $\nu$ satisfies a strengthening of the generalized nestedness condition introduced in McCann&Pass 2020. If time permitted we also present an applications of the ideas introduced: we also use the multi-marginal formulation to characterize solutions to the multi-marginal problem by an ordinary differential equation, yielding a new numerical method for it.

Feb 04 13:00 Anton Arnold:

Feb 11 13:00 Tobias Wöhrer: TBA

Feb 18 13:00 Frantisek Stampach: tba

• Applied Mathematics Seminar

Contact: christopher.prior@durham.ac.uk

Jan 18 13:00

Jan 25 13:00

Topology has become a much-discussed part of current research in solid-state magnetism, providing an organising principle to classify field theories, and their ground states and excitations, that are now regularly realized in magnetic materials. Examples include topological excitations such as skyrmions which exist in the spin textures of an expanding range of magnetic systems, and one-dimensional spin-chain systems, where topological considerations are key in understanding their properties. Central to this story is the role of the sine-Gordon model, which was important in motivating Skyrme's work and also in understanding the properties of spin chains using field theories. From this starting point, I will review some of the states that we might expect to realize in magnetic materials, and provide two sets of examples of where and how these have been found. Firstly, I will present examples spin chains and ladders formed of molecular building blocks, where the versatility of carbon chemistry allows access to spin Luttinger liquids, and sine-Gordon and Haldane chains. Secondly I shall discuss materials that host magnetic skyrmions and related excitations, along with the prospects for finding still more of these in the future.
• Arithmetic Study Group

Usual Venue: MCS3070

Contact: jack.g.shotton@durham.ac.uk

Jan 25 13:05

The theory of unlikely intersections makes predictions about how endomorphism algebras vary in families of abelian varieties. I will explain some of these predictions and outline methods used to prove results of this type using reduction theory of arithmetic groups.

Feb 08 13:05 James Newton:

Mar 01 13:05 Alice Pozzi:

Mar 08 13:00 Daniele Dorigoni: Modular graph forms, Poincare series and iterated integrals

Mar 15 13:05 Simon Myerson:

• Centre for Particle Theory Colloquium

Usual Venue: OC218

Contact: stefano.cremonesi@durham.ac.uk

Jan 20 14:00 Alessandro Torrielli: Integrable scattering of massless particles and the AdS/CFT correspondence

After a brief introduction to some of the impact which integrable methods and the Bethe ansatz have had on the study of the AdS/CFT correspondence in string theory, we will focus on the axiomatic approach to S-matrix theory in 1+1 dimensions. We will highlight the issues that arise when the particles are massless, and how this is in fact connected to Zamolodchikov's way of describing two-dimensional conformal field theories by means of integrability techniques. We will then mention how the axiomatic approach extends to form-factors, which are the gate to access the n-point functions of the theory. If time permits, we will briefly depict how this finds a contemporary application in the area of the AdS_3/CFT_2 correspondence.

Feb 03 14:00 Djuna Croon: TBA

Mar 03 14:00 Luigi Del Debbio: TBA

Mar 17 14:00 Arttu Rajantie: TBA

• CPT Student Seminar

Contact: hugo.fortin@durham.ac.uk

No upcoming seminars have been scheduled (not unusual during summer breaks).

• Department Research Colloquium

Usual Venue: MCS0001

No upcoming seminars have been scheduled (not unusual during summer breaks).

• Distinguished and Public Lectures

Contact: p.e.dorey@durham.ac.uk

No upcoming seminars have been scheduled (not unusual during summer breaks).

• Ergodic Theory and Dynamics

Usual Venue: MCS3070

Contact: gabriel.fuhrmann@durham.ac.uk

No upcoming seminars have been scheduled (not unusual during summer breaks).

• Geometry and Topology Seminar

Recordings of past seminars can be found HERE.

Jan 20 13:00 Jesús Núñez-Zimbrón: Harmonic functions on spaces with Ricci curvature bounded below

The so-called spaces with the Riemannian curvature-dimension conditions (RCD spaces) are metric measure spaces which are not necessarily smooth but admit a notion of “Ricci curvature bounded below and dimension bounded above”. These spaces arise naturally as Gromov-Hausdorff limits of Riemannian manifolds with these conditions and, in contrast to manifolds, RCD spaces typically have topological or metric singularities. Nevertheless a considerable amount of Riemannian geometry can be recovered for these spaces. In this talk I will present recent work joint with Guido De Philippis, in which we show that the gradients of harmonic functions vanish at certain singular points of the space. I will mention two applications of this result which are new on smooth manifolds: there does not exist an a priori estimate on the modulus of continuity of the gradient of harmonic functions depending only on lower bounds of the sectional curvature and there is no a priori Calderón-Zygmund inequality for the Laplacian with bounds depending only on the sectional curvature.

Jan 27 13:05 Michelle Daher: TBA

TBA

Feb 03 13:00 Ana Lucia Garcia Pulido: TBA

TBA

Feb 24 13:05 Danica Kosanović: Embedding spaces

TBA
• HEP Journal Club

Contact: tin.sulejmanpasic@durham.ac.uk

No upcoming seminars have been scheduled (not unusual during summer breaks).

• Maths HEP Lunchtime Seminar

Note: if held in person (please see abstract), the usual room is MCS2068; otherwise on zoom.

Jan 21 13:00 Costis Papageorgakis: Towards Solving CFTs with Artificial Intelligence

I will introduce a novel numerical approach for solving the conformal-bootstrap equations with Reinforcement Learning. I will apply this to the case of two-dimensional CFTs, successfully identifying well-known theories like the 2D Ising model and the 2D CFT of a compact scalar, but the method can be used to study arbitrary (unitary or non-unitary) CFTs in any spacetime dimension.

Jan 28 13:00 Javier Magán: TBA

Feb 04 13:00 Alexandre Belin: TBA

Mar 11 13:00 Federico Zerbini: TBA

Mar 18 13:00 Irene Valenzuela: TBA

• Probability Seminar

Usual Venue: MCS2068

Contact: ellen.g.powell@durham.ac.uk

Jan 24 00:00 Clare Wallace: TBC

TBC

Jan 31 00:00 Agnes Backhausz: TBC

TBC

Feb 07 00:00 Jon Peterson: TBC

TBC

Feb 14 00:00 Pierre-Francois Rodriguez: TBC

TBC

Feb 21 00:00 Malin Palö Forsström: TBC

TBC

Mar 07 00:00 Daniel Ueltschi: TBC

TBC

Mar 14 00:00 Damian Clancy: TBC

TBC
• Pure Maths Colloquium

Usual Venue: MCS0001

Contact: jack.g.shotton@durham.ac.uk

Jan 24 13:00 Graeme Wilkin: Morse theory, old and new

Morse theory is an old subject with a long history of spectacular applications to different problems in geometry, topology and analysis. I will review some of this history due to the work of such luminaries as Morse, Bott, Milnor and Smale, before moving on to more modern applications of Atiyah & Bott, Kirwan and Witten. If time permits, I will talk about more recent work of my own which applies a number of these ideas to singular spaces.

Feb 07 13:00 James Newton:

Feb 14 13:00 Yue Ren:

Feb 21 13:00 Julian Scheuer:

Feb 28 13:00 Reem Yassawi:

Mar 07 13:00 Heather Harrington: TBC

TBC

• Spectra and Moduli

Usual Venue: MCS3070

Contact: michael.r.magee@durham.ac.uk

No upcoming seminars have been scheduled (not unusual during summer breaks).

• Statistics Seminar

Usual Venue: MCS2068

Feb 14 13:00 Giusi Moffa: TBC

TBC

Feb 28 13:00 Wenkai Xu: tba

tba

May 23 13:00 Theodore Papamarkou: tba

tba