Seminars in Mathematical Sciences

Seminars in the next week
Nov 10 (Tue)

14:00 MCS2068 APDEFrancesco Salerno (SSM Napoli/Durham): On Saint-Venant Type Inequalities

In classical shape optimization, the ball often arises as an extremizer. In this talk, we investigate how this picture changes for the k-torsional rigidity, a functional associated with k-Hessian equations, under quermassintegral constraints. After introducing the geometric and analytic background, we discuss the role of the ball across the different choices of operator and constraint. Our main result shows that, in suitable regimes, the ball is a saddle shape: arbitrarily small admissible perturbations can both increase and decrease the functional.

This talk is based on joint work with Alba Lia Masiello and Gloria Paoli.

Venue: MCS2068

Nov 11 (Wed)

11:00 MJC2004 ApplRose Hinz (Newcastle University): Low Prandtl Rotating Convection in the Presence of Magnetic Friction

The winds of Jupiter have motivated many studies across the years, from the iconic equatorial bands to the Great Red Spot. While the dynamics of these systems are mostly understood, recent imagery from NASA's Juno spacecraft has discovered spectacular cyclones on the Jovian polar regions. Currently, there exists eight circumpolar vortices at north pole and five at the south pole, all "orbiting" a central vortex. The circumpolar vortices have largely remained a mystery until their discovery, evading global atmospheric models of Jupiter. They have largely not changed since the first flyby of 2016, aside from the appearance of a reoccurring intruding vortex at the south pole in 2019 and 2021.

This presentation will be on two subjects. The first is discussing a new regime we discovered by modelling rapidly rotating, incompressible, low Prandtl Rayleigh-Benard convections. At low Prandtl numbers, we produce large scale oscillations of Large Scale Vortices (LSVs), a phenomenon we have dubbed bursting. While bursting has been observed in the past for convection, this has not been documented for vortices. The second subject will be on applying a magnetic friction to a saturated low Prandtl case in place of a full MHD simulation to estimate the conductivity required to halt any LSV generation. This can then be used to provide a rough estimate to the depth of Jupiter's polar vortices.

Venue: MJC2004

Nov 12 (Thu)

11:00 zoom A&CAlok Laddha (Chennai Mathematical Institute): A double scaling limit of N=4 SYM and Carroll holography

Venue: zoom

Online: https://teams.microsoft.com/meet/3710561111767549?p=Pw5BZGLuwYyzRje4DP

13:00 MCS3070 E&PDr Sam Fearn (Durham): A beginner guide to the STACK API

The STACK API allows STACK questions to be viewed and marked (and tested) outside of a Moodle environment. One valuable use-case for this is the embedding of STACK questions as examples directly within course notes (in html format). This enables students to better practise questions relative to the specific part of the course notes that they are currently studying. In this seminar, we demonstrate a simple method for converting course materials to html (using Pandoc) and embedding stack questions within the resulting html using the STACK API.

Venue: MCS3070 (MAGIC)

Online: https://teams.microsoft.com/l/meetup-join/19%3ameeting_MTVjYWIzMTMtNjYxNy00YTQzLWI0OGYtMGQxMTc0MTQ0Nzgw%40thread.v2/0?context=%7b%22Tid%22%3a%227250d88b-4b68-4529-be44-d59a2d8a6f94%22%2c%22Oid%22%3a%226cb8930b-1559-4659-8c60-d0b762855115%22%7d

14:00 MCS2068 ASGFredrik Stromberg (Nottingham): TBA

Venue: MCS2068

14:00 MC0001 ProbQuentin Berger (Université Sorbonne Paris Nord): 2D directed polymers, the Stochastic Heat Flow and the KPZ equation

I will review some of the progress on the directed polymer model in dimension d=2, whose partition functions can be seen as a discretised version of the stochastic heat equation. Recent results have shown that, in a suitable (and subtle) critical window of parameters, the model converges to a disordered limit, namely the Critical 2D Stochastic Heat Flow (SHF) introduced by Caravenna, Sun and Zygouras. This SHF is a non-Gaussian stochastic process of measures on R^2, and a lot of its properties have been studied over the last years. In this talk, I will first take some time to explain the (idea of the) construction of the SHF and then review some of the recent advances on its relation to the KPZ equation.

Venue: MC0001

Nov 13 (Fri)

13:00 MCS2068 HEPMAnton Kapustin (Caltech): Locality, higher symmetries, and anomalies: an operator-algebraic approach

In the usual Euclidean path-integral picture, higher symmetries are represented by invertible topological defects, and ’t Hooft anomalies are described by anomaly inflow from a topological action in one dimension higher. Is there a corresponding construction that starts directly from the algebra of local operators and its symmetries? To address this question, I will describe a mathematically precise framework based on localized symmetry transformations and their commutators. To each spatial region U, one associates a group of transformations localized in U. Locality implies that the commutator of transformations localized in regions U and V is localized in their intersection. From these data one can extract a system of higher groups, one per cover of space. Both anomalies and higher symmetries are encoded in this system of higher groups. The framework is designed to treat algebraic QFT and quantum lattice systems in a common language. The guiding idea is that topology emerges from the interplay of symmetry and locality.

Venue: MCS2068

14:00 MCS2068 G&TMichael Kohn (Durham): \( \mathfrak{sl}_p \)-homology over \( \mathbb{F}_p \)

\( \mathfrak{sl}_N \) homology is a quantum invariant of knots and links, generalising Khovanov homology. In this talk we will provide a brief introduction to how this is defined via objects called foams. We will also introduce s-invariants, which have applications in 4-manifold topology. We will then show that for the case of N a prime p, and working over \( \mathbb{F}_p \), the chain complex that this theory associates to a link diagram has a remarkably simple decomposition. From this, we can deduce new results and reprove existing results regarding s-invariants and the structure of \( \mathfrak{sl}_p \) homology.

Venue: MCS2068

Nov 16 (Mon)

13:00 MCS2068 ProbKhoa Le (University of Leeds): Regularization by Fractional Noise for Differential Equations with Singular Drift

We study differential equations with time-dependent drifts that are merely integrable in space and time, driven by additive fractional Brownian motion with Hurst parameter H<1/2​. Although the corresponding deterministic equations may be highly non-unique, the irregularity of the noise restores strong well-posedness. Under a natural subcriticality condition on the space-time integrability of the drift, together with conditions required for a change-of-measure argument, we prove strong existence and path-by-path uniqueness. We also obtain quantitative stability with respect to the initial condition and the drift, both pathwise and in moment norms, and construct a Hölder-continuous semiflow. As H approaches 1/2, the admissible regime recovers, up to an endpoint, the classical Brownian scaling condition of Krylov and Röckner (2005). I will explain the main ideas of the proof, which combine stochastic sewing, Lyons' rough-path estimates, and a quantitative John-Nirenberg inequality for stochastic processes with vanishing oscillations. Base on a joint work with Oleg Butkovsky and Toyomu Matsuda.

Venue: MCS2068

14:00 MCS2068 StatMichael Goldstein (Durham University): Open Statistical Inference

Formal accounts of statistical inference are usually based around the notion of closed inference. By this we mean all of the ingredients (model form, parametric choices, probabilistic specification, etc) are fixed a priori. When new information is received, inferences (for example, about likely values of the model parameters) are made according to pre-specified rules established by the formal system (for example, by use of Bayes theorem).

However, real world statistical inferences are rarely as tidy as this. Modelling, data exploration, diagnostic testing and inference are intertwined in ways which do not align well with such formal accounts of statistical inference. Further, there are general areas of uncertain inference which rely on aspects of statistical reasoning but are not well described by this kind of formalism. (For example, most forms of human reasoning, problems of Uncertainty Quantification for complex computer models, and much of reasoning by AI.)

To be able to make principled inferential statements corresponding to our actual procedures, we need the notion of open statistical inference. This describes problems for which the specification of all of the elements need not be fully described a priori, involving models which are not constrained to remain unchanged in form over time. Further, we may not be able to pre-specify the precise inferential process that we intend to follow.

We will derive, under very weak temporal constraints, certain conditions that any open inference should obey. These conditions provide a natural framework for analysing open inferences, supported constructively by new methodological tools for this purpose. In particular, they allow us to give a meaningful logical framework for closed inferences within this more general formalism.

Venue: MCS2068

Nov 17 (Tue)

13:00 MCS2068 PureJoel Moreira (Warwick): TBA

Venue: MCS2068


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Upcoming Seminars by Series

Click on series to expand.

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• Amplitudes and Correlators

Contact: arthur.lipstein@durham.ac.uk

Nov 12 11:00 Alok Laddha (Chennai Mathematical Institute): A double scaling limit of N=4 SYM and Carroll holography

Venue: zoom

• Analysis and PDE

Usual Venue: MCS2068

Contact: yohance.a.osborne@durham.ac.uk

Nov 10 14:00 Francesco Salerno (SSM Napoli/Durham): On Saint-Venant Type Inequalities

In classical shape optimization, the ball often arises as an extremizer. In this talk, we investigate how this picture changes for the k-torsional rigidity, a functional associated with k-Hessian equations, under quermassintegral constraints. After introducing the geometric and analytic background, we discuss the role of the ball across the different choices of operator and constraint. Our main result shows that, in suitable regimes, the ball is a saddle shape: arbitrarily small admissible perturbations can both increase and decrease the functional.

This talk is based on joint work with Alba Lia Masiello and Gloria Paoli.

Venue: MCS2068

• Applied Mathematics

Usual Venue: MCS3070

Contact: andrew.krause@durham.ac.uk

Nov 11 11:00 Rose Hinz (Newcastle University): Low Prandtl Rotating Convection in the Presence of Magnetic Friction

The winds of Jupiter have motivated many studies across the years, from the iconic equatorial bands to the Great Red Spot. While the dynamics of these systems are mostly understood, recent imagery from NASA's Juno spacecraft has discovered spectacular cyclones on the Jovian polar regions. Currently, there exists eight circumpolar vortices at north pole and five at the south pole, all "orbiting" a central vortex. The circumpolar vortices have largely remained a mystery until their discovery, evading global atmospheric models of Jupiter. They have largely not changed since the first flyby of 2016, aside from the appearance of a reoccurring intruding vortex at the south pole in 2019 and 2021.

This presentation will be on two subjects. The first is discussing a new regime we discovered by modelling rapidly rotating, incompressible, low Prandtl Rayleigh-Benard convections. At low Prandtl numbers, we produce large scale oscillations of Large Scale Vortices (LSVs), a phenomenon we have dubbed bursting. While bursting has been observed in the past for convection, this has not been documented for vortices. The second subject will be on applying a magnetic friction to a saturated low Prandtl case in place of a full MHD simulation to estimate the conductivity required to halt any LSV generation. This can then be used to provide a rough estimate to the depth of Jupiter's polar vortices.

Venue: MJC2004

• Arithmetic Study Group

Usual Venue: MCS2068

Contact: johannes.girsch@durham.ac.uk

Nov 12 14:00 Fredrik Stromberg (Nottingham): TBA

Venue: MCS2068

Nov 19 14:00 Sun Kai Leung (Oxford): TBA

TBA

Venue: MCS2068

Nov 26 14:00 Sean Dewar (KU Leuven): TBA

Venue: MCS2068

Dec 03 14:00 Justin Trias (Aix-Marseille Universite): TBA

Venue: MCS2068

Dec 10 14:00 Robert Osburn (Cork): TBA

TBA

Venue: MCS2068

Jan 21 14:00 Shaun Stevens (UEA): TBA

Venue: MCS2068

Feb 04 14:00 Andrew Graham (Oxford): TBA

Venue: MCS2068

Feb 11 14:00 Ingrid Vukusic (York): TBA

TBA

Venue: MCS2068

Feb 18 14:00 Akshat Mugdal (Warwick): TBA

Venue: MCS2068

Feb 25 14:00 Sean Cotner (Bonn): TBA

Venue: MCS2068

• CPT Colloquium

Usual Venue: OC218

Contact: mohamed.anber@durham.ac.uk

For more information, see HERE.


No upcoming seminars have been scheduled (not unusual outside term time).

• Department Research Colloquium

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).

• Distinguished Lectures

Usual Venue: MCS0001

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

Nov 18 14:00 Tanniemola Liverpool (Bristol): Detours and shortcuts: journeys in non-equilibrium statistical mechanics

Venue: MJC2012

• Education and Pedagogy

Usual Venue: MCS3052

Contact: andrew.krause@durham.ac.uk

Nov 12 13:00 Dr Sam Fearn (Durham): A beginner guide to the STACK API

The STACK API allows STACK questions to be viewed and marked (and tested) outside of a Moodle environment. One valuable use-case for this is the embedding of STACK questions as examples directly within course notes (in html format). This enables students to better practise questions relative to the specific part of the course notes that they are currently studying. In this seminar, we demonstrate a simple method for converting course materials to html (using Pandoc) and embedding stack questions within the resulting html using the STACK API.

Venue: MCS3070 (MAGIC)

• Gandalf

Usual Venue: MCS3070

Contact: daniel.n.disney@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• Generalised Symmetries

Usual Venue: MCS3070

Contact: yi-lok-enoch.leung@durham.ac.uk

Nov 23 10:00 Benjamin Muntz (University of Nottingham): TBA

Venue: MCS3070

Dec 09 13:00 Alonso Perez-Lona (Max Planck Institute for Mathematics in the Sciences): TBA

Venue: MCS3070

• Geometry and Topology

Usual Venue: MCS2068

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

Nov 13 14:00 Michael Kohn (Durham): \( \mathfrak{sl}_p \)-homology over \( \mathbb{F}_p \)

\( \mathfrak{sl}_N \) homology is a quantum invariant of knots and links, generalising Khovanov homology. In this talk we will provide a brief introduction to how this is defined via objects called foams. We will also introduce s-invariants, which have applications in 4-manifold topology. We will then show that for the case of N a prime p, and working over \( \mathbb{F}_p \), the chain complex that this theory associates to a link diagram has a remarkably simple decomposition. From this, we can deduce new results and reprove existing results regarding s-invariants and the structure of \( \mathfrak{sl}_p \) homology.

Venue: MCS2068

Nov 20 14:00 Luke Jeffreys (Bristol): On McMullen's expander graph conjecture for SL(2,Z)-orbits

Square-tiled surfaces (aptly named) are surfaces obtained by gluing together a collection of unit squares along their sides (the square torus being the simplest example). These surfaces are special cases of translation surfaces, whose moduli space carries a natural action of the group SL(2,R). The famous works of Eskin\u2013Mirzakhani and Eskin\u2013Mirzakhani\u2013Mohammadi were concerned with understanding the orbits of this action.

This SL(2,R)-action restricts to an action of SL(2,Z) on square-tiled surfaces, and the orbits under this restricted action can be transformed into finite regular graphs. It is a long-standing conjecture of McMullen that a specific family of these orbit graphs in genus two forms a family of expander graphs. I will discuss the history of this conjecture and recent progress towards it obtained in joint work with Carlos Matheus.

Venue: MCS2068

Nov 20 15:00 Philipp Bartmann (Potsdam): TBA

Venue: MCS2068

Nov 27 14:00 Emily Roff (Edinburgh): TBA

Venue: MCS2068

Dec 04 14:00 Simon Willerton (Sheffield): TBA

Venue: MCS2068

Jan 29 14:00 Marco Radeschi (Torino): TBA

Venue: MCS2068

Feb 12 14:00 Kasia Wyczesany (Leeds): TBA

Venue: MCS2068

• HEP Journal Club

Usual Venue: MCS3070

Contact: mendel.t.nguyen@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• HEP Lunchtime

Usual Venue: MCS2068

Contact: p.e.dorey@durham.ac.uk,parita.r.shah@durham.ac.uk,tobias.p.hansen@durham.ac.uk

Nov 13 13:00 Anton Kapustin (Caltech): Locality, higher symmetries, and anomalies: an operator-algebraic approach

In the usual Euclidean path-integral picture, higher symmetries are represented by invertible topological defects, and ’t Hooft anomalies are described by anomaly inflow from a topological action in one dimension higher. Is there a corresponding construction that starts directly from the algebra of local operators and its symmetries? To address this question, I will describe a mathematically precise framework based on localized symmetry transformations and their commutators. To each spatial region U, one associates a group of transformations localized in U. Locality implies that the commutator of transformations localized in regions U and V is localized in their intersection. From these data one can extract a system of higher groups, one per cover of space. Both anomalies and higher symmetries are encoded in this system of higher groups. The framework is designed to treat algebraic QFT and quantum lattice systems in a common language. The guiding idea is that topology emerges from the interplay of symmetry and locality.

Venue: MCS2068

Nov 20 13:00 Prahar Mitra (Southampton University): TBA

Venue: MCS2068

Nov 27 13:00 Mariana Carrillo Gonzalez (Southampton University): TBA

Venue: MCS2068

Dec 04 13:00 Daniel Brennan (University of Birmingham): TBA

Venue: MCS2068

Dec 11 13:00 Alessandro Georgoudis (Queen Mary University of London): TBA

Venue: MCS2068

• Probability

Usual Venue: MCS2068

Contact: tyler.helmuth@durham.ac.uk,oliver.kelsey-tough@durham.ac.uk

Nov 12 14:00 Quentin Berger (Université Sorbonne Paris Nord): 2D directed polymers, the Stochastic Heat Flow and the KPZ equation

I will review some of the progress on the directed polymer model in dimension d=2, whose partition functions can be seen as a discretised version of the stochastic heat equation. Recent results have shown that, in a suitable (and subtle) critical window of parameters, the model converges to a disordered limit, namely the Critical 2D Stochastic Heat Flow (SHF) introduced by Caravenna, Sun and Zygouras. This SHF is a non-Gaussian stochastic process of measures on R^2, and a lot of its properties have been studied over the last years. In this talk, I will first take some time to explain the (idea of the) construction of the SHF and then review some of the recent advances on its relation to the KPZ equation.

Venue: MC0001

Nov 16 13:00 Khoa Le (University of Leeds): Regularization by Fractional Noise for Differential Equations with Singular Drift

We study differential equations with time-dependent drifts that are merely integrable in space and time, driven by additive fractional Brownian motion with Hurst parameter H<1/2​. Although the corresponding deterministic equations may be highly non-unique, the irregularity of the noise restores strong well-posedness. Under a natural subcriticality condition on the space-time integrability of the drift, together with conditions required for a change-of-measure argument, we prove strong existence and path-by-path uniqueness. We also obtain quantitative stability with respect to the initial condition and the drift, both pathwise and in moment norms, and construct a Hölder-continuous semiflow. As H approaches 1/2, the admissible regime recovers, up to an endpoint, the classical Brownian scaling condition of Krylov and Röckner (2005). I will explain the main ideas of the proof, which combine stochastic sewing, Lyons' rough-path estimates, and a quantitative John-Nirenberg inequality for stochastic processes with vanishing oscillations. Base on a joint work with Oleg Butkovsky and Toyomu Matsuda.

Venue: MCS2068

Nov 23 13:00 Michael Magee (University of Durham):

Venue: MCS2068

Dec 07 13:00 Mateusz Piorkowski (University of Durham):

Venue: MCS2068

• Pure Maths Colloquium

Usual Venue: MCS2068

Contact: alexander.mangerel@durham.ac.uk

Nov 17 13:00 Joel Moreira (Warwick): TBA

Venue: MCS2068

Nov 24 13:00 Giannis Platis (Patras): TBA

Venue: MCS2068

Dec 01 13:00 Rob Kurinczuk (Sheffield): TBA

Venue: MCS2068

Jan 27 13:00 Marco Radeschi (Torino): TBA

Venue: MCS2068

Feb 09 13:00 Tim Browning (UCL): TBA

Venue: MCS2068

Feb 23 13:00 Tara Brendle (Glasgow): TBA

Venue: MCS2068

Mar 16 13:00 Rémi Coulon (Dijon): TBA

Venue: MCS2068

• Spectra and Moduli

Usual Venue: MCS3070

Contact: joe.thomas@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• Statistics

Usual Venue: MCS2068

Contact: andrew.iskauskas@durham.ac.uk

Nov 16 14:00 Michael Goldstein (Durham University): Open Statistical Inference

Formal accounts of statistical inference are usually based around the notion of closed inference. By this we mean all of the ingredients (model form, parametric choices, probabilistic specification, etc) are fixed a priori. When new information is received, inferences (for example, about likely values of the model parameters) are made according to pre-specified rules established by the formal system (for example, by use of Bayes theorem).

However, real world statistical inferences are rarely as tidy as this. Modelling, data exploration, diagnostic testing and inference are intertwined in ways which do not align well with such formal accounts of statistical inference. Further, there are general areas of uncertain inference which rely on aspects of statistical reasoning but are not well described by this kind of formalism. (For example, most forms of human reasoning, problems of Uncertainty Quantification for complex computer models, and much of reasoning by AI.)

To be able to make principled inferential statements corresponding to our actual procedures, we need the notion of open statistical inference. This describes problems for which the specification of all of the elements need not be fully described a priori, involving models which are not constrained to remain unchanged in form over time. Further, we may not be able to pre-specify the precise inferential process that we intend to follow.

We will derive, under very weak temporal constraints, certain conditions that any open inference should obey. These conditions provide a natural framework for analysing open inferences, supported constructively by new methodological tools for this purpose. In particular, they allow us to give a meaningful logical framework for closed inferences within this more general formalism.

Venue: MCS2068

• Stats4Grads

Contact: adam.stone2@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

Special Series

These link to some of the special events hosted by the Department:


• [LMS|EPSRC] Durham Symposia (from 1974)
• Collingwood Lectures (from 1984)