Seminars in Mathematical Sciences

Seminars in the next week
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): Finding infinite patterns in sets with positive density

Old questions in additive combinatorics and Ramsey theory ask what infinite patterns are unavoidable in sets of integers numbers with positive density (i.e. that account for a positive proportion of all numbers), but until recently, there were no positive answers. In the last few years, a new technique was developed to address such questions, making use of ergodic theory and dynamical systems, which were previously restricted to handling finite patterns. In this talk I will briefly survey the history of the subject and explain the connection to ergodic theory. Then I will describe how we used this technique to answer a question of Paul Erdos regarding infinite sumsets. The talk will be based on joint work with Bryna Kra, Florian Richter and Donald Robertson.

Venue: MCS2068

Nov 18 (Wed)

11:00 zoom A&CAswini Bala (IISER Pune): Towards a Parke–Taylor Analogue in AdS/dS

The remarkable simplicity of the Parke–Taylor formula revealed that quantum field theory could be understood far beyond conventional Feynman-diagram expansions. This insight led to BCFW recursion, geometric formulations of scattering amplitudes, and many related developments. A longstanding question is whether comparable structures exist for observables in AdS/dS and conformal field theories. Despite substantial progress, these correlators are generally far more complicated than their flat-space counterparts, and compact expressions remain rare even for four point function. In this talk, I will present a framework that exposes their underlying geometric structure and provides a BCFW-like construction of higher-point correlators. I will also discuss the double copy relations and exact color kinematics Jacobi identity found in the Grassmannian correlators. I will conclude by describing how close we are to a Parke–Taylor-like formula for AdS/dS correlators.

Venue: zoom

Online: https://teams.microsoft.com/meet/3435782711036019?p=9gvssdCVJmAHtyXqls

14:00 MJC2012 D&PLTanniemola Liverpool (Bristol): Detours and shortcuts: journeys in non-equilibrium statistical mechanics

Venue: MJC2012

Nov 19 (Thu)

14:00 MCS2068 ASGSun Kai Leung (Oxford): TBA

TBA

Venue: MCS2068

Nov 20 (Fri)

13:00 MCS2068 HEPMPrahar Mitra (Southampton University): TBA

Venue: MCS2068

14:00 MCS2068 G&TLuke 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-Mirzakhani and Eskin-Mirzakhani-Mohammadi 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

15:00 MCS2068 G&TPhilipp Bartmann (Potsdam): Eigenvalue estimates of the discrete Hodge Laplacian across dimensions

We will show that the eigenvalues of the discrete Hodge Laplacian of a finite simplicial complex can be estimated by the eigenvalues in lower dimensions and certain geometric constants. As a result, we obtain new criteria for vanishing cohomology and prove a recent conjecture of O on the dimensional monotonicity of the largest eigenvalues. If time permits, we will also apply these results to the Alexander dual and obtain analogous estimates in terms of the eigenvalues in higher dimensions.

Venue: MCS2068


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Upcoming Seminars by Series

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• Amplitudes and Correlators

Contact: arthur.lipstein@durham.ac.uk

Nov 18 11:00 Aswini Bala (IISER Pune): Towards a Parke–Taylor Analogue in AdS/dS

The remarkable simplicity of the Parke–Taylor formula revealed that quantum field theory could be understood far beyond conventional Feynman-diagram expansions. This insight led to BCFW recursion, geometric formulations of scattering amplitudes, and many related developments. A longstanding question is whether comparable structures exist for observables in AdS/dS and conformal field theories. Despite substantial progress, these correlators are generally far more complicated than their flat-space counterparts, and compact expressions remain rare even for four point function. In this talk, I will present a framework that exposes their underlying geometric structure and provides a BCFW-like construction of higher-point correlators. I will also discuss the double copy relations and exact color kinematics Jacobi identity found in the Grassmannian correlators. I will conclude by describing how close we are to a Parke–Taylor-like formula for AdS/dS correlators.

Venue: zoom

• Analysis and PDE

Usual Venue: MCS2068

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

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

• Applied Mathematics

Usual Venue: MCS3070

Contact: andrew.krause@durham.ac.uk

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

• Arithmetic Study Group

Usual Venue: MCS2068

Contact: johannes.girsch@durham.ac.uk

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

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

• 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 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-Mirzakhani and Eskin-Mirzakhani-Mohammadi 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): Eigenvalue estimates of the discrete Hodge Laplacian across dimensions

We will show that the eigenvalues of the discrete Hodge Laplacian of a finite simplicial complex can be estimated by the eigenvalues in lower dimensions and certain geometric constants. As a result, we obtain new criteria for vanishing cohomology and prove a recent conjecture of O on the dimensional monotonicity of the largest eigenvalues. If time permits, we will also apply these results to the Alexander dual and obtain analogous estimates in terms of the eigenvalues in higher dimensions.

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 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 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): Toda soliton condensates with random scattering data

Solitons are localized waves displaying stunning particle-like behavior. They appear in numerous integrable PDEs like the KdV equation, the NLS equation, and, on the discrete side, the Toda lattice. Large ensembles of solitons give rise to a so-called `soliton gas' which is described by Zakharov's kinetic theory, later extended by El and Kamchatnov. Soliton gases of maximal density are called soliton condensates.     In joint work with Guido Mazzuca (arXiv:2611.12748) we study a class of Toda soliton condensates using the Deift-Zhou nonlinear steepest descent method. The characteristics of the individual solitons, i.e. their amplitudes and phases, are assumed to be independent random variables. Despite this randomness we show that in the soliton condensate limit, the solution converges deterministically to a modulated elliptic (genus $1$) or hyperelliptic (genus $2$) wave. The precise genus depends on the exact location in the space-time diagram, which exhibits slow modulation in space and time. Contrary to previous studies of soliton gases using Riemann-Hilbert methods, we observe genuinely nonlinear boundaries between different phases. As a corollary we prove that with high probability the soliton gas kinetic equation, the Whitham modulation equations and the nonlinear dispersion relations hold.     This work is supported by the European Union’s Horizon Europe research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 101272799 (Aztec RHP).

Venue: MCS2068

• Pure Maths Colloquium

Usual Venue: MCS2068

Contact: alexander.mangerel@durham.ac.uk

Nov 17 13:00 Joel Moreira (Warwick): Finding infinite patterns in sets with positive density

Old questions in additive combinatorics and Ramsey theory ask what infinite patterns are unavoidable in sets of integers numbers with positive density (i.e. that account for a positive proportion of all numbers), but until recently, there were no positive answers. In the last few years, a new technique was developed to address such questions, making use of ergodic theory and dynamical systems, which were previously restricted to handling finite patterns. In this talk I will briefly survey the history of the subject and explain the connection to ergodic theory. Then I will describe how we used this technique to answer a question of Paul Erdos regarding infinite sumsets. The talk will be based on joint work with Bryna Kra, Florian Richter and Donald Robertson.

Venue: MCS2068

Nov 24 13:00 Giannis Platis (Patras): Horizontal curvatures of surfaces in 3-dimensional, contact sub-Riemannian Lie groups

In this talk we study horizontal curvatures for surfaces embedded in three-dimensional contact sub-Riemannian Lie groups. Using a Riemannian approximation scheme, we derive explicit formulas for horizontal Gauss curvature, horizontal mean curvature, and symplectic distortion for surfaces embedded in three dimensional Lie groups with a sub-Riemannian structure obtained by a contact form. We focus on two primary examples: the Heisenberg group and the affine-additive group. We classify surfaces of revolution within these groups that exhibit constant horizontal curvatures, often expressing their profiles through elementary or elliptic integrals.

This is a joint work with A. Pinamonti (Trento, Italy), E. Bubani (Fribourg, Switzerland) and D. Tsolis (Patras, Greece).

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)