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): 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)
14:00 MJC2012 D&PLTanniemola Liverpool (Bristol): Detours and shortcuts: journeys in non-equilibrium statistical mechanics
Nov 19 (Thu)
14:00 MCS2068 ASGSun Kai Leung (Oxford): TBA
Nov 20 (Fri)
13:00 MCS2068 HEPMPrahar Mitra (Southampton University): TBA
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
Click on title to see abstract.
Back to Homepage
Click on series to expand.
Usual Venue: MCS3070
Contact: andrew.krause@durham.ac.uk
No upcoming seminars have been scheduled (not unusual outside term time).
Usual Venue: MCS2068
Contact: johannes.girsch@durham.ac.uk
Nov 19 14:00 Sun Kai Leung (Oxford): TBA
Nov 26 14:00 Sean Dewar (KU Leuven): TBA
Dec 03 14:00 Justin Trias (Aix-Marseille Universite): TBA
Dec 10 14:00 Robert Osburn (Cork): TBA
Jan 21 14:00 Shaun Stevens (UEA): TBA
Feb 04 14:00 Andrew Graham (Oxford): TBA
Feb 11 14:00 Ingrid Vukusic (York): TBA
Feb 18 14:00 Akshat Mugdal (Warwick): TBA
Feb 25 14:00 Sean Cotner (Bonn): TBA
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).
Usual Venue: MCS3052
Contact: andrew.krause@durham.ac.uk
No upcoming seminars have been scheduled (not unusual outside term time).
Usual Venue: MCS3070
Contact: yi-lok-enoch.leung@durham.ac.uk
Nov 23 10:00 Benjamin Muntz (University of Nottingham): TBA
Dec 09 13:00 Alonso Perez-Lona (Max Planck Institute for Mathematics in the Sciences): TBA
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-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
Dec 04 14:00 Simon Willerton (Sheffield): TBA
Jan 29 14:00 Marco Radeschi (Torino): TBA
Feb 12 14:00 Kasia Wyczesany (Leeds): TBA
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
Nov 27 13:00 Mariana Carrillo Gonzalez (Southampton University): TBA
Dec 04 13:00 Daniel Brennan (University of Birmingham): TBA
Dec 11 13:00 Alessandro Georgoudis (Queen Mary University of London): TBA
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):
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
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
Jan 27 13:00 Marco Radeschi (Torino): TBA
Feb 09 13:00 Tim Browning (UCL): TBA
Feb 23 13:00 Tara Brendle (Glasgow): TBA
Mar 16 13:00 Rémi Coulon (Dijon): TBA
Usual Venue: MCS3070
Contact: joe.thomas@durham.ac.uk
No upcoming seminars have been scheduled (not unusual outside term time).
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
