Nov 09 (Mon)
13:00 MCS2068 ProbEleanor Archer (Université Paris Dauphine - PSL): Limits of massive spanning forests
The lambda spanning forest of a graph G is a random subgraph that generalises the notion of the uniform spanning tree. It was recently shown by D'Achille, Enriquez and Melotti that on the complete graph with n vertices, these forests admit a (local) limit as n goes to infinity. This limit can fall into three regimes depending on whether the parameter lambda grows faster than, slower than, or at the same rate as n. We generalise their result to show that the same limits appear for any sequence of (almost) regular graphs with degrees tending to infinity, provided that lambda is tuned correctly as a function of the degree parameter.
The proof exploits fundamental links between uniform spanning trees and loop-erased random walks. This joint work with Breki Pálsson (University of Iceland).
Venue: MCS2068
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 12 (Thu)
13:00 MCS3070 E&PDr Sam Fearn (Durham): A beginner guide to the STACK API
14:00 MCS2068 ASGFredrik Stromberg (Nottingham): TBA
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
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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
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 12 14:00 Fredrik Stromberg (Nottingham): TBA
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
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)
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): TBA
Nov 20 15:00 Philipp Bartmann (Potsdam): TBA
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 09 13:00 Eleanor Archer (Université Paris Dauphine - PSL): Limits of massive spanning forests
The lambda spanning forest of a graph G is a random subgraph that generalises the notion of the uniform spanning tree. It was recently shown by D'Achille, Enriquez and Melotti that on the complete graph with n vertices, these forests admit a (local) limit as n goes to infinity. This limit can fall into three regimes depending on whether the parameter lambda grows faster than, slower than, or at the same rate as n. We generalise their result to show that the same limits appear for any sequence of (almost) regular graphs with degrees tending to infinity, provided that lambda is tuned correctly as a function of the degree parameter.
The proof exploits fundamental links between uniform spanning trees and loop-erased random walks. This joint work with Breki Pálsson (University of Iceland).
Venue: MCS2068
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):
Dec 07 13:00 Mateusz Piorkowski (University of Durham):
Usual Venue: MCS2068
Contact: alexander.mangerel@durham.ac.uk
Nov 17 13:00 Joel Moreira (Warwick): TBA
Nov 24 13:00 Giannis Platis (Patras): TBA
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).
