Oct 21 (Tue)
13:00 MCS2068 APDECodina Cotar (University College London): Some new results on non-convex random gradient Gibbs measures
In this talk we consider a class of gradient models with and without disorder. The simplest example of such models is the (lattice) Gaussian Free Field, which has quadratic potential V(s)=s^2/2. A well
known result of Funaki and Spohn asserts that, for any uniformly-convex potential V, the possible
infinite-volume measures of this type are uniquely characterized by the tilt, which is a vector in R^d. We show that this model is disorder relevant with respect to the question of uniqueness of gradient Gibbs measures when disorder is added to the system. We also discuss some functional inequalities connected to the model (such as Poincaré, log-Sobolev). No previous knowledge of gradient models will be assumed in the talk. This is based on joint works with Simon Buchholz and Florian Schweiger.
Venue: MCS2068
14:00 MCS2068 ASGColton Griffin (University of Pennsylvania): Higher-dimensional vertex algebras
Vertex (operator) algebras were originally defined by Borcherds and Frenkel-Lepowksy-Meurman in the study of the monster group and affine Lie algebras, taking inspiration from bosonic string theory. Since their inception, they have been shown to be closely related to modular forms, geometric Langlands, and the moduli space of stable pointed curves. More specifically, one may use these objects to construct sheaves of coinvariants on the moduli space of stable complex curves. Under certain niceness assumptions, these sheaves are induced by vector bundles with explicit formulae for their Chern classes using the representation theory of vertex algebras. On their own, vertex algebras are intricate objects to study from a representation-theoretic perspective as well.
With such rich structure for curves, it is natural to ask if there are vertex algebraic analogues suitable for the study of higher-dimensional geometric objects. We describe a family of such analogues, which we call “cohomological vertex algebras.” These are obtained by replacing Laurent series in the definition of a vertex algebra with the Čech cohomology of schemes modeling infinitesimal neighborhoods in higher-dimensional spaces.
We will start by motivating the definition of a vertex algebra and its many axioms from a non-geometric perspective; after doing so, we will describe how to modify the definition to obtain cohomological vertex algebras. Time permitting, we will then discuss the construction of coinvariants and conformal blocks on higher-dimensional varieties.
Venue: MCS2068
Oct 23 (Thu)
13:00 MCS2068 G&TJohn Parker (Durham University): Real hyperbolic on the outside, complex hyperbolic on the inside (1)
The title of the talk is the title of a paper by Richard Schwartz (Inventiones 2003) where he constructs a complex hyperbolic orbifold whose boundary is homeomorphic to a closed real hyperbolic three-manifold. The fundamental group of the orbifold is an index two subgroup of a group generated by three reflections where certain products of the reflections have particular finite orders. The proof is by way of an explicit construction of a fundamental polyhedron. In these talks I will discuss a joint project with Yohei Komori and Makoto Sakuma where we take the first step to generalise Schwartz’s construction. Namely, we give a topological construction of a candidate fundamental domain, and thereby we are able to describe the topology of the boundary manifold explicitly in terms of the finite orders of the products of reflections. In particular, we are able to topologically identify Schwartz’s boundary manifold.
Venue: MCS2068
14:00 MCS2068 ProbJoão de Oliveira Madeira (University of Oxford): How Can Seed Banks Evolve in Plants? A Stochastic Dynamics Approach
In this talk, we study how varying environmental conditions influence the evolution of seed banks in plants. Our model is a modification of the WrightFisher model with finite-age seed bank, introduced by Kaj, Krone and Lascoux. We distinguish between wild type individuals, producing only nondormant seeds, and mutants, producing seeds with finite dormancy. To understand how environments shape the establishment of seed banks, we analyse the process under diffusive scaling. The results support the biological insight that seed banks are favoured under adverse and fluctuating environments. Mathematically, our analysis reduces to a stochastic dynamical system forced onto a manifold by a large drift, which converges under scaling to a diffusion on the manifold. By projecting the system onto its linear counterpart, we derive an explicit formula for the limiting diffusion coefficients. This provides a general framework for deriving diffusion approximations in models with strong drift and nonlinear constraints. This is a joint work with Alison Etheridge.
Venue: MCS2068
Oct 24 (Fri)
13:00 MCS0001 HEPMNicola Dondi (ICTP Trieste): SymTFTs for continuous spacetime symmetries
Symmetry Topological Field Theories (SymTFTs) are topological field theories that encode the symmetry structure of global symmetries in terms of a theory in one higher dimension. While SymTFTs for internal (global) symmetries have been highly successful in characterizing symmetry aspects in the last few years, a corresponding framework for spacetime symmetries remains unexplored. We propose an extension of the SymTFT framework to include spacetime symmetries. In particular, we propose a SymTFT for the conformal symmetry in various spacetime dimensions. We demonstrate that certain BF-type theories, closely related to topological gravity theories, possess the correct topological operator content and boundary conditions to realize the conformal algebra of conformal field theories living on boundaries. As an application, we show how effective theories with spontaneously broken conformal symmetry can be derived from the SymTFT, and we elucidate how conformal anomalies can be reproduced in the presence of even-dimensional boundaries.
Venue: MCS0001
Oct 27 (Mon)
13:00 MCS2068 StatBen Swallow (St. Andrews):
Oct 28 (Tue)
13:00 MCS2068 APDEMarius Tiba (King's College London): Stability of Geometric and Functional Inequalities
The Brunn-Minkowski inequality is a fundamental result in convex geometry and analysis, closely related to the isoperimetric inequality. It states that for (open) sets A and B in R^d, we have |A+B|^{1/d} \geq |A|^{1/d}+|B|^{1/d}. Here A+B={x+y : x \in A, y \in B}. Equality holds if and only if A and B are homothetic and convex sets in R^d.
The Prekopa-Leindler inequality is a functional generalization of the Brunn-Minkowski inequality with important applications to high dimensional probability theory. If t \in (0,1) and f,g,h : R^d -> R_+ are continuous functions with bounded support such that h(z) = \sup_{z = tx + (1-t)y} f^t(x) g^{1-t}(y), then \int h dx \geq (\int f dx)^t (\int g dx)^{1-t}. Equality holds if and only if f and g are homothetic (i.e. f=ag(x+b)) and log-concave (i.e. \log(f) is concave). The Borell-Brascamp-Lieb inequality is a strengthening of the Prekopa-Leindler inequality, replacing the geometric mean with other means.
The stability of these inequalities has been intensely studied lately. The stability of the Brunn-Minkowski inequality states that if we are close to equality, then A and B must be close to being homothetic and convex. Similarly, the stability of the Prekopa-Leindler and Borell-Brascamp-Lieb inequalities states that if we are close to equality, then f and g must be close to being homothetic and concave. In this talk, we present sharp stability results for the Brunn-Minkowski, Prekopa-Leindler and Borell-Brascamp-Lieb inequalities, establishing the exact dependency between the two notions of closeness, thus concluding a long line of research on these problems.
This talk is based on joint work with Alessio Figalli and Peter van Hintum.
Venue: MCS2068
14:00 MCS2068 ASGVictoria Schleis (Durham University): General linear monoids over hyperfields
Click on title to see abstract.
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Click on series to expand.
Usual Venue: MCS2068
Contact: yohance.a.osborne@durham.ac.uk
Oct 21 13:00 Codina Cotar (University College London): Some new results on non-convex random gradient Gibbs measures
In this talk we consider a class of gradient models with and without disorder. The simplest example of such models is the (lattice) Gaussian Free Field, which has quadratic potential V(s)=s^2/2. A well
known result of Funaki and Spohn asserts that, for any uniformly-convex potential V, the possible
infinite-volume measures of this type are uniquely characterized by the tilt, which is a vector in R^d. We show that this model is disorder relevant with respect to the question of uniqueness of gradient Gibbs measures when disorder is added to the system. We also discuss some functional inequalities connected to the model (such as Poincaré, log-Sobolev). No previous knowledge of gradient models will be assumed in the talk. This is based on joint works with Simon Buchholz and Florian Schweiger.
Venue: MCS2068
Oct 28 13:00 Marius Tiba (King's College London): Stability of Geometric and Functional Inequalities
The Brunn-Minkowski inequality is a fundamental result in convex geometry and analysis, closely related to the isoperimetric inequality. It states that for (open) sets A and B in R^d, we have |A+B|^{1/d} \geq |A|^{1/d}+|B|^{1/d}. Here A+B={x+y : x \in A, y \in B}. Equality holds if and only if A and B are homothetic and convex sets in R^d.
The Prekopa-Leindler inequality is a functional generalization of the Brunn-Minkowski inequality with important applications to high dimensional probability theory. If t \in (0,1) and f,g,h : R^d -> R_+ are continuous functions with bounded support such that h(z) = \sup_{z = tx + (1-t)y} f^t(x) g^{1-t}(y), then \int h dx \geq (\int f dx)^t (\int g dx)^{1-t}. Equality holds if and only if f and g are homothetic (i.e. f=ag(x+b)) and log-concave (i.e. \log(f) is concave). The Borell-Brascamp-Lieb inequality is a strengthening of the Prekopa-Leindler inequality, replacing the geometric mean with other means.
The stability of these inequalities has been intensely studied lately. The stability of the Brunn-Minkowski inequality states that if we are close to equality, then A and B must be close to being homothetic and convex. Similarly, the stability of the Prekopa-Leindler and Borell-Brascamp-Lieb inequalities states that if we are close to equality, then f and g must be close to being homothetic and concave. In this talk, we present sharp stability results for the Brunn-Minkowski, Prekopa-Leindler and Borell-Brascamp-Lieb inequalities, establishing the exact dependency between the two notions of closeness, thus concluding a long line of research on these problems.
This talk is based on joint work with Alessio Figalli and Peter van Hintum.
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: herbert.gangl@durham.ac.uk
Oct 21 14:00 Colton Griffin (University of Pennsylvania): Higher-dimensional vertex algebras
Vertex (operator) algebras were originally defined by Borcherds and Frenkel-Lepowksy-Meurman in the study of the monster group and affine Lie algebras, taking inspiration from bosonic string theory. Since their inception, they have been shown to be closely related to modular forms, geometric Langlands, and the moduli space of stable pointed curves. More specifically, one may use these objects to construct sheaves of coinvariants on the moduli space of stable complex curves. Under certain niceness assumptions, these sheaves are induced by vector bundles with explicit formulae for their Chern classes using the representation theory of vertex algebras. On their own, vertex algebras are intricate objects to study from a representation-theoretic perspective as well.
With such rich structure for curves, it is natural to ask if there are vertex algebraic analogues suitable for the study of higher-dimensional geometric objects. We describe a family of such analogues, which we call “cohomological vertex algebras.” These are obtained by replacing Laurent series in the definition of a vertex algebra with the Čech cohomology of schemes modeling infinitesimal neighborhoods in higher-dimensional spaces.
We will start by motivating the definition of a vertex algebra and its many axioms from a non-geometric perspective; after doing so, we will describe how to modify the definition to obtain cohomological vertex algebras. Time permitting, we will then discuss the construction of coinvariants and conformal blocks on higher-dimensional varieties.
Venue: MCS2068
Oct 28 14:00 Victoria Schleis (Durham University): General linear monoids over hyperfields
Nov 04 14:00 Yu-Chen Sun (University of Bristol):
Nov 11 14:00 Robin Bartlett (Glasgow University): Moduli spaces of mod p Galois representations and explicit equations for the crystalline locus of a fixed Hodge type.
Nov 25 14:00 Dante Luber (Queen Mary University of London): Matroid theory, algebra, and computation
Matroids combinatorially abstract independence properties of
finite dimensional linear algebra. They have become ubiquitous in
modern mathematics, and yield connections between graph theory,
algebra, polyhedral geometry, optimization, and beyond. Special
matroids capture the properties of point line arrangementments in
complex 2-projective space. The moduli space of all line arrangements
corresponding to a matroid is known as its realization space. After an
introduction to matroid theory, we will discuss how we have used the
OSCAR software system to study large datasets of matroids, isolating
examples whose realization spaces have interesting algebro-geometric
Venue: MCS2068
Dec 02 14:00 Jay Taylor (University of Manchester):
Dec 09 14:00 Fredrik Stromberg (University of Nottingham):
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: MCS2068
Contact: fernando.galaz-garcia@durham.ac.uk
Oct 23 13:00 John Parker (Durham University): Real hyperbolic on the outside, complex hyperbolic on the inside (1)
The title of the talk is the title of a paper by Richard Schwartz (Inventiones 2003) where he constructs a complex hyperbolic orbifold whose boundary is homeomorphic to a closed real hyperbolic three-manifold. The fundamental group of the orbifold is an index two subgroup of a group generated by three reflections where certain products of the reflections have particular finite orders. The proof is by way of an explicit construction of a fundamental polyhedron. In these talks I will discuss a joint project with Yohei Komori and Makoto Sakuma where we take the first step to generalise Schwartz’s construction. Namely, we give a topological construction of a candidate fundamental domain, and thereby we are able to describe the topology of the boundary manifold explicitly in terms of the finite orders of the products of reflections. In particular, we are able to topologically identify Schwartz’s boundary manifold.
Venue: MCS2068
Oct 30 13:00 John Parker (Durham University): Real hyperbolic on the outside, complex hyperbolic on the inside (2)
The title of the talk is the title of a paper by Richard Schwartz (Inventiones 2003) where he constructs a complex hyperbolic orbifold whose boundary is homeomorphic to a closed real hyperbolic three-manifold. The fundamental group of the orbifold is an index two subgroup of a group generated by three reflections where certain products of the reflections have particular finite orders. The proof is by way of an explicit construction of a fundamental polyhedron. In these talks I will discuss a joint project with Yohei Komori and Makoto Sakuma where we take the first step to generalise Schwartz’s construction. Namely, we give a topological construction of a candidate fundamental domain, and thereby we are able to describe the topology of the boundary manifold explicitly in terms of the finite orders of the products of reflections. In particular, we are able to topologically identify Schwartz’s boundary manifold.
Venue: MCS2068
Nov 13 13:00 Pierre Will (Université Grenoble Alpes): TBA
Nov 20 13:00 Amy Herron (University of Bristol): Triangle Presentations in ~A_2 Bruhat-Tits Buildings
The 1-skeleton of an ~A_2 Bruhat-Tits building is isomorphic to the Cayley graph of an abstract group with relations coming from triangle presentations. This abstract group either embeds into PGL(3, Fq((x))) or PGL(3, Qq), or else is exotic. Currently, the complete list of triangle presentations is only known for projective planes of orders q=2 or 3. However, one abstract group that embeds into PGL(3,Fq((x))) for any prime power q is known via the trace function corresponding to the finite field of order q^3. I found a new method to derive this group via perfect difference sets. This method demonstrates a previously unknown connection between difference sets and ~A_2 buildings. Moreover, this method makes the final computation of triangle presentations easier, which is computationally valuable for large q.
Venue: MCS2068
Nov 27 13:00 Yan Rybalko (University of Oslo): Generic regularity of the two-component Novikov system
In my talk I will discuss the generic regularity of the Cauchy problem for the two-component Novikov system. This system is integrable (i.e., it is bi-Hamiltonian, has a Lax pair, and an infinite number of conservation laws), and admits peakon solutions of the form p(t)exp(-|x-q(t)|). Another important feature of the Novikov system is the wave-breaking phenomenon: the solutions remain bounded for all times, but the slope can blow-up in finite time. In our work, we show that there exists an open dense subset of C^k regular initial data, such that the corresponding global solutions persist the regularity for all t,x except, possibly, a finite number of piecewise C^{k-1} characteristic curves. Our approach builds on the work by Bressan and Chen, which relies on transforming solutions from Eulerian variables to a new set of Bressan-Constantin variables, in which all possible singularities of the original solutions are resolved. Then, applying the Thoms transversality theorem to the map related to the wave-breaking, we can construct an appropriate open dense subset of C^k regular initial data.
The talk is based upon the following papers:
K.H. Karlsen, Ya. Rybalko, "Generic regularity and a Lipschitz metric for the two-component Novikov system," in preparation.
K.H. Karlsen, Ya. Rybalko, "Global semigroup of conservative weak solutions of the two-component Novikov equation," Nonlinear Analysis: Real World Applications 86, 104393 (2025). DOI: 10.1016/j.nonrwa.2025.104393.
Venue: MCS2068
Jan 22 13:00 Chunyang Hu (Durham University): TBA
Mar 06 13:00 Julian Scheuer (Goethe University Frankfurt): TBA
Usual Venue: MCS0001
Contact: p.e.dorey@durham.ac.uk,enrico.andriolo@durham.ac.uk,tobias.p.hansen@durham.ac.uk
Oct 24 13:00 Nicola Dondi (ICTP Trieste): SymTFTs for continuous spacetime symmetries
Symmetry Topological Field Theories (SymTFTs) are topological field theories that encode the symmetry structure of global symmetries in terms of a theory in one higher dimension. While SymTFTs for internal (global) symmetries have been highly successful in characterizing symmetry aspects in the last few years, a corresponding framework for spacetime symmetries remains unexplored. We propose an extension of the SymTFT framework to include spacetime symmetries. In particular, we propose a SymTFT for the conformal symmetry in various spacetime dimensions. We demonstrate that certain BF-type theories, closely related to topological gravity theories, possess the correct topological operator content and boundary conditions to realize the conformal algebra of conformal field theories living on boundaries. As an application, we show how effective theories with spontaneously broken conformal symmetry can be derived from the SymTFT, and we elucidate how conformal anomalies can be reproduced in the presence of even-dimensional boundaries.
Venue: MCS0001
Oct 31 13:00 Max Hutt (Imperial College London): TBA
Nov 07 13:00 Stathis Vitouladitis (Université Libre de Bruxelles): Entanglement asymmetry and the limits of symmetry breaking
Entanglement asymmetry is a novel diagnostic of symmetry breaking, rooted in quantum information theory, particularly effective at capturing such effects within subsystems. In this talk, I will first introduce this observable, outline recent developments, and then generalise it to higher-form symmetries, with applications to topological phases and systems with continuous symmetry breaking. As a main application, I will establish an entropic Mermin-Wagner-Coleman theorem, valid for both 0-form and higher-form symmetries, and extended to subregions. These entropic theorems not only detect but also quantify symmetry breaking. In Goldstone phases (when allowed), the Rényi and entanglement asymmetries, increase monotonically with subregion size. Along the way, I will clarify subtleties in defining and computing entanglement asymmetry by Euclidean path integral methods and present standalone results on the entanglement entropy of gauge fields.
Venue: MCS0001
Nov 14 13:00 Christian Copetti (Oxford): TBA
Nov 21 13:00 Ida Zadeh (Southampton): TBA
Nov 28 13:00 Tim Meier (Santiago de Compostela): TBA
Dec 05 13:00 Marco Meineri (Torino): TBA
Dec 12 13:00 Sungwoo Hong (KAIST, Taejon): TBA
Usual Venue: MCS2068
Contact: tyler.helmuth@durham.ac.uk,oliver.kelsey-tough@durham.ac.uk
Oct 23 14:00 João de Oliveira Madeira (University of Oxford): How Can Seed Banks Evolve in Plants? A Stochastic Dynamics Approach
In this talk, we study how varying environmental conditions influence the evolution of seed banks in plants. Our model is a modification of the WrightFisher model with finite-age seed bank, introduced by Kaj, Krone and Lascoux. We distinguish between wild type individuals, producing only nondormant seeds, and mutants, producing seeds with finite dormancy. To understand how environments shape the establishment of seed banks, we analyse the process under diffusive scaling. The results support the biological insight that seed banks are favoured under adverse and fluctuating environments. Mathematically, our analysis reduces to a stochastic dynamical system forced onto a manifold by a large drift, which converges under scaling to a diffusion on the manifold. By projecting the system onto its linear counterpart, we derive an explicit formula for the limiting diffusion coefficients. This provides a general framework for deriving diffusion approximations in models with strong drift and nonlinear constraints. This is a joint work with Alison Etheridge.
Venue: MCS2068
Nov 20 14:00 PiNE (University of Edinburgh): No seminar PiNE in Edinburgh.
PiNE will take place in Edinburgh, see https://www.maths.dur.ac.uk/PiNE/25-11-20/index.html. Accordingly we will not have a seminar this week.
Venue: MCS2068
Usual Venue: MCS3070
Contact: joe.thomas@durham.ac.uk
No upcoming seminars have been scheduled (not unusual outside term time).
