Nov 06 (Thu)
13:00 MCS2068 G&TJohn Parker (Durham University): Real hyperbolic on the outside, complex hyperbolic on the inside (3)
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 ProbWilliam Da Silva (University of Vienna): The longest increasing subsequence of Brownian separable permutons
The Brownian separable permutons form a one-parameter family of permutons, which are the universal scaling limits of pattern-avoiding permutations. In this talk, we will be interested in the length of the longest increasing subsequence (LIS) in permutations of size n sampled from the Brownian permutons. We give an answer to the celebrated Ulam-Hammersley problem in this context: what is the behaviour of LIS as n goes to infinity? A significant portion of the talk will be dedicated to our motivation behind the problem, emphasising connections to various objects in probability and combinatorics, such as random decorated trees, random graphs, directed planar maps and SLE/LQG. The talk is based on joint work with Arka Adhikari, Jacopo Borga, Thomas Budzinski and Delphin Sénizergues.
Venue: MCS2068
Nov 07 (Fri)
13:00 MCS0001 HEPMStathis 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 10 (Mon)
13:00 MCS2068 StatLouis Aslett (Durham): Confidential Accept-Reject
Federated learning enables statistical models to be fitted using distributed data sets, without the need to bring those data sets to a single location. Although this holds promise for collaborative model fitting while preserving the data privacy of each participant, a careful analysis may still be required to understand the privacy implications of both federated learning outputs and summaries exchanged during fitting. We present work-in-progress, proposing a federated, privacy-preserving accept-reject mechanism which exploits modern homomorphic secret sharing methods. This mechanism enables a range of Monte Carlo algorithms involving an accept-reject step to be converted into federated equivalents, also with the potential to complement privacy properties of existing federated Monte Carlo algorithms that already incorporate an accept-reject step. In addition to this, we provide a practical software implementation enabling live federated learning across the internet between different parties, secured by both encrypted and signed shares, to authenticate participants and prevent man-in-the-middle attacks.
Venue: MCS2068
14:00 MCS3070 HEPJAndrea Conti (University of Oviedo): Codimension-2 Super-(Conformal) Monodromy Defects
Recently, there has been an increasing interest in the study of defects in quantum field theories, with holography providing a powerful framework to explore various aspects of these super-(conformal) gauge theories. In this talk, I will discuss supergravity solutions that are dual to codimension-2 superconformal monodromy defects. These solutions are obtained using gauged supergravities in D=4,5,6 and 7 dimensions. I will present a prescription to compute the defect entanglement entropy, outlining the renormalization procedure needed to regularise its divergencies, which I will discuss in detail. In some cases, we are also able to express this quantity in terms of the free energy/Weyl anomaly of the defect and its conformal weight. If time allows, I will also discuss some new results for non-conformal monodromy defects.
Venue: MCS3070
Nov 11 (Tue)
13:00 MCS2068 APDEIngrid Amaranta Membrillo Solis (Queen Mary University of London): Inverse spectral problems for orbifolds via the HodgeLaplace operator
Orbifolds extend the concept of manifolds by allowing singularities that arise in a controlled way from group actions. They naturally appear in many geometric and physical settings, for example, as quotient spaces of symmetries, moduli spaces with isotropy, and as local models of singular spaces in mathematical physics. A fundamental problem in the spectral theory of orbifolds is whether the spectrum of a differential operator uniquely determines the underlying geometric or topological structure. This raises two natural questions:
(1) Can spectral data distinguish orbifolds with singularities from smooth manifolds?
(2) What geometric and topological features of the singular set can be recovered from spectral data?
Using heat invariants of the spectra of the HodgeLaplace operator, we address these questions and examine how spectral information encodes the singular structure of orbifolds. This talk is based on joint work with Katie Gittins, Carolyn Gordon, Juan Pablo Rossetti, Mary Sandoval, and Liz Stanhope.
Venue: MCS2068
14:00 MCS2068 ASGRobin Bartlett (Queen Mary University of London): Moduli spaces of Galois representations and explicit equations for the crystalline locus.
Moduli spaces of representations of the absolute Galois group of a p-adic field play an important role in many aspects of the Langlands correspondence. In this talk I will discuss the least well understood situation, which is when the coefficients of these representations have characteristic p, and explain how sufficient control of the geometry of these moduli spaces leads to concrete new instances of the Langlands correspondence.
Towards the end of the talk I will say a little about recent joint work with Bao Le-Hung and Brandon Levin. We are able to control the singularities of these moduli spaces in several new cases, using explicit equations derived from Plücker coordinates. As an application we extend modularity lifting theorems proved by Kisin for two dimensional Galois representations of a totally real extension of Q, to three dimensional representations.
Venue: MCS2068
Nov 13 (Thu)
13:00 MCS2068 G&TPierre Will (Université Grenoble Alpes): Complex hyperbolic quasi-Fuchsian groups
In this talk, I will discuss the complex hyperbolic
analogue of quasi-Fuchsian deformations of Fuchsian groups. More
precisely, starting from a Fuchsian group, we can make it act on the
complex hyperbolic space by embedding it in the stabiliser of a totally
geodesic subspace. A natural question is then to try to deform this
embedding. The question is : what happens ?
After describing a few classical results, I will discuss a joint work
with Falbel and Guilloux where we consider this question from the point
of view the shape of the limit set. I will introduce the notion of a
"slim curve", a notion that extends that of a Legendrian curve, and
discuss whether or not the limit set can have this property, and what it implies
on the action of the group.
Venue: MCS2068
14:00 MCS2068 ProbEmma Bailey (University of Bristol): Interpolation statistics for unlikely values of unitary characteristic polynomials
The logarithm of a unitary characteristic polynomial is a Gaussian random variable when one draws the matrix under Haar measure. Large deviation principles and some precise deviations for this random variable are known following work of Hughes-Keating-OConnell and Féray-Méliot-Nikeghbali. Motivated by a conjecture regarding the leading coefficient of the moments of the Riemann zeta function, we study a particular interpolating regime in the right-tail. This is joint work with Sebastian Ortiz.
Venue: MCS2068
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Usual Venue: MCS2068
Contact: yohance.a.osborne@durham.ac.uk
Nov 11 13:00 Ingrid Amaranta Membrillo Solis (Queen Mary University of London): Inverse spectral problems for orbifolds via the HodgeLaplace operator
Orbifolds extend the concept of manifolds by allowing singularities that arise in a controlled way from group actions. They naturally appear in many geometric and physical settings, for example, as quotient spaces of symmetries, moduli spaces with isotropy, and as local models of singular spaces in mathematical physics. A fundamental problem in the spectral theory of orbifolds is whether the spectrum of a differential operator uniquely determines the underlying geometric or topological structure. This raises two natural questions:
(1) Can spectral data distinguish orbifolds with singularities from smooth manifolds?
(2) What geometric and topological features of the singular set can be recovered from spectral data?
Using heat invariants of the spectra of the HodgeLaplace operator, we address these questions and examine how spectral information encodes the singular structure of orbifolds. This talk is based on joint work with Katie Gittins, Carolyn Gordon, Juan Pablo Rossetti, Mary Sandoval, and Liz Stanhope.
Venue: MCS2068
Nov 18 13:00 Gonçalo Dos Reis (University of Edinburgh): TBC
Nov 25 13:00 Lukas Koch (University of Sussex): Uniform Lipschitz estimates for regularised optimal transport
I will discuss how to obtain Lipschitz estimates for regularised optimal transport problems using a variational approach. In particular, this gives Lipschitz regularity for entropic optimal transport independent of the regularisation parameter. A crucial step in the approach are local \(L^\infty\)-estimates, which are of independent interest. The talk is based on joint work with Rishabh Gvalani (ETH).
Venue: MCS2068
Dec 02 13:00 Estefania Loayza Romero (University of Strathclyde): TBC
Dec 09 13:00 Giacomo Borghi (Heriot-Watt University): TBC
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
Nov 11 14:00 Robin Bartlett (Queen Mary University of London): Moduli spaces of Galois representations and explicit equations for the crystalline locus.
Moduli spaces of representations of the absolute Galois group of a p-adic field play an important role in many aspects of the Langlands correspondence. In this talk I will discuss the least well understood situation, which is when the coefficients of these representations have characteristic p, and explain how sufficient control of the geometry of these moduli spaces leads to concrete new instances of the Langlands correspondence.
Towards the end of the talk I will say a little about recent joint work with Bao Le-Hung and Brandon Levin. We are able to control the singularities of these moduli spaces in several new cases, using explicit equations derived from Plücker coordinates. As an application we extend modularity lifting theorems proved by Kisin for two dimensional Galois representations of a totally real extension of Q, to three dimensional representations.
Venue: MCS2068
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
Nov 06 13:00 John Parker (Durham University): Real hyperbolic on the outside, complex hyperbolic on the inside (3)
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): Complex hyperbolic quasi-Fuchsian groups
In this talk, I will discuss the complex hyperbolic
analogue of quasi-Fuchsian deformations of Fuchsian groups. More
precisely, starting from a Fuchsian group, we can make it act on the
complex hyperbolic space by embedding it in the stabiliser of a totally
geodesic subspace. A natural question is then to try to deform this
embedding. The question is : what happens ?
After describing a few classical results, I will discuss a joint work
with Falbel and Guilloux where we consider this question from the point
of view the shape of the limit set. I will introduce the notion of a
"slim curve", a notion that extends that of a Legendrian curve, and
discuss whether or not the limit set can have this property, and what it implies
on the action of the group.
Venue: MCS2068
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: MCS3070
Contact: mendel.t.nguyen@durham.ac.uk
Nov 10 14:00 Andrea Conti (University of Oviedo): Codimension-2 Super-(Conformal) Monodromy Defects
Recently, there has been an increasing interest in the study of defects in quantum field theories, with holography providing a powerful framework to explore various aspects of these super-(conformal) gauge theories. In this talk, I will discuss supergravity solutions that are dual to codimension-2 superconformal monodromy defects. These solutions are obtained using gauged supergravities in D=4,5,6 and 7 dimensions. I will present a prescription to compute the defect entanglement entropy, outlining the renormalization procedure needed to regularise its divergencies, which I will discuss in detail. In some cases, we are also able to express this quantity in terms of the free energy/Weyl anomaly of the defect and its conformal weight. If time allows, I will also discuss some new results for non-conformal monodromy defects.
Venue: MCS3070
Usual Venue: MCS0001
Contact: p.e.dorey@durham.ac.uk,enrico.andriolo@durham.ac.uk,tobias.p.hansen@durham.ac.uk
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 University): The Numerical Bootstrap of Points and Lines
I will describe how to constrain the conformal field theory data attached to boundary conditions of two dimensional theories, using the numerical bootstrap. Even for rational theories, it is hard to construct examples of boundary conditions which break all symmetry except Virasoro, let alone classify them. Yet, as always, the OPE data associated with each conformal boundary condition obeys crossing and unitarity. The ensuing constraints can be organized in a semidefinite program, which allows exploration of a multi-dimensional parameter space involving bulk and boundary data.
Venue: MCS0001
Dec 12 13:00 Sungwoo Hong (KAIST, Taejon): TBA
Usual Venue: MCS2068
Contact: tyler.helmuth@durham.ac.uk,oliver.kelsey-tough@durham.ac.uk
Nov 06 14:00 William Da Silva (University of Vienna): The longest increasing subsequence of Brownian separable permutons
The Brownian separable permutons form a one-parameter family of permutons, which are the universal scaling limits of pattern-avoiding permutations. In this talk, we will be interested in the length of the longest increasing subsequence (LIS) in permutations of size n sampled from the Brownian permutons. We give an answer to the celebrated Ulam-Hammersley problem in this context: what is the behaviour of LIS as n goes to infinity? A significant portion of the talk will be dedicated to our motivation behind the problem, emphasising connections to various objects in probability and combinatorics, such as random decorated trees, random graphs, directed planar maps and SLE/LQG. The talk is based on joint work with Arka Adhikari, Jacopo Borga, Thomas Budzinski and Delphin Sénizergues.
Venue: MCS2068
Nov 13 14:00 Emma Bailey (University of Bristol): Interpolation statistics for unlikely values of unitary characteristic polynomials
The logarithm of a unitary characteristic polynomial is a Gaussian random variable when one draws the matrix under Haar measure. Large deviation principles and some precise deviations for this random variable are known following work of Hughes-Keating-OConnell and Féray-Méliot-Nikeghbali. Motivated by a conjecture regarding the leading coefficient of the moments of the Riemann zeta function, we study a particular interpolating regime in the right-tail. This is joint work with Sebastian Ortiz.
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
Nov 27 14:00 Omer Angel (University of British Columbia): min/max trees
On a regular tree, assign each vertex a random independent value. Two players alternate choosing a child of the current vertex. When reaching level n, player 1 pays player 2 the cumulative sum of the values along the chosen path. We show that in certain cases the value of this game converges as n\to\infty, and discuss the challenges in extending our results. Joint with Gourab Ray and Yinon Spinka.
Venue: MCS2068
Dec 04 14:00 Kohei Suzuki (Department of Mathematics, Durham University): Interacting Brownian Motions, Wasserstein Gradient Flow and Ricci Curvature
In this talk, we focus on an infinite-dimensional model of interacting Brownian motions: Dyson Brownian motion at soft-edge scaling. Its stationary process is the Airy line ensemble, a central object in KPZ universality. We show that its time-marginal law forms a Wasserstein gradient flow of the relative entropy in the space of probability measures over the infinite-dimensional configuration space an infinite-dimensional analogue of Jordan-Kinderlehrer-Otto theory. This yields an optimal transport-first construction of the model, bridging Airy line ensemble/KPZ and optimal transport. From a metric-geometric viewpoint, our result shows that the configuration space endowed with the Airy_2 point process is an RCD space, a space having a uniform lower Ricci curvature bound in the sense of Lott-Villani/Sturm. As an application, (a) we establish various new functional inequalities (e.g., HWI, Brunn-Minkowski, dimension-free Harnack) for the model; (b) we discover a new propagation-of-rigidity phenomenon: the time-marginal law exhibits number rigidity in the sense of Ghosh and Peres, revealing a formation of a random crystal by long-range repulsively interacting Brownian motions. This talk is based on arXiv:2509.06869<https://arxiv.org/abs/2509.06869>.
Venue: MCS2068
Usual Venue: MCS3070
Contact: joe.thomas@durham.ac.uk
No upcoming seminars have been scheduled (not unusual outside term time).
Usual Venue: MCS2068
Contact: hyeyoung.maeng@durham.ac.uk,andrew.iskauskas@durham.ac.uk
Nov 10 13:00 Louis Aslett (Durham): Confidential Accept-Reject
Federated learning enables statistical models to be fitted using distributed data sets, without the need to bring those data sets to a single location. Although this holds promise for collaborative model fitting while preserving the data privacy of each participant, a careful analysis may still be required to understand the privacy implications of both federated learning outputs and summaries exchanged during fitting. We present work-in-progress, proposing a federated, privacy-preserving accept-reject mechanism which exploits modern homomorphic secret sharing methods. This mechanism enables a range of Monte Carlo algorithms involving an accept-reject step to be converted into federated equivalents, also with the potential to complement privacy properties of existing federated Monte Carlo algorithms that already incorporate an accept-reject step. In addition to this, we provide a practical software implementation enabling live federated learning across the internet between different parties, secured by both encrypted and signed shares, to authenticate participants and prevent man-in-the-middle attacks.
Venue: MCS2068
Dec 01 13:00 Markus Rau (Newcastle):
