Seminars in Mathematical Sciences

Seminars in the next week
Oct 08 (Wed)

16:00 zoom A&CKirill Krasnov and Chanon Hasuwannakit (University of Nottingham): Gravity MHV amplitudes from Berends-Giele currents.

The presentation will be based on a recent arxiv preprint 2507.13943<https://arxiv.org/abs/2507.13943>

Both of the authors of this preprint are planning to speak. We will start by explaining the calculation in the original Berends-Giele 1988 paper, which showed how the Parke-Taylor formula for YM MHV amplitudes can be proven by Feynman diagram calculations, combined with the idea of a recursion relation for these amplitudes. The calculation proceeds in two steps. First, one computes what can be called the all-plus BG current. The derivation is reasonably straightforward, but the current computed does not contribute to any non-vanishing scattering amplitude. Nevertheless, this current exhibits much of the structure of the Parke-Taylor MHV formula. One then proceeds with a much harder calculation of what can be called all-but-one-plus BG current. The combinatorics of this is more non-trivial, but nevertheless an explicit solution is possible. It is from this all-but-one-plus current that the MHV amplitude is eventually extracted.

We then proceed to the computation of exactly the same logic for gravity. To produce Feynman rules of manageable complexity we use the chiral first order formulation of GR. This reasonably quickly leads to the recurrence relations for both the all-plus and all-but-one-plus BG currents. The arising recursion relations are doubles of those in the YM case. The combinatorics of the solution to the all-plus recurrence relation is much more involved than in the YM case, and the solution is a sum over trees. As in the YM case, the all-plus current already exhibits much of the structure of the MHV formula, in its NSVW version. However, to obtain the MHV amplitudes one needs to compute the all-but-one-plus currents. The combinatorics of this is even more non-trivial, but an explicit solution is again possible. We sketch the details of all these computations.

Venue: zoom

Zoom: https://teams.microsoft.com/l/meetup-join/19%3ameeting_Y2EyMTViYTQtZGNjOS00OWQzLTg2Y2UtOGVjZTg1MWE5MzY2%40thread.v2/0?context=%7b%22Tid%22%3a%227250d88b-4b68-4529-be44-d59a2d8a6f94%22%2c%22Oid%22%3a%22b3bc112c-becb-4457-9b61-f52ec1816855%22%7d

Oct 09 (Thu)

13:00 MCS2068 G&TSusovan Pal (Vrije Universiteit Brussel): Manifolds with rough boundaries, and asymptotics of the graph Laplacian

Manifold learning algorithms often assume that data lie on or near a smooth lower-dimensional manifold M embedded in a higher dimensional Euclidean space, and that the Laplace–Beltrami operator of M can be approximated by graph Laplacian constructed from the data. However, analogous results for singular geometric spaces (for instance, spaces with boundaries or cusps) remain largely unexplored. In this talk, I will present recent work analyzing the asymptotic behavior of the unnormalized graph Laplacian on manifolds with rough (non-smooth) boundaries, which we refer to as manifolds with kinks, corners or cusps being special cases. In contrast with the smooth case—where convergence is to the Laplace–Beltrami operator—we show that the limiting behavior involves a first-order boundary operator, namely a generalized normal derivative. Numerical simulations support and illustrate the theoretical results. Aside from the usual motivation of nonlinear dimensionality reduction, we also show one application on edge detection in image processing.

Venue: MCS2068

14:00 MCS2068 ProbAndrew Wade (University of Durham): One-dimensional particle clouds with elastic collisions

I will talk about an interacting particle system of a finite number of labelled particles on the integer lattice, in which particles have intrinsic masses and left/right jump rates. The (weak) order of the particles is preserved by a collision rule, which is `elastic' in the sense that the net rate of flow of mass is independent of the present configuration, in contrast to the exclusion process, for example. If a particle is the minimal-label particle at its site when it tries to jump left, the jump is executed. If not, `momentum' is transferred to increase the rate of jumping left of the minimal-label particle. Similarly for jumps to the right. The main result is that the particle masses and jump rates determine explicitly, via a concave majorant of a simple `potential' function associated to the masses and jump rates, a unique partition of the system into maximal stable subsystems. I will try to indicate some connections to adjacent models, including diffusions with rank-based coefficients. This is joint work with M Menshikov (Durham) and S Popov (Porto).

Venue: MCS2068

Oct 10 (Fri)

13:00 MCS0001 HEPMSameer Murthy (King's College London): TBA

Venue: MCS0001

Oct 14 (Tue)

13:00 MCS2068 APDEAlexander Pushnitski (King's College London): Inverse Spectral Problems for Non-Selfadjoint Schrödinger Operators

For a self-adjoint Schrödinger operator H on the positive semi-axis with a real-valued potential q, the celebrated Borg-Marchenko theorem establishes a one-to-one correspondence between the potential and its spectral measure. When the potential q is complex-valued, the operator is non-selfadjoint, and the classical theory no longer applies. In the talk I will present a new framework, developed in joint recent work with František Štampach (TU Prague), to address the non-selfadjoint inverse problem. We introduce the notion of a 'spectral pair' - comprising a measure and an auxiliary complex-valued function - which generalizes the spectral measure. We then establish an analogue of the Borg-Marchenko theorem, establishing a one-to-one correspondence between spectral pairs and complex potentials q. This approach is also applicable to inverse problems for non-selfadjoint Jacobi matrices.

Venue: MCS2068

14:00 MCS2068 ASGVictor Abrashkin (Durham University): Ramification via deformation

Venue: MCS2068


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• Amplitudes and Correlators

Usual Venue: zoom

Contact: arthur.lipstein@durham.ac.uk

Oct 08 16:00 Kirill Krasnov and Chanon Hasuwannakit (University of Nottingham): Gravity MHV amplitudes from Berends-Giele currents.

The presentation will be based on a recent arxiv preprint 2507.13943<https://arxiv.org/abs/2507.13943>

Both of the authors of this preprint are planning to speak. We will start by explaining the calculation in the original Berends-Giele 1988 paper, which showed how the Parke-Taylor formula for YM MHV amplitudes can be proven by Feynman diagram calculations, combined with the idea of a recursion relation for these amplitudes. The calculation proceeds in two steps. First, one computes what can be called the all-plus BG current. The derivation is reasonably straightforward, but the current computed does not contribute to any non-vanishing scattering amplitude. Nevertheless, this current exhibits much of the structure of the Parke-Taylor MHV formula. One then proceeds with a much harder calculation of what can be called all-but-one-plus BG current. The combinatorics of this is more non-trivial, but nevertheless an explicit solution is possible. It is from this all-but-one-plus current that the MHV amplitude is eventually extracted.

We then proceed to the computation of exactly the same logic for gravity. To produce Feynman rules of manageable complexity we use the chiral first order formulation of GR. This reasonably quickly leads to the recurrence relations for both the all-plus and all-but-one-plus BG currents. The arising recursion relations are doubles of those in the YM case. The combinatorics of the solution to the all-plus recurrence relation is much more involved than in the YM case, and the solution is a sum over trees. As in the YM case, the all-plus current already exhibits much of the structure of the MHV formula, in its NSVW version. However, to obtain the MHV amplitudes one needs to compute the all-but-one-plus currents. The combinatorics of this is even more non-trivial, but an explicit solution is again possible. We sketch the details of all these computations.

Venue: zoom

• Analysis and PDE

Usual Venue: MCS2068

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

Oct 14 13:00 Alexander Pushnitski (King's College London): Inverse Spectral Problems for Non-Selfadjoint Schrödinger Operators

For a self-adjoint Schrödinger operator H on the positive semi-axis with a real-valued potential q, the celebrated Borg-Marchenko theorem establishes a one-to-one correspondence between the potential and its spectral measure. When the potential q is complex-valued, the operator is non-selfadjoint, and the classical theory no longer applies. In the talk I will present a new framework, developed in joint recent work with František Štampach (TU Prague), to address the non-selfadjoint inverse problem. We introduce the notion of a 'spectral pair' - comprising a measure and an auxiliary complex-valued function - which generalizes the spectral measure. We then establish an analogue of the Borg-Marchenko theorem, establishing a one-to-one correspondence between spectral pairs and complex potentials q. This approach is also applicable to inverse problems for non-selfadjoint Jacobi matrices.

Venue: MCS2068

• 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: herbert.gangl@durham.ac.uk

Oct 14 14:00 Victor Abrashkin (Durham University): Ramification via deformation

Venue: MCS2068

Oct 21 14:00 Colton Griffin (University of Pennsylvania):

Venue: MCS2068

Nov 04 14:00 Yu-Chen Sun (University of Bristol):

Venue: MCS2068

Nov 11 14:00 Robin Bartlett (University of Glasgow):

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):

Venue: MCS2068

Dec 09 14:00 Fredrik Stromberg (University of Nottingham):

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 and Public Lectures

Usual Venue: MCS0001

Contact: sabine.boegli@durham.ac.uk,alpar.r.meszaros@durham.ac.uk

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

• 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).

• Geometry and Topology

Usual Venue: MCS2068

Contact: fernando.galaz-garcia@durham.ac.uk

Oct 09 13:00 Susovan Pal (Vrije Universiteit Brussel): Manifolds with rough boundaries, and asymptotics of the graph Laplacian

Manifold learning algorithms often assume that data lie on or near a smooth lower-dimensional manifold M embedded in a higher dimensional Euclidean space, and that the Laplace–Beltrami operator of M can be approximated by graph Laplacian constructed from the data. However, analogous results for singular geometric spaces (for instance, spaces with boundaries or cusps) remain largely unexplored. In this talk, I will present recent work analyzing the asymptotic behavior of the unnormalized graph Laplacian on manifolds with rough (non-smooth) boundaries, which we refer to as manifolds with kinks, corners or cusps being special cases. In contrast with the smooth case—where convergence is to the Laplace–Beltrami operator—we show that the limiting behavior involves a first-order boundary operator, namely a generalized normal derivative. Numerical simulations support and illustrate the theoretical results. Aside from the usual motivation of nonlinear dimensionality reduction, we also show one application on edge detection in image processing.

Venue: MCS2068

Oct 16 13:00 Raphael Zentner (Durham University): TBA

TBA

Venue: MCS2068

Nov 13 14:00 Jan Rybalko (University of Oslo): TBA

TBA

Venue: MCS2068

Nov 20 14:00 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

Jan 22 14:00 Chunyang Hu (Durham University): TBA

TBA

Venue: MCS2068

Mar 06 13:00 Julian Scheuer (Goethe University Frankfurt): 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: MCS0001

Contact: p.e.dorey@durham.ac.uk,enrico.andriolo@durham.ac.uk,tobias.p.hansen@durham.ac.uk

Oct 10 13:00 Sameer Murthy (King's College London): TBA

Venue: MCS0001

Oct 17 13:00 Neil Lambert (King's College London): TBA

Venue: MCS0001

Oct 24 13:00 Nicola Dondi (ICTP Trieste): TBA

Venue: MCS0001

Oct 31 13:00 Max Hutt (Imperial College London): TBA

Venue: MCS0001

Nov 07 13:00 Stathis Vitouladitis (Université Libre de Bruxelles): TBA

Venue: MCS0001

Nov 14 13:00 Christian Copetti (Oxford): TBA

Venue: MCS0001

Nov 21 13:00 Ida Zadeh (Southampton): TBA

Venue: MCS0001

Nov 28 13:00 Tim Meier (Santiago de Compostela): TBA

Venue: MCS0001

Dec 05 13:00 Marco Meineri (Torino): TBA

Venue: MCS0001

Dec 12 13:00 Sungwoo Hong (KAIST, Taejon): TBA

Venue: MCS0001

• Probability

Usual Venue: MCS2068

Contact: tyler.helmuth@durham.ac.uk,oliver.kelsey-tough@durham.ac.uk

Oct 09 14:00 Andrew Wade (University of Durham): One-dimensional particle clouds with elastic collisions

I will talk about an interacting particle system of a finite number of labelled particles on the integer lattice, in which particles have intrinsic masses and left/right jump rates. The (weak) order of the particles is preserved by a collision rule, which is `elastic' in the sense that the net rate of flow of mass is independent of the present configuration, in contrast to the exclusion process, for example. If a particle is the minimal-label particle at its site when it tries to jump left, the jump is executed. If not, `momentum' is transferred to increase the rate of jumping left of the minimal-label particle. Similarly for jumps to the right. The main result is that the particle masses and jump rates determine explicitly, via a concave majorant of a simple `potential' function associated to the masses and jump rates, a unique partition of the system into maximal stable subsystems. I will try to indicate some connections to adjacent models, including diffusions with rank-based coefficients. This is joint work with M Menshikov (Durham) and S Popov (Porto).

Venue: MCS2068

• Pure Maths Colloquium

Usual Venue: MCS2068

Contact: michael.r.magee@durham.ac.uk

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

• 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: hyeyoung.maeng@durham.ac.uk,andrew.iskauskas@durham.ac.uk

Oct 27 13:00 Ben Swallow (St. Andrews):

Venue: MCS2068

Nov 03 13:00 Sam Livingstone (UCL):

Venue: MCS2068

Dec 01 13:00 Markus Rau (Newcastle):

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)