Seminars in Mathematical Sciences

Seminars in the next week
Jan 23 (Fri)

13:00 MCS0001 HEPMParita Shah (Durham University): Dualities, Integrable Deformations, and Quantum Corrections in String Theory

In this talk, I will give an overview of my PhD work on dualities and integrable structures in string theory, with a particular emphasis on T-duality as both a conceptual symmetry and a practical solution-generating tool. I will explain how integrable deformations of string sigma models can be embedded into the duality-covariant framework of Double Field Theory, where T-duality is realized geometrically. I will also describe how the Double Field Theory formalism can be used to analyze higher-order \u03b1\u2032-corrections to supergravity backgrounds, highlighting a special class of geometries where quantum corrections take a particularly simple form. The talk will also discuss extensions of non-Abelian T-duality that lead to new classes of string backgrounds. These results illustrate how duality-covariant methods provide insight into the structure of string theory across different regimes.

Venue: MCS0001

Jan 26 (Mon)

13:00 MCS2068 StatAdam Iqbal, Rakan Al Rekayan (Durham): TBA

TBA

Venue: MCS2068

14:00 MCS2068 PureFred Diamond (King's College London): Modularity of elliptic curves, and beyond, and beneath

In his celebrated work completed in 1995, Wiles, in part with Taylor, proved that every semistable elliptic curve over Q is modular, in the sense that its L-function is also that of a modular form. Their methods were subsequently extended by Breuil, Conrad, Taylor and myself to prove the modularity of all elliptic curves over Q. The Modularity Theorem can be viewed as a special case of Langlands reciprocity conjectures, which continue to see exciting advances stemming from Wiles’ work in combination with further innovations.

In addition to its most famous consequence, namely Fermat’s Last Theorem, modularity also underpins all major progress on the Birch--Swinnerton-Dyer Conjecture. Like the Modularity Theorem, the Birch--Swinnerton-Dyer Conjecture can also be viewed as an instance of a vast family of conjectures, in this case relating arithmetic invariants to special values of L-functions. After giving an overview of Wiles’ method and some subsequent developments, I’ll explain how the proof of the Modularity Theorem is itself related, by work of Hida, to another instance of these conjectures, namely for certain adjoint L-functions.

Venue: MCS2068

Jan 27 (Tue)

14:00 MCS2068 ASGFred Diamond (King's College): Geometric Serre weights and Jochnowitz modules for Hilbert modular forms (mod p)

Part of Serre’s Conjecture (now a theorem of Khare and Wintenberger) predicts the minimal weight of a modular form giving rise to any (odd, irreducible) two-dimensional characteristic p representation of the absolute Galois group of Q. I’ll explain a generalization of the weight part of Serre’s conjecture involving Galois groups over totally real fields and Hilbert modular forms, viewed as sections of line bundles on Hilbert modular varieties (and so includes, for example, forms of partial weight one). I’ll also discuss partial results towards it, and explain the statement of a refinement that captures additional structure in this context. This is joint work variously with Sasaki, Kassaei and Wiersema.

Venue: MCS2068

Jan 29 (Thu)

13:00 MCS2068 G&TDaniel Disney (Durham): Sub-Riemannian Structures on Exotic 7-Spheres

Sub-Riemannian structures of high codimension (greater than one) are rare on 7-manifolds. Until recently, only three such examples were known on any of the homotopy 7-spheres: two on the standard 7-sphere and one on the Gromoll--Meyer exotic sphere. In this talk I will describe new examples of step-2, codimension-3 sub-Riemannian structures on every homotopy (exotic) 7-sphere.

Venue: MCS2068

14:00 MCS2068 ProbIrene Ayuso Ventura (University of Durham): Imry-Ma phenomenon for the hard-core model on Z^2.

In this talk I will present recent joint work with Leandro Chiarini, Tyler Helmuth, and Ellen Powell on the hard-core model on ℤ², a model of independent sets on the square lattice. We show that under weak random disorder, this model has no phase transition in two dimensions. This behavior is known as the Imry–Ma phenomenon, whose most classical example is the random-field Ising model. Our proof is inspired by the Aizenman–Wehr argument for the random-field Ising model, but relies on spatial symmetries rather than internal spin symmetries.

Venue: MCS2068

Jan 30 (Fri)

13:00 MCS0001 HEPMNeil Turok (Edinburgh University): TBA

Venue: MCS0001


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Upcoming Seminars by Series

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• Amplitudes and Correlators

Contact: arthur.lipstein@durham.ac.uk

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

• Analysis and PDE

Usual Venue: MCS2068

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

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

• 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

Jan 27 14:00 Fred Diamond (King's College): Geometric Serre weights and Jochnowitz modules for Hilbert modular forms (mod p)

Part of Serre’s Conjecture (now a theorem of Khare and Wintenberger) predicts the minimal weight of a modular form giving rise to any (odd, irreducible) two-dimensional characteristic p representation of the absolute Galois group of Q. I’ll explain a generalization of the weight part of Serre’s conjecture involving Galois groups over totally real fields and Hilbert modular forms, viewed as sections of line bundles on Hilbert modular varieties (and so includes, for example, forms of partial weight one). I’ll also discuss partial results towards it, and explain the statement of a refinement that captures additional structure in this context. This is joint work variously with Sasaki, Kassaei and Wiersema.

Venue: MCS2068

Feb 03 14:00 Max Koelbl (Osaka University):

Venue: MCS2068

Feb 05 14:00 David Helm (Imperial College, London (note the unusual day!)):

Venue: MCS3070

Feb 24 14:00 Oleksiy Klurman (University of Bristol):

Venue: MCS2068

Mar 03 14:00 Heejong Lee (KIAS):

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

Jan 29 13:00 Daniel Disney (Durham): Sub-Riemannian Structures on Exotic 7-Spheres

Sub-Riemannian structures of high codimension (greater than one) are rare on 7-manifolds. Until recently, only three such examples were known on any of the homotopy 7-spheres: two on the standard 7-sphere and one on the Gromoll--Meyer exotic sphere. In this talk I will describe new examples of step-2, codimension-3 sub-Riemannian structures on every homotopy (exotic) 7-sphere.

Venue: MCS2068

Feb 05 13:00 Sarah Whitehouse (Sheffield): Homotopy theory and geometry related to multicomplexes

A multicomplex is a variant of a bicomplex and these structures arise naturally in many geometric, topological and algebraic contexts; for example, from filtered simplicial sets. I will explain some recent joint work with Joana Cirici and Muriel Livernet which explores homotopy theories related to the two spectral sequences of a truncated multicomplex. There are potential applications to the study of homotopy types of almost and generalized complex manifolds.

Venue: MCS2068

Feb 12 13:00 Tom Nye (Newcastle): Metric geometry for statistics in spaces of trees, forests and graphs

Venue: MCS2068

Feb 19 13:00 Raphael Zentner (Durham): TBA

Venue: MCS2068

Feb 26 13:00 Brendan Guilfoyle (Munster Technological University): TBA

Venue: MCS2068

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

Venue: MCS2068

Mar 12 13:00 Andy Wand (Glasgow): TBA

Venue: MCS2068

Apr 30 13:00 Anthea Monod (Imperial): 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

Jan 23 13:00 Parita Shah (Durham University): Dualities, Integrable Deformations, and Quantum Corrections in String Theory

In this talk, I will give an overview of my PhD work on dualities and integrable structures in string theory, with a particular emphasis on T-duality as both a conceptual symmetry and a practical solution-generating tool. I will explain how integrable deformations of string sigma models can be embedded into the duality-covariant framework of Double Field Theory, where T-duality is realized geometrically. I will also describe how the Double Field Theory formalism can be used to analyze higher-order \u03b1\u2032-corrections to supergravity backgrounds, highlighting a special class of geometries where quantum corrections take a particularly simple form. The talk will also discuss extensions of non-Abelian T-duality that lead to new classes of string backgrounds. These results illustrate how duality-covariant methods provide insight into the structure of string theory across different regimes.

Venue: MCS0001

Jan 30 13:00 Neil Turok (Edinburgh University): TBA

Venue: MCS0001

Feb 06 13:00 Fiona Seibold (Ecole Polytechnique Lausanne): TBA

Venue: MCS0001

Feb 13 13:00 Ayan Kumar Patra (Durham University): TBA

Venue: MCS0001

Feb 20 13:00 Carlos Nunez (Swansea University): TBA

Venue: MCS0001

Feb 27 13:00 Paul Fendley (Oxford University): TBA

Venue: MCS0001

Mar 06 13:00 Olalla Castro Alvaredo (City University London): TBA

Venue: MCS0001

Mar 13 13:00 Costantinos Papageorgakis (Queen Mary University London): TBA

Venue: MCS0001

Mar 20 13:00 Donal O'Connell (Edinburgh University): TBA

Venue: MCS0001

Mar 27 13:00 Sean Hartnoll (Cambridge University): TBA

Venue: MCS0001

• Probability

Usual Venue: MCS2068

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

Jan 29 14:00 Irene Ayuso Ventura (University of Durham): Imry-Ma phenomenon for the hard-core model on Z^2.

In this talk I will present recent joint work with Leandro Chiarini, Tyler Helmuth, and Ellen Powell on the hard-core model on ℤ², a model of independent sets on the square lattice. We show that under weak random disorder, this model has no phase transition in two dimensions. This behavior is known as the Imry–Ma phenomenon, whose most classical example is the random-field Ising model. Our proof is inspired by the Aizenman–Wehr argument for the random-field Ising model, but relies on spatial symmetries rather than internal spin symmetries.

Venue: MCS2068

Feb 05 14:00 Jannis Dause (TU Berlin): Duality in Non-Markovian Stochastic Control problems using Rough Stochastic Differential Equations

The classical stochastic optimal control framework is heavily based on the Markovianity of the underlying dynamics e.g., through the use of the dynamic programming principle and the subsequent derivation of the Hamilton-Jacobi-Bellman equation. In this talk we will focus on a certain class of non-Markovian stochastic control problem arising e.g., from optimal control under stochastic volatility.

In particular we will consider controlled doubly-stochastic differential equations driven by two independent Brownian noises B and W, where the coefficients depend progressively on the noise W. Extending previous work of [Diehl, Friz,Gassiat '17] by methods from BS(P)DE-theory, we are then able to relate this stochastic control problem to a penalized version of the original control problem, where W can now be treated as a 'frozen', i.e., deterministic (but irregular) path. Most importantly this 'dual problem' is now Markovian and may thus be treated by classical methods.

The main technical tool allowing us handle the dual problem will be the recently introduced theory of Rough Stochastic Differential Equations (RSDEs) [Friz, Hoquet, Lê '21], which provides a generalized framework of classical SDE Theory and Lyons' Rough Differential Equations.

This is joint work with Peter Bank, Peter K. Friz and Filippo de Feo.

Venue: MCS2068

Feb 12 14:00 Julian Ransford (University of Cambridge): TBA

TBA

Venue: MCS2068

Feb 19 14:00 Giorgios Vaskedis (Newcastle University): TBA

TBA

Venue: MCS2068

• Pure Maths Colloquium

Usual Venue: MCS2068

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

Jan 26 14:00 Fred Diamond (King's College London): Modularity of elliptic curves, and beyond, and beneath

In his celebrated work completed in 1995, Wiles, in part with Taylor, proved that every semistable elliptic curve over Q is modular, in the sense that its L-function is also that of a modular form. Their methods were subsequently extended by Breuil, Conrad, Taylor and myself to prove the modularity of all elliptic curves over Q. The Modularity Theorem can be viewed as a special case of Langlands reciprocity conjectures, which continue to see exciting advances stemming from Wiles’ work in combination with further innovations.

In addition to its most famous consequence, namely Fermat’s Last Theorem, modularity also underpins all major progress on the Birch--Swinnerton-Dyer Conjecture. Like the Modularity Theorem, the Birch--Swinnerton-Dyer Conjecture can also be viewed as an instance of a vast family of conjectures, in this case relating arithmetic invariants to special values of L-functions. After giving an overview of Wiles’ method and some subsequent developments, I’ll explain how the proof of the Modularity Theorem is itself related, by work of Hida, to another instance of these conjectures, namely for certain adjoint L-functions.

Venue: MCS2068

• 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

Jan 26 13:00 Adam Iqbal, Rakan Al Rekayan (Durham): TBA

TBA

Venue: MCS2068

Feb 02 13:00 Jon Cockayne (Southampton): TBA

TBA

Venue: MCS2068

Feb 09 13:00 Juraj Medzihorsky (Durham): TBA

TBA

Venue: MCS2068

Feb 16 13:00 Vanda Inacio (Edinburgh): TBA

TBA

Venue: MCS2068

Feb 23 13:00 Long Tran-Thanh (Warwick): TBA

TBA

Venue: MCS2068

Mar 02 13:00 Helen Ogden (Southampton): TBA

TBA

Venue: MCS2068

Mar 09 13:00 Irini Moustaki (LSE): TBA

TBA

Venue: MCS2068

Mar 16 13:00 Mengchu Li (Birmingham): TBA

TBA

Venue: MCS2068

Mar 23 13:00 Rasa Remenyte-Prescott (Nottingham): TBA

TBA

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)