Seminars in Mathematical Sciences

Seminars in the next week
Aug 11 (Mon)

12:00 MCS2068 ProbZhen Wu (School of Mathematics, Shandong University, Jinan, P.R. China): Mean Field Games and Control via Forward Backward Stochastic Differential Equations

Mean field theory provides a powerful framework for analyzing large-scale interacting particle systems, with broad applications in game and control theory. In such system, competitive optimization by individual particles leads to $N$-particle games, while cooperative optimization yields social optima problems. Due to the high dimensionality and coupling among particles, direct analysis of such systems is often intractable. A common approach is to consider the limit behavior of a representative particle, leading to mean field game and mean field control problems. These limiting problems are typically characterized by infinite-dimensional partial differential equations such as the master equation and the Hamilton–Jacobi equation. Two main approaches are used to study their well-posedness: the probabilistic method and the analytical PDE approach. This talk focuses on the probabilistic method, utilizing the theory of forward backward stochastic differential equations (FBSDEs) to address linear-quadratic mean field games with non-monotone data and linear-quadratic mean field control problems with non-convex data. It can be shown that the corresponding master equation and the Hamilton–Jacobi equation admit unique classical solution. The propagation of chaos property for the related trajectories can also be proved.

This is a joint with a workshop on Stochastic Analysis, Stochastic Controls and Ergodic Theory organised by Chunrong Feng and Huaizhong Zhao, and is the key-note talk of that workshop.

Venue: MCS2068


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Current and Upcoming Events

These events are hosted in and/or organised by members of the Department (follow links for details):

Aug 18 [TLC101] Workshop: Branching Processes, Quasi-Stationary Distributions, and Front Propagation

Upcoming Seminars by Series

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• Amplitudes and Correlators

Usual Venue: zoom

Contact: arthur.lipstein@durham.ac.uk

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

• Analysis and PDE

Usual Venue: MCS3070

Contact: sabine.boegli@durham.ac.uk

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

• Applied Mathematics

Usual Venue: MCS2068

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

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

• 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).

• Ergodic Theory and Dynamics

Usual Venue: MCS3070

Contact: gabriel.fuhrmann@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: martin.p.kerin@durham.ac.uk

Mar 06 14:00 Julian Scheuer (Goethe University Frankfurt): TBA

Venue: MCS2068

• HEP Journal Club

Usual Venue: MCS3070

Contact: andrea.grigoletto@durham.ac.uk,nakarin.lohitsiri@durham.ac.uk

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

• HEP Lunchtime

Usual Venue: MCS0001

Contact: silvia.nagy@durham.ac.uk,enrico.andriolo@durham.ac.uk,tobias.p.hansen@durham.ac.uk

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

• Probability

Usual Venue: MCS2068

Contact: kohei.suzuki@durham.ac.uk

Aug 11 12:00 Zhen Wu (School of Mathematics, Shandong University, Jinan, P.R. China): Mean Field Games and Control via Forward Backward Stochastic Differential Equations

Mean field theory provides a powerful framework for analyzing large-scale interacting particle systems, with broad applications in game and control theory. In such system, competitive optimization by individual particles leads to $N$-particle games, while cooperative optimization yields social optima problems. Due to the high dimensionality and coupling among particles, direct analysis of such systems is often intractable. A common approach is to consider the limit behavior of a representative particle, leading to mean field game and mean field control problems. These limiting problems are typically characterized by infinite-dimensional partial differential equations such as the master equation and the Hamilton–Jacobi equation. Two main approaches are used to study their well-posedness: the probabilistic method and the analytical PDE approach. This talk focuses on the probabilistic method, utilizing the theory of forward backward stochastic differential equations (FBSDEs) to address linear-quadratic mean field games with non-monotone data and linear-quadratic mean field control problems with non-convex data. It can be shown that the corresponding master equation and the Hamilton–Jacobi equation admit unique classical solution. The propagation of chaos property for the related trajectories can also be proved.

This is a joint with a workshop on Stochastic Analysis, Stochastic Controls and Ergodic Theory organised by Chunrong Feng and Huaizhong Zhao, and is the key-note talk of that workshop.

Venue: MCS2068

• Pure Maths Colloquium

Usual Venue: MCS0001

Contact: raphael.zentner@durham.ac.uk

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

• Spectra and Moduli

Usual Venue: MCS3070

Contact: irving.d.calderon-camacho@durham.ac.uk,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

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

• 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)