May 18 (Mon)
14:00 MCS2068 PureAnna Roig-Sanchis (Nice): Minimal surfaces in large dimensional spheres
Since the work of Lagrange in the 18th century, minimal surfaces have been an important topic in differential geometry, geometric analysis, and mathematical physics. While there are many examples of minimal surfaces in Euclidean space, much less is known about minimal surfaces in spheres. In this colloquium, I will first give a very general introduction to minimal surfaces and show some classical examples. Then, I will present recent joint work with Michele Ancona, François Labourie and Jérémy Toulisse in which we prove the existence of negatively curved minimal surfaces in spheres of sufficiently large dimension, answering a question of Shing-Tung Yau.
Venue: MCS2068
May 19 (Tue)
13:00 MCS2068 APDENicolò De Bernardi (Padova): On the Local Turnpike Property in Mean Field Control and Games
We study the local stability of solutions to ergodic and discounted Mean Field Games systems around stationary equilibria with quadratic Hamiltonians. We introduce a new stability assumption for the stationary equilibria, allowing for non-monotone couplings, and show that this weaker condition still yields a (local) exponential turnpike property for solutions close to the stationary one. We also provide an interpretation in terms of spectral properties of an operator, which might be encoded in the MFG system and help construct non-trivial examples. This talk is based on joint work with M. Cirant (Padova).
Venue: MCS2068
14:00 MCS2068 APDEHei Jie (Jack) Lam (Durham): Well-posedness and quantitative convergence for distributed equilibria of displacement monotone \(N\)-player games with interaction through controls
In this talk we will study the wellposedness of distributed equilibria of \(N\)-player games under displacement semi-monotonicity and convexity assumptions, in which the running cost of a player depends also on the controls used by other players. We consider running costs that are not necessarily separable, resulting in a set of consistency/fixed point relations on infinite dimensional spaces. We will also talk about quantitative convergence results (both for optimal trajectories/control and value functions) for the \(N\)-player games to the corresponding Mean Field Games of Controls (MFGC). Our approach works for both stochastic and deterministic cases but in this talk we will focus on the deterministic case (distributed equilibria coincides with open-loop equilibria in this case), where further quantitative convergence results can be proved for the gradients of value functions. This talk is based on joint work with Alpár Mészáros (Durham University).
Venue: MCS2068
May 20 (Wed)
16:00 zoom A&CRichard van Dongen (University of Mons): Self-dual holography
In flat space, self-dual theories are powerful toy models for studying their parent theories. Here we develop an AdS/CFT framework for such self-dual theories and we discuss the holographic relation between chiral higher-spin gravity and Chern-Simons vector models. As an example, we discuss the relation between Yang-Mills and self-dual Yang-Mills in AdS. For mixed boundary conditions, explicit three- and four-point correlation functions in Yang-Mills are presented in several gauges, and we show how the self-dual limit emerges. The same correlators will be presented for the higher-spin extension of self-dual Yang-Mills.
Venue: zoom
Online: https://teams.microsoft.com/meet/339251256565219?p=sDSSfadviwywbE9ZSE
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Contact: arthur.lipstein@durham.ac.uk
May 20 16:00 Richard van Dongen (University of Mons): Self-dual holography
In flat space, self-dual theories are powerful toy models for studying their parent theories. Here we develop an AdS/CFT framework for such self-dual theories and we discuss the holographic relation between chiral higher-spin gravity and Chern-Simons vector models. As an example, we discuss the relation between Yang-Mills and self-dual Yang-Mills in AdS. For mixed boundary conditions, explicit three- and four-point correlation functions in Yang-Mills are presented in several gauges, and we show how the self-dual limit emerges. The same correlators will be presented for the higher-spin extension of self-dual Yang-Mills.
Venue: zoom
Usual Venue: MCS2068
Contact: yohance.a.osborne@durham.ac.uk
May 19 13:00 Nicolò De Bernardi (Padova): On the Local Turnpike Property in Mean Field Control and Games
We study the local stability of solutions to ergodic and discounted Mean Field Games systems around stationary equilibria with quadratic Hamiltonians. We introduce a new stability assumption for the stationary equilibria, allowing for non-monotone couplings, and show that this weaker condition still yields a (local) exponential turnpike property for solutions close to the stationary one. We also provide an interpretation in terms of spectral properties of an operator, which might be encoded in the MFG system and help construct non-trivial examples. This talk is based on joint work with M. Cirant (Padova).
Venue: MCS2068
May 19 14:00 Hei Jie (Jack) Lam (Durham): Well-posedness and quantitative convergence for distributed equilibria of displacement monotone \(N\)-player games with interaction through controls
In this talk we will study the wellposedness of distributed equilibria of \(N\)-player games under displacement semi-monotonicity and convexity assumptions, in which the running cost of a player depends also on the controls used by other players. We consider running costs that are not necessarily separable, resulting in a set of consistency/fixed point relations on infinite dimensional spaces. We will also talk about quantitative convergence results (both for optimal trajectories/control and value functions) for the \(N\)-player games to the corresponding Mean Field Games of Controls (MFGC). Our approach works for both stochastic and deterministic cases but in this talk we will focus on the deterministic case (distributed equilibria coincides with open-loop equilibria in this case), where further quantitative convergence results can be proved for the gradients of value functions. This talk is based on joint work with Alpár Mészáros (Durham University).
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
No upcoming seminars have been scheduled (not unusual outside term time).
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: martin.p.kerin@durham.ac.uk
Jun 11 13:00 Zhang Rongkai (Osaka): Rigidity of the Borell-Brascamp-Lieb inequality
Optimal transport theory has been a powerful tool in
analysis on geometric spaces with curvature bounded since its
introduction into geometric analysis. In this talk, I will first briefly
introduce the application of the optimal transport theory on Riemannian
manifolds and show an interpolation inequality. I will then focus on the
recent work of mine, rigidity on curvature and measure of the
Borell-Brascamp-Lieb inequality on weighted Riemannian manifolds
satisfying the curvature dimension condition. I will also discuss the
Brunn-Minkowski inequality and its rigidity, as well as a few open
questions related.
Venue: MCS2068
Usual Venue: MCS2068
Contact: michael.r.magee@durham.ac.uk
May 18 14:00 Anna Roig-Sanchis (Nice): Minimal surfaces in large dimensional spheres
Since the work of Lagrange in the 18th century, minimal surfaces have been an important topic in differential geometry, geometric analysis, and mathematical physics. While there are many examples of minimal surfaces in Euclidean space, much less is known about minimal surfaces in spheres. In this colloquium, I will first give a very general introduction to minimal surfaces and show some classical examples. Then, I will present recent joint work with Michele Ancona, François Labourie and Jérémy Toulisse in which we prove the existence of negatively curved minimal surfaces in spheres of sufficiently large dimension, answering a question of Shing-Tung Yau.
Venue: MCS2068
Usual Venue: MCS3070
Contact: joe.thomas@durham.ac.uk
No upcoming seminars have been scheduled (not unusual outside term time).
