UCL Colloquium Schedule
Thursday, 16 October 2025, 4-5pm Location: 500, 25 Gordon St
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Speaker: Patrick Farrell (Oxford)
Title: The latent variable proximal point algorithm for variational problems with inequality constraints
Abstract:
The latent variable proximal point (LVPP) algorithm is a new framework for solving infinite-dimensional variational problems with inequality constraints. Such problems arise in many applications of mathematics, including in contact and friction, economics, finance, and glaciology, The algorithm is a saddle point reformulation of the Bregman proximal point algorithm. At the continuous level, the two formulations are equivalent, but the saddle point formulation is more amenable to discretisation.
LVPP yields numerical methods with observed mesh-independence for obstacle problems, contact, fracture, plasticity, and others besides. In many cases this mesh independence is achieved for the first time. The framework also extends to more complex constraints, providing means to enforce convexity in the Monge-Ampère equation and gracefully handling quasi-variational inequalities, where the underlying constraint depends implicitly on the unknown solution.
In this talk we describe the LVPP algorithm in a general form and apply it to a number of problems from across mathematics.
Thursday, 30 October 2025, 4-5pm Location: 500, 25 Gordon St
Internal Colloquium
Speaker: Mahir Hadzic (UCL)
Title: On rigorous description of stellar implosion
Abstract:
I will review recent progress on rigorous description of formation of imploding singularities for self-gravitating fluids, i.e. stars. I will highlight the crucial role of self-similarity and its interaction with nonlinear structures within equations of fluid dynamics, which can conspire to give rise to star implosion examples. Time permitting, I will present our recent result with Y. Guo, J. Jang, and M. Schrecker on nonlinear stability of such solutions, which ties together ideas from spectral theory, dynamical systems, and nonlinear PDE.
Thursday, 13 November 2025, 4-5pm Location: 500, 25 Gordon St
Speaker: Vladimir Dokchitser (UCL)
Title: Elliptic curves
Abstract:
The arithmetic of elliptic curves has played a central role in number theory over the past 100 years, and has given rise to many beautiful mathematical results. I will discuss elliptic curves from the classical standpoint of trying to solve Diophantine equations. The aim will be both to explain how we think about these creatures and to give an overview of what we can and, more typically, can't prove about them.
Thursday, November 27, 4-5pm Location:500, 25 Gordon St
Speaker: TBA
Title:
Abstract:
Thursday, December 11, 4-5pm Location:500, 25 Gordon St
Speaker: Iain Smears (UCL)
Title: Analysis and numerical analysis of mean field games
Abstract:
Every day, we make decisions in hope of beneficial outcomes, under significant uncertainty about the future and complex interactions with many others. In mathematical terms, this is a game theoretic problem for a large population of interacting agents, or players, that make decisions in continuous time. Mean field games are models of such problems that focus on the setting of many indistinguishable players, each with small impact on the game, and where the interactions are of mean field type, i.e. depending only on the overall distribution of players. These models find numerous applications in research and industry, from economics to ecology, as well as engineering, urban growth, pedestrian dynamics, and multi-agent reinforcement learning algorithms used by companies such as Google DeepMind.
Mathematically, the Nash equilibria of the game are characterised by the solutions of a coupled system of nonlinear partial differential equations. The first equation is a Hamilton—Jacobi—Bellman equation that evolves backwards in time, whose solution determines players' optimal choices of controls. The second equation is a forward-in-time Kolmogorov—Fokker—Planck equation for the evolution of the player density across the state space of the game. The nonlinear coupling and forward-backward structure are among the features that make these systems particularly mathematically interesting.
In this talk, I will discuss the analysis of the existence, uniqueness, and numerical approximation of solutions of these systems.
In particular, I will focus on analytical challenges that arise when the players face multiple equally optimal decisions. In this setting, the problem can no longer be described by standard partial differential equations, but rather by a system of partial differential inclusions of set-valued operators.
You'll find the old colloquium schedules
here.
