Calendar

Posted January 4, 2026
Last modified January 8, 2026

Control and Optimization Seminar Questions or comments?

Alberto Bressan, Penn State Eberly Family Chair Professor
Dynamic Blocking Problems for a Model of Fire Confinement

A classical problem in the Calculus of Variations asks to find a curve with a given length, which encloses a region of maximum area. In this talk I shall discuss the seemingly opposite problem of finding curves enclosing a region with minimum area. Problems of this kind arise naturally in the control of forest fires, where firemen seek to construct a barrier, minimizing the total area of the region burned by the fire. In this model, a key parameter is the speed at which the barrier is constructed. If the construction rate is too slow, the fire cannot be contained. After describing how the fire propagation can be modeled in terms of a PDE, the talk will focus on three main questions: (1) Can the fire be contained within a bounded region? (2) If so, is there an optimal strategy for constructing the barrier, minimizing the total value of the land destroyed by the fire? and (3) How can we find optimal strategies? Problem (1) is still largely open. See https://sites.psu.edu/bressan/2-research/ for a cash prize that has been offered for its solution since 2011.

Posted January 9, 2026
Last modified January 15, 2026

Informal Analysis Seminar Questions or comments?

TBD

tbd

Posted January 15, 2026

Informal Geometry and Topology Seminar Questions or comments?

Nilangshu Bhattacharyya, Louisiana State University
TBD

TBD

Posted December 1, 2025
Last modified January 9, 2026

Control and Optimization Seminar Questions or comments?

Jameson Graber, Baylor University NSF CAREER Awardee
Remarks on Potential Mean Field Games

Mean field games were introduced about 20 years ago to model the limit of N-player differential games as N goes to infinity. There are many applications to economics, finance, social sciences and biology. In many interesting cases the Nash equilibrium turns out to be a critical point for a functional, called the potential, in which case the game itself is called potential. In this case I will present several mathematical results on potential mean field games, which are directly connected to the theory of optimal control of PDE. For related work, see https://doi.org/10.1007/s40687-024-00494-3.