Research Interests:
 Hyperbolic conservation laws and nonlinear wave equations
 Control problems for moving sets, dynamic blocking problems
 Controlled growth and shape optimization in biology
 Modeling and optimization of traffic flow on networks
 Optimal control, noncooperative games, and applications to economics and finance
Brief surveys of recent results and open problems
Slides of recent talks
 Optimal control of propagation fronts and moving sets, (SJTU, 2021).
 A posteriori error estimates for approximate solutions to hyperbolic conservation laws, (Paris, 2021).
 On the optimal shape of tree roots and branches, (Toronto, 2018).
 Uniqueness questions for hyperbolic conservation laws, (Oxford, 2018).
 Global solutions of the BurgersHilbert equation, (Cambridge, 2018).
 Uniqueness and generic singularities for some classes of nonlinear wave equations (Oxford, 2018)

Optima and equilibria for a model of traffic flow (2013)
(animation: Model 1) (animation: Model 2) (animation: instability of Nash equilibrium, Model 2) 
Dynamic blocking problems
for a model of fire propagation (Waterloo, 2011)
(animation: onespiral strategy) (animation: onespiral strategy) (animation: nonisotropic case)  Controlling Lagrangian systems by active constraints (2010)
Survey papers

Flows on networks: recent results and perspectives.
EMS Surveys in Mathematical Sciences 1 (2014), 47111
(with
S.Canic, M.Garavello, M.Herty, and B.Piccoli)

Dynamic blocking problems for a model of fire propagation.
In Advances in Applied Mathematics, Modeling,
and Computational Science, pp.~1140.
R.Melnik and I.Kotsireas editors. Fields Institute Communications, Springer, New York, 2013.

Contractive metrics for nonsmooth evolutions.
In: Nonlinear Partial Differential Equations,
The Abel Symposium 2010,
pp.1336. H.Holden and K.Karlsen Eds.,
SpringerVerlag, 2012.
 Globally optimal and Nash equilibrium
solutions for traffic flow on networks. Proceedings
of the conference
on Hyperbolic Problems: Theory, Numerics and Applications,
in Padova 2012. AIMS, 2014.

Open questions in the theory of hyperbolic conservation laws.
In: Nonlinear Conservation Laws and Applications, pp.122.
IMA Volumes in Mathematics and its Applications, Vol.153.
A.Bressan, G.Q.Chen, M.Lewicka, and D.Wang editors,
SpringerVerlag, 2011.
 Patchy feedbacks for
stabilization and optimal control.
In Geometric Control and
Nonsmooth Analysis, pp.2864. F.Ancona, A.Bressan, P.Cannarsa,
F.H.Clarke and P.Wolenski
Eds., World Scientific 2008 (with F.Ancona).

Impulsive control of Lagrangian systems and locomotion in fluids,
Discr. Cont. Dynam. Syst. 20 (2008), 135.

Singularities of stabilizing feedbacks,
Rend. Sem. Mat. Univ. Pol. Torino 56 (1998), 87104.
 Differential inclusions without convexity. A survey of
directionally continuous selections,
in: Proceedings of the
World Congress of Nonlinear Analysts '92,
V.Lakshmikantham Ed.,
W.de Gruyter, Berlin (1996), 20812088.