Biography
Alberto Bressan obtained in Ph.D. in 1982 from University of Colorado, Boulder. He was then a researcher at the University of Padova in Italy from 1982 to 1986. He was then hired as an Associate Professor at University of Colorado, Boulder, where he stayed from 1986 to 1991. He then moved to Italy where he became a Professor at S.I.S.S.A. in Trieste from 1991 until 2003. Since 2003, he is a Professor at Penn State University. Professor Bressan received numerous accolades including being a plenary speaker at the ICM in Beijing in 2002 and being a fellow of the American Mathematical Society in 2012. His research interests are diverse and include hyperbolic conservation laws, nonlinear wave equations, controlled growth and shape optimization in biology, traffic flow on networks, optimal control and differential inclusions.
posed on the 1-torus. Based on their numerics, Cho, Okamoto, & Shōji conjectured in their 2016 paper that: (C1) any singularity in the complex plane of time arising from inhomogeneous initial data is a branch singularity, and (C2) real initial data will exist globally in real time. If true, Conjecture 1 would suggest a strong incompatibility with the Painlevé property, a property closely associated with integrable systems. While Masuda proved (C1) in 1983 for close-to-constant initial data, a generalization to other initial data is not known. Using computer assisted proofs we establish a branch singularity in the complex plane of time for specific, large initial data which is not close-to-constant.
