menuicon

About the School

Abstracts

Mathew Langford
Assistant Professor (Tenure Track) @ the University of Tennessee Knoxville & ARC DECRA Fellow @ University of Newcastle, Australia.
Professor Langford obtained his PhD @ the Australian National University (ANU) in Canberra, Australia, in 2015 under the supervision of Ben Andrews and James McCoy. He was an Alexander von Humboldt Fellow @ the Freie Universität Berlin from 2015-2017. Since August 2017, Langford is Associate Professor (tenure track) @ the University of Tennessee Knoxville. Since 2020, Langford is on leave from UTK to carry out an ARC DECRA Fellowship @ the University of Newcastle. Recently appeared Professor Langford's new book on ''Extrinsic Geometric Flows'' (coauthored with Ben Andrews, Bennett Chow and Christine Guenther)!
The atomic structure of ancient grain boundaries

I will present a series of far-reaching new existence and structure results for convex ancient solutions to mean curvature flow. An interesting picture (conjectured by Huisken and Sinestrari) emerges: convex ancient and translating solutions in slab regions decompose into certain canonical configurations of Grim Reapers, subject to certain necessary constraints. In particular, we construct new families of solutions with discrete symmetries as well as families of solutions which possess only a single reflection symmetry. These include many eternal solutions which do not evolve by translation (resolving a conjecture of White in the negative). Prior to these results, the only known examples were the rotationally symmetric ancient pancake and the rotationally symmetric flying wing translators. Several interesting questions remain open, however.

This is joint work with Theodora Bourni and Giuseppe Tinaglia.

Back to Program


Francesco Maggi
Professor @ University of Texas at Austin, United States.
Professor Maggi obtained his PhD in 2004 @ University of Firenze, Italy, under the supervision of Paolo Marcellini. He was posdoctoral associate @ the Max Planck Institute Leipzig, Germany, in 2004, associate professor @ the University of Duisburg-Essen, Germany, in 2005, @ University of Firenze from 2005-2011, @ University of Texas at Austin from 2012-2015, and became full professor @ University of Texas at Austin in 2016. In addition, Professor Maggi was research scientist at ICTP Trieste in Italy from 2016-2017 and was a member of the Institute of Advanced Study, Princton, in 2019.
Symmetry results for Plateau's surfaces

By employing the method of moving planes in a novel way, we extend some classical symmetry and rigidity results for smooth minimal surfaces to surfaces that have singularities of the sort typically observed in soap films.

This talk is based on joint work with Jacob Bernstein at Johns Hopkins University, appeared in preprint form on arXiv 2003.01784.

Back to Program