Wednesday January 30, 2019 4:00 PM Math Tower 5127
 Silvia Ghinassi, Jack Burkart, Stony Brook University
Organizational meetingPlease join us to discuss the topic of this semester seminar. All are welcome.
[Spoiler: the topic will most likely be "regularity theory for minimal surfaces in higher codimension" (see this survey by De Lellis, https://bit.ly/2TnBNnE) so geometers are more than welcome...]

Wednesday February 06, 2019 4:00 PM Math Tower 5127
 Silvia Ghinassi, Stony Brook University
FedererFleming Theory of Integral CurrentsWe will introduce integral currents and other basics of geometric measure theory. No prior GMT knowledge will be assumed.

Wednesday February 13, 2019 4:00 PM Math Tower 5127
 Jack Burkart, Stony Brook University
FedererFleming Theory of Integral Currents  Part IICurrents are generalized surfaces. Last week we discussed the definition and the properties of currents a` la De Rham and we learned that, while their functional analytic properties make it very easy to obtain minimizers, those are not the minimizers you are looking for. So we introduced the concept of integer rectifiable currents and this week we will try to learn why this is the right class of objects to look at.

Wednesday February 20, 2019 4:00 PM Math Tower 5127
 Jacob Mazor, Stony Brook University
First considerations in regularity theoryWe finish our introduction to currents by looking at the case of codimension 1 currents: this is special as integral currents of codimension 1 were in fact introduced before the foundational paper by Federer and Fleming, by De Giorgi and Caccioppoli as sets of finite perimeter.
We then move on to discuss some first considerations in regularity theory: after an overview of the known regularity results for codimension 1 and for higher codimension, we will start developing some preliminaries, such as monotonicty formulas and its consequences.

