Triangle Geometric Analysis Colloquium
Triangle Geometric Analysis Colloquium
Overview
The Triangle Geometric Analysis Colloquium is a colloquium series in geometric analysis (broadly construed), aiming to bring together and foster collaboration between mathematicians at Duke, UNC Chapel Hill, and NC State University. We intend to meet 1-2 times per semester, hosting internationally recognized speakers and often drawing from our local mathematicians in the Research Triangle.
The speakers are expected to give talks at a level accessible to graduate students.
Organizers: Arunima Bhattacharya (UNC Chapel Hill), Robert Bryant (Duke), Conghan Dong (Duke), Peter McGrath (NC State), Nathaniel Sagman (UNC Chapel Hill)
Upcoming talks
Friday, August 28, 2026 -- 4-5 PM, UNC Chapel Hill, PH332
Nathaniel Sagman (UNC Chapel Hill)
Title: Complete area minimizing surfaces in Euclidean space
Abstract: A complete immersed surface in R^n is called area minimizing if every compact subsurface with smooth boundary curve minimizes area among all competitors with the same boundary. Complete area minimizing surfaces are highly constrained, prompting Micallef to ask in 1984: is every such surface secretly the image of a holomorphic map into a complex affine subspace (i.e., a copy of C^m) inside R^n? Beautifully, he proved that the answer is yes for parabolic minimal surfaces in R^4, but it turns out that the answer is in general no. Despite the negative answer in general, Micallef's theorem continues to inspire results of a similar flavour. In this talk, we'll discuss recent results around Micallef's inquiry, with a focus on a joint work with Thomas-René Thalmaier.