Karen Uhlenbeck The Abel Prize interview 2019

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00:35 Uhlenbeck’s childhood in New Jersey and expectation from her parents • 2:02 Why mathematics? • 3:16 Enrollment in university as Physics major and her first experience with mathematics • 6:22 The honours programme at Michigan University and starting out in the mathematics field • 10:22 The PhD. at Courant Institute of New York and Brandeis University in Boston and choosing Richard Palais as her thesis advisor • 13:30 What is global analysis? The essentiality of making estimates • 16:40 Finding minimal surfaces of higher dimension • 19:22 Uhlenbeck’s paper on “Regularity for a class of non-linear elliptic systems”, extending the De Giorgi–Nash– Moser results. • 24:18 The 1980’s and Uhlenbeck’s many highly influential papers and the origins of the bubble theory with J. Sacks • 29:23 Why are the Yang–Mills equations important, and why is gauge invariance important? • 33:30 considering the development of global analysis can we say talk about “the unreasonable effect that physics has had on mathematics”, turning Wigner’s famous quote on the head • 36:20 The four manifold theory, its dramatic development and original connection to physics • 37:44 Being a good mathematician, perseverance, concentration, and moments of epiphany • 40:53 Uhlenbech and Yau’s work and the impact on the field of complex geometry as well as in physics. How did this work come about? • 44:57 “Problem as the lifeblood of mathematics” Hilbert said: Are there still big problems around for global analysis and gauge theory in particular? What direction will mathematics take, has it lived up to your predictions from 1988? • 49:09 Reflecting on being a female in the field of mathematics • 51:25 Prejudices against women and minorities in mathematics still exist, what is the situation like today for these underrepresented groups? • 56:57 The Park City Mathematical Institute initiative • 58:18 Uhlenbeck will use the prize money to invest back in the under-represented minorities through the Edge-foundation and the institute for advanced studies • Interview in written. Notices of the American Mathematical Society: • https://www.ams.org/journals/notices/... • Karen Uhlenbeck is interviewed by the two mathematicians Christian Skau and Bjørn Ian Dundas. • Produced by UniMedia, Yvonne Pettrém og Arve Nordland

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