Karen Uhlenbeck - The Abel Prize interview 2019

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