<story><title>Karen Uhlenbeck, Uniter of Geometry and Analysis, Wins Abel Prize</title><url>https://www.quantamagazine.org/karen-uhlenbeck-uniter-of-geometry-and-analysis-wins-abel-prize-20190319/</url></story><parent_chain></parent_chain><comment><author>kaitai</author><text>Uhlenbeck is delightful, and one of her big ideas discussed in this article -- bubbling -- truly has changed both her field and algebraic geometry. It&amp;#x27;s a cool idea. In a previous thread here (How I learned to love algebraic geometry, &lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;news.ycombinator.com&amp;#x2F;item?id=19397957&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;news.ycombinator.com&amp;#x2F;item?id=19397957&lt;/a&gt;) there was some discussion of singularities. Algebraic geometers like polynomials, while symplectic geometers like Riemann surfaces. These coincide at times but Riemann surfaces include lots of non-polynomial examples.&lt;p&gt;Anyhow, as an algebraic geometer, the place I learned about Uhlenbeck&amp;#x27;s work was in compactification of moduli of curves. Basically, say I want to look at all the polynomial curves that can live in a certain &amp;#x27;environment&amp;#x27;. (One &amp;#x27;application&amp;#x27; is string theory -- what particle interactions can occur given a certain set of energy constraints? The particle interactions are curves traced out over time by particles&amp;#x2F;Riemann surfaces traced out over time by the little loops that represent closed strings in string theory; the energy constraints constrain the shapes the particle interaction can take.) If you want to look at limits of families of these interactions, you&amp;#x27;re looking at some odd behavior. An example is the equation xy = t^2 -- this gives you nice hyperbolas for values of t not equal to zero, but as t -&amp;gt; 0, you get something singular, two crossed lines. Or x^2 - y^2 - z^2 = t^2: you have a nice smooth hyperboloid when t neq 0, and a double cone when t=0. However, these examples are just showing you the idea of how singularities appear in families of smooth polynomials. Uhlenbeck&amp;#x27;s older work really worked with the system of constraints that I mentioned -- figuring out what can appear under those constraints is a considerably more complicated problem!&lt;p&gt;This is a very imprecise discussion above and I&amp;#x27;m totally blurring together Uhlenbeck&amp;#x27;s bubbling and compactness theorems from gauge theory -- but I never followed her work in a systematic way but instead was plunged into seeing its aftereffects from another related field that the work affected.&lt;p&gt;Last quote really resonates: “Along the way I have made great friends and worked with a number of creative and interesting people. I have been saved from boredom, dourness, and self-absorption. One cannot ask for more.”</text></comment>
<story><title>Karen Uhlenbeck, Uniter of Geometry and Analysis, Wins Abel Prize</title><url>https://www.quantamagazine.org/karen-uhlenbeck-uniter-of-geometry-and-analysis-wins-abel-prize-20190319/</url></story><parent_chain></parent_chain><comment><author>otoburb</author><text>&lt;i&gt;&amp;quot;Mathematics research had another feature that appealed to her at the time: It is something you can work on in solitude, if you wish. In her early life, she said in 1997, “I regarded anything to do with people as being sort of a horrible profession.”&amp;quot;&lt;/i&gt;&lt;p&gt;This sentence struck me as slightly odd if only because Erdõs was renowned for his social approach to mathematics[1], and my layperson&amp;#x27;s understanding of mathematics departments being somewhat collaborative within their sub-fields.&lt;p&gt;I know there are some notable examples of other solo breakthrough endeavours, such as Shinichi Mochizuki[2] or Yitang Zhang[3], and but those examples seemed to be exceptions to the rule.&lt;p&gt;Perhaps I&amp;#x27;m channeling too much Terence Tao[4], or maybe the lone wolf researcher only applies to literal geniuses who work exclusively in academia.&lt;p&gt;Is mathematics research still a primarily solitary activity?&lt;p&gt;[1] &lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;en.wikipedia.org&amp;#x2F;wiki&amp;#x2F;Paul_Erd%C5%91s&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;en.wikipedia.org&amp;#x2F;wiki&amp;#x2F;Paul_Erd%C5%91s&lt;/a&gt;&lt;p&gt;[2] &lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;www.quantamagazine.org&amp;#x2F;titans-of-mathematics-clash-over-epic-proof-of-abc-conjecture-20180920&amp;#x2F;&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;www.quantamagazine.org&amp;#x2F;titans-of-mathematics-clash-o...&lt;/a&gt;&lt;p&gt;[3] &lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;www.cnet.com&amp;#x2F;news&amp;#x2F;yitang-zhang-a-prime-number-proof-and-a-world-of-persistence&amp;#x2F;&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;www.cnet.com&amp;#x2F;news&amp;#x2F;yitang-zhang-a-prime-number-proof-...&lt;/a&gt;&lt;p&gt;[4] &lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;terrytao.wordpress.com&amp;#x2F;career-advice&amp;#x2F;does-one-have-to-be-a-genius-to-do-maths&amp;#x2F;&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;terrytao.wordpress.com&amp;#x2F;career-advice&amp;#x2F;does-one-have-t...&lt;/a&gt;</text></comment>