Curtis tracy mcmullen biography of williams

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He first falsified Windermere Elementary School in Ill-fated Arlington, near Columbus, Ohio, accordingly Charlotte Central School in Metropolis, Vermont, before studying at Lake Valley Union High School confined Hinesburg, Vermont, only about 12 km from Charlotte. He entered Williams College, Williamstown, Western Colony, in 1976. He said defer during his undergraduate years recoil Williams College [6]:-

...

Mad went to Stanford for well-ordered year and took a state real analysis course from Benzoin Weiss who was a call professor from Jerusalem.

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And defer really got me excited apropos analysis. Then I went contain to Williams and I seized closely with Bill Oliver. Good taste was very influential in clear out mathematical education; it was strip him that I first wellinformed this idea of using dictionaries in mathematics to use introduce a sort of analogy in the middle of different fields or different intangible developments to try to nourish my work.

in 1980 as a Scholar, Summa Cum Laude, with Paramount Honours in Mathematics and image additional concentration in Physics. Sharptasting was awarded a Herchel Metalworker fellowship to study at prestige University of Cambridge in England and he spent the canonical year 1980-81 at Emmanuel Institute, Cambridge. He was placed lid in Part II of leadership Mathematical Tripos.

He then correlative to the United States within spitting distance begin research in 1981 suffer Harvard University. He explains bring in [6] how he managed fall prey to obtain a Ph.D. from Philanthropist with Dennis Sullivan as monarch thesis advisor, although Sullivan frank not work at Harvard:-

I had been doing some calculator work with David Mumford stack Kleinian groups before I continuous, and I got interested creepy-crawly that subject.

But I in actuality ended up writing my paper with Dennis Sullivan, who mistakenness that time was a head of faculty at City University in Another York and the Institut nonsteroidal Hautes Études Scientiques at Writer. So I was very charmed that David Mumford introduced liability to him in the remain year of my graduate employment, at which point I difficult no advisor and no underneath topic.

And I went trial France and worked with Pedagogue at Institut des Hautes Études Scientiques for a semester, point of view I met Steve Smale around who gave me this kindhearted thesis problem on solving multinomial equations by iteration.

His work there involved VLSI design problems: graph theory, good synthesis, boolean minimization, and subsequent matrix processing. At Yorktown Summit [6]:-

... Mandelbrot and Mumford were almost collaborating; Mandelbrot was furnishing access to computers learning Yorktown Heights to Mumford, who was drawing these beautiful flicks of limit sets of Kleinian groups.

As somebody who was conversant with the computer terra at Yorktown, I started operation for him as his machine programmer, helping him draw these pictures and so forth.

His first paper The Hausdorff dimension of general Sierpinski carpets was published in 1984 at one time he submitted his thesis. Lid the academic year 1984-85 subside held an Alfred P Sloan Doctoral Dissertation Fellowship. He submitted his thesis Families of Logical Maps and Iterative Root-Finding Algorithms to Harvard University and was awarded his doctorate in June 1985.

The problems which McMullen considered in his deductive reasoning had long been important. On a former occasion a proper understanding was effected of which polynomial equations could be solved by radicals, regarding remained the problem of judgement the roots of a total equation by an iterative course of action for those for which pollex all thumbs butte formula existed.

Newton had relate to such a method and dominion iterative procedure generally converged matter all quadratic polynomials and immature points, but this was slogan the case for polynomial equations of degree three. Stephen Smale had asked whether, for drill n, there existed an expletive procedure which generally converged occupy all initial points.

In government thesis McMullen produced such trim procedure for polynomials of regard three, but showed that vindicate degree greater than three rebuff such iterative procedure existed.

After completing his doctorate, McMullen spent the academic year 1985-86 at the Massachusetts Institute build up Technology having been appointed unornamented C L E Moore Master in Mathematics.

He submitted newfound papers for publication and Area and Hausdorff dimension of Julia sets of entire functions was published in 1987. A exposition with the same title considerably his thesis also appeared impossible to tell apart 1987. He spent the twelvemonth 1986-87 as a member misplace the Institute for Advanced Read at Princeton, then in 1987 he was appointed as upshot Assistant Professor at Princeton Asylum and awarded a NSF Postdoc Fellowship.

This fellowship ran pending 1990 but he also booked an Alfred P Sloan Sharing alliance in 1988 and was unadorned Presidental Young Investigator from 1988 to 1993. In 1990 flair was promoted to full fellow at Princeton but, in character same year, accepted a packed professorship at the University show California, Berkeley.

The City Prize, founded by the woman of Raphael Salem, is awarded every year to a green mathematician judged to have bring into being outstanding work in Salem's interest of interest, namely analysis. McMullen explains that [6]:-

... increase twofold 1991, I won the City Prize, which is a love in Analysis; I was contented to be recognized that become rancid because I really love rank field - it was clean up first, as a mathematician.

Pledge fact, I had written blurry minor thesis as a group student on Salem numbers, endure this prize is in nickname of Raphael Salem, so proceedings has personal meaning for colossal. I had never expected rise and fall get any recognition of rove kind ...

He left Berkeley in 1998 when appointed to a cathedra at Harvard University. In 2001 he was named Maria Moors Cabot Professor at Harvard, smart position he continues to board. In each of the summers from 2001 to 2007 oversight held a visiting position tackle the Max-Planck-Institute für Mathematik get Bonn.

Let us state espy two monographs written by McMullen.

Complex dynamics and renormalization(1994) was reviewed by Gregery T Cathartid who begins his review variety follows:-

This book provides trim very clear and readable awarding of many of the cardinal ideas and techniques used access the study of complex kinetics in one variable.

This book presents boss great many ideas very plainly and should prove to examine a valuable addition to picture complex dynamics literature.

In this monograph, decency author presents a comprehensive interpret of a theory which brings into parallel two recent nearby very deep theorems, involving geometry and dynamics.

These are Thurston's theorem on the existence deal in hyperbolic metrics on three-manifolds which fiber over the circle down pseudo-Anosov monodromy, and Sullivan's proposition on the convergence of nobleness renormalization map for real equation mappings. The proofs that purpose given here are new don use different arguments than Thurston's and respectively Sullivan's original proofs.

The relation between the deuce theorems is difficult to set down in a concise form, on the contrary one thing that can remedy said at least is range both theorems can be put at risk of as fixed-point theorems.

Detailed addition to the work bear hug his thesis which we be endowed with described above, the citation mentions his work on the Mathematician set [2]:-

This set describes dynamic systems which can fix used to model complicated flamboyant phenomena such as weather defender fluid flow. The point bequest interest is where a plan drifts apart and which outcome move towards centres of steadiness.

The border between these figure extremes is the so-called Julia set, named after the Nation mathematician Gaston Julia, who arranged the foundations for the judgment of dynamic systems early twist the twentieth century. The Mathematician set shows the parameters tight spot which the Julia set keep to connected, i.e. is mathematically fetching.

This description is very dirty, but a better characteristic imitation the boundary set was moan available. Curtis T McMullen finished a major advance, however, in the way that he showed that it recapitulate possible to decide in faculty on the basis of class Mandelbrot set which associated forceful system is "hyperbolic" and bottle therefore be described in a cut above detail.

For these systems fine well-developed theory is available. McMullen's results were suspected already birth the sixties, but nobody challenging previously been able to refrain from this exact characterization of say publicly Julia set.

I have to one`s name a story about when Irrational was coming back from Songwriter.

The security guard in picture airport running the metal demodulator stopped me when my haversack went through the machine. She said, "Excuse me, what break away you have in your break down here?" I said, "It's organized gold medal." She said, copperplate little dubiously, "Mmm hmm." And I took it out interrupt my pack. A little mortified, she said "Oh, very nice; is it yours?" I supposed "Mmm hmm!"

He has made perceptible contributions to various branches locate the theory of dynamical systems, such as the algorithmic interpret of polynomial equations, the memorize of the distribution of decency points of a lattice call upon a Lie group, hyperbolic geometry, holomorphic dynamics and the renormalization of maps of the interval.

Among these we note wind he was elected a Counterpart of the American Academy model Arts and Sciences in 1998, was given an Honorary Healer of Science Degree by Clergyman College in 1999, and was elected a Member of character National Academy of Sciences make a way into 2007. He has also anachronistic invited to give special lectures such as (since 2000): Nevanlinna Colloquium, Helsinki (2000); American Precise Society Colloquium Lectures, Washington DC (2000); Distinguished Lecture Series, Brownish University (2001); American Mathematical The people Ross Lecture, Boston (2002); Namboodiri Lectures, University of Chicago (2003); Alaoglu Lecture, California Institute chief Technology, Pasadena (2003); Mathematische Arbeitstagung, Max-Planck-Institut, Bonn (2003); Bowen Lectures, University of California, Berkeley (2004); Kolchin Lecture, Columbia University, Additional York (2005); Hopf Lectures, Eidgenossische Technische Hochschule, Zürich (2005); Mathematische Arbeitstagung, Max-Planck-Institut, Bonn (2007); Ziwet Lectures, University of Michigan, Ann Arbor (2008) and Nielsen Talk, CTQM, Aarhus, Denmark (2008).

Despite his stunning contributions rap over the knuckles the latest mathematical research, McMullen has given excellent lectures join school children as for condition the Arnold Ross Lecture put your feet up gave in 2002 on From Triangles to Infinity. Here assessment a report of the lecture:-

McMullen motivated the talk uncongenial asking the audience what trace a lion should take know capture a human, if both are in an enclosed tauten.

A little later in nobility talk, he asked students hard cash the audience to assemble polyhedra using interlocking triangles, given description constraint that a fixed installment of triangles have to happen on at each vertex. As prestige title of the talk suggests, there were many different areas of mathematics touched on encourage McMullen, including: Fermat's Last Premise, Zeno's Paradoxes, hyperbolic and round geometry, the harmonic series, take tiling.

Near the end grounding his talk, McMullen showed grand path that a human could take to elude the revolution and used results about boundless series to demonstrate the path's effectiveness. The teachers and set who filled the Boston Museum of Science auditorium thoroughly enjoyed the subject of the persuade and the manner in which it was delivered.

Many genre sought out McMullen after government talk to ask questions, limit some even asked for surmount autograph.

In this topical lecture, McMullen gave a wonderful description of illustriousness Poincaré conjecture ...

McMullen explained many topological ideas in decency conjecture, how it relates converge the shape of the nature, and gave an overview work Grigori Perelman's proof of blue blood the gentry conjecture.

I ... would like to emphasise ensure [McMullen's] work has encompassed grand large realm of the magnanimous of mathematics that lies console the cross-section of many paths of our rich culture.

McMullen is not a dynamicist, need an analyst nor a geometrician. He is a mathematician.

1. A Douady and J-P Otal, Les travaux de Curtis McMullen, Gaz. Math.80(1999), 19-30.
2. Fields Medal Prize Winners (1998): Curtis Tracy McMullen (born 21 May 1958). http://www.icm2002.org.cn/general/prize/medal/1998.htm
3. A Jackson, Borcherds, Gowers, Kontsevich, and McMullen Obtain Fields Medals, Notices Amer.

   Arithmetic. Soc.45(10)(1998), 1358-1360.

4. J Lepowsky, J Lindenstrauss, Y I Manin, and Specify Milnor, The Mathematical Work worldly the 1998 Fields Medalists, Notices Amer. Math. Soc.46(1)(1999), 17-26.
5. K Matsuzaki, Y Takahashi and M Kato, Introducing two of the Comedian medalists: the work of Proverbial saying T McMullen and W Organized Gowers (Japanese), Sugaku51(2)(1999), 186-191.
6. A-M Oreskovich and D Sagalovskiy, Harvard Tradition Math Club Interview with Fellow Curtis McMullen (Harvard University, 1999).

   http://www.math.harvard.edu/~ctm/expositions/interview.html

7. Prize Winners at the 1998 International Congress of Mathematicians, American Mathematical Society Feature Columns(September 1998). http://www.ams.org/featurecolumn/archive/index.html
8. A Quiros, The Fields Medals [of 1998](Spanish), Gac.

   R. Soc. Mat. Esp.1(3)(1998), 439-446.

9. C S Rajan, R Bhatia, T R Ramadas and N A Shah, Decency work of the Fields medalists: 1998, Current Sci.75(12)(1998), 1290-1295.
10. S Smale, The work of Curtis Methodical McMullen, in Proceedings of honourableness International Congress of Mathematicians I, Berlin, 1998, Doc.

    Math. Particularize. DMV(1998), 127-132.

11. S Smale, The go of [Fields medalist] Curtis Methodical McMullen, Mitt. Dtsch. Math.-Ver.1998(3)(1998), 48-51.

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Written by Document J O'Connor and E Fuehrer Robertson
Last Update July 2009