Jump to content

Tomasz Mrowka: Difference between revisions

From Wikipedia, the free encyclopedia
Browse history interactively
← Previous editNext edit →
Content deleted Content added
VisualWikitext
KasparBot (talk | contribs)
1,549,811 edits
embed authority control with wikidata information
Reorganized, expanded research & career info.
Line 19: Line 19:
}}
}}


'''Tomasz Mrowka''' (born September 8, 1961) is an [[United States|American]] [[mathematician]]. He has been the Singer Professor of Mathematics at [[Massachusetts Institute of Technology]] since 2010, from 2007 to 2010 he was the Simons Professor of Mathematics. A graduate of MIT, he received the Ph.D. from [[University of California, Berkeley]] in 1988 under the direction of [[Clifford Taubes]] and [[Robion Kirby]]. He joined the MIT mathematics faculty as professor in 1996, following faculty appointments at [[Stanford]] and at [[Caltech]] (professor 1994–96).
'''Tomasz Mrowka''' (born September 8, 1961) is an [[United States|American]] [[mathematician]] specializing in [[differential geometry]] and [[gauge theory]]. He is the Singer Professor of Mathematics and head of the [[MIT Mathematics Department|Department of Mathematics]] at [[Massachusetts Institute of Technology]].

⚫
Mrowka's research is in [[differential geometry]] and [[gauge theory]]. A prior Sloan fellow and Young Presidential Investigator, he was selected for a Clay Mathematics Visiting Professorship in 1995. In 2007, he received the [[Oswald Veblen Prize in Geometry]] from the [[American Mathematical Society|AMS]] jointly with [[Peter Kronheimer]], "for their joint contributions to both three- and four-dimensional [[topology]] through the development of deep analytical techniques and applications." He is a Fellow of the [[American Academy of Arts & Sciences]].


Mrowka is married to MIT mathematics professor [[Gigliola Staffilani]].<ref>{{citation |url=http://www.boston.com/news/science/articles/2008/04/28/a_life_of_unexpected_twists_takes_her_from_farm_to_math_department/ |newspaper=[[Boston Globe]] |title=A life of unexpected twists takes her from farm to math department |date=April 28, 2008 |first=Billy |last=Baker}}. [http://www.ias.ac.in/womeninscience/Mathematician.pdf Archived by the Indian Academy of Sciences, Women in Science initiative].</ref>
Mrowka is married to MIT mathematics professor [[Gigliola Staffilani]].<ref>{{citation |url=http://www.boston.com/news/science/articles/2008/04/28/a_life_of_unexpected_twists_takes_her_from_farm_to_math_department/ |newspaper=[[Boston Globe]] |title=A life of unexpected twists takes her from farm to math department |date=April 28, 2008 |first=Billy |last=Baker}}. [http://www.ias.ac.in/womeninscience/Mathematician.pdf Archived by the Indian Academy of Sciences, Women in Science initiative].</ref>


== Career ==
==Oswald Veblen Prize in Geometry==
A 1983 graduate of MIT, he received the PhD from [[University of California, Berkeley]] in 1988 under the direction of [[Clifford Taubes]] and [[Robion Kirby]]. He joined the MIT mathematics faculty as professor in 1996, following faculty appointments at [[Stanford]] and at [[Caltech]] (professor 1994–96).<ref>{{Cite web|title = Tomasz Mrowka {{!}} MIT Mathematics|url = http://math.mit.edu/directory/profile.php?pid=192|website = math.mit.edu|accessdate = 2015-09-18}}</ref> At MIT, he was the Simons Professor of Mathematics from 2007-2010, and was named the Simons Professor of Mathematics in 2010. He was named head of the Department of Mathematics in 2014.<ref name=":0">{{Cite web|title = Tomasz Mrowka named head of the Department of Mathematics|url = http://news.mit.edu/2014/tomasz-mrowka-named-head-department-mathematics-1210|accessdate = 2015-09-18}}</ref>
The award citation mentions three papers that Mrowka and Kronheimer wrote together.


⚫
A prior Sloan fellow and Young Presidential Investigator, he was selected for a Clay Mathematics Visiting Professorship in 1995. In 2007, he received the [[Oswald Veblen Prize in Geometry]] from the [[American Mathematical Society|AMS]] jointly with [[Peter Kronheimer]], "for their joint contributions to both three- and four-dimensional [[topology]] through the development of deep analytical techniques and applications."<ref name=":1">{{Cite web|url = http://www.ams.org/notices/200704/comm-veblen-web.pdf|title = 2007 Veblen Prize|date = April 2007|accessdate = |website = American Mathematical Society|publisher = |last = |first = }}</ref> He was named a Guggenheim Fellow in 2010, and in 2011 received the [[Doob Prize]] with [[Peter B. Kronheimer]] for their book ''Monopoles and Three-Manifolds'' ([[Cambridge University Press]], 2007).<ref>[http://www.ams.org/news/ams-news-releases/ams-news-releases Kronheimer and Mrowka Receive 2011 Doob Prize]</ref> He is a Fellow of the [[American Academy of Arts & Sciences]].
The first paper in 1995 deals with [[Donaldson's polynomial invariants]] and introduced [[Kronheimer–Mrowka basic class]], which have been used to prove a variety of results about the topology and geometry of [[4-manifold]]s, and partly motivated Witten's introduction of the [[Seiberg–Witten invariants]].


== Research ==
The second paper proves the so-called [[Thom conjecture]] and was one of the first deep applications of the then brand new Seiberg–Witten equations to four-dimensional topology.
Mrowka’s work combines analysis, geometry, and [[topology]], specializing in the use of [[Partial differential equation|partial differential equations]], such as the [[Yang–Mills theory|Yang-Mills equations]] from particle physics to analyze low-dimensional mathematical objects.<ref name=":0" /> Jointly with [[Robert Gompf]], he discovered four-dimensional models of space-time topology.<ref>{{Cite journal|title = Irreducible 4-Manifolds Need not be Complex|url = http://www.jstor.org/stable/2946635|journal = Annals of Mathematics|date = 1993-07-01|pages = 61-111|volume = 138|series = Second Series|issue = 1|doi = 10.2307/2946635|first = Robert E.|last = Gompf|first2 = Tomasz S.|last2 = Mrowka}}</ref>


In the third paper in 2004, Mrowka and Kronheimer used their earlier development of [[Floer homology#Seiberg–Witten Floer homology|Seiberg–Witten monopole Floer homology]] to prove the [[Property P conjecture]] for [[knot theory|knots]]. The citation says: "The proof is a beautiful work of synthesis which draws upon advances made in the fields of gauge theory, [[symplectic geometry|symplectic]] and [[contact geometry]], and [[foliation]]s over the past 20 years,".
In joint work with Peter Kronheimer, Mrowka settled many long-standing conjectures, three of which earned them the 2007 Veblen Prize. The award citation mentions three papers that Mrowka and Kronheimer wrote together. The first paper in 1995 deals with [[Donaldson's polynomial invariants]] and introduced [[Kronheimer–Mrowka basic class]], which have been used to prove a variety of results about the topology and geometry of [[4-manifold]]s, and partly motivated Witten's introduction of the [[Seiberg–Witten invariants]].<ref>{{Cite journal|url = http://www.math.harvard.edu/~kronheim/structhm.pdf|title = Embedded surfaces and the structure of Donaldson's polynomial invariants|last = Kronheimer|first = Peter|date = 1995|journal = J. Differential Geom|doi = |pmid = |access-date = |last2 = Mrowka|first2 = Tomasz|issue = 3|volume = 41|pages = 573-34}}</ref> The second paper proves the so-called [[Thom conjecture]] and was one of the first deep applications of the then brand new Seiberg–Witten equations to four-dimensional topology.<ref>{{Cite journal|title = The Genus of Embedded Surfaces in the Projective Plane|url = http://dx.doi.org/10.4310/MRL.1994.v1.n6.a14|journal = Mathematical Research Letters|date = 1994-01-01|volume = 1|issue = 6|doi = 10.4310/mrl.1994.v1.n6.a14|first = P. B.|last = Kronheimer|first2 = T. S.|last2 = Mrowka}}</ref> In the third paper in 2004, Mrowka and Kronheimer used their earlier development of [[Floer homology#Seiberg–Witten Floer homology|Seiberg–Witten monopole Floer homology]] to prove the [[Property P conjecture]] for [[knot theory|knots]].<ref>{{Cite journal|title = Witten’s conjecture and Property P|url = http://www.msp.org/gt/2004/8-1/p07.xhtml|journal = Geometry & Topology|date = 2004-01-01|volume = 8|issue = 1|doi = 10.2140/gt.2004.8.295|first = Peter B|last = Kronheimer|first2 = Tomasz S|last2 = Mrowka}}</ref> The citation says: "The proof is a beautiful work of synthesis which draws upon advances made in the fields of gauge theory, [[symplectic geometry|symplectic]] and [[contact geometry]], and [[foliation]]s over the past 20 years."<ref name=":1" />


In further recent work with Kronheimer, Mrowka showed that a certain subtle combinatorially-defined knot invariant introduced by [[Mikhail Khovanov]] can detect “[[Unknotting problem|knottedness]].”<ref>{{Cite journal|title = Khovanov homology is an unknot-detector|url = http://link.springer.com/article/10.1007/s10240-010-0030-y|journal = Publications mathématiques de l'IHÉS|date = 2011-02-11|issn = 0073-8301|pages = 97-208|volume = 113|issue = 1|doi = 10.1007/s10240-010-0030-y|language = en|first = P. B.|last = Kronheimer|first2 = T. S.|last2 = Mrowka}}</ref>
==Doob Prize==
In 2011 Mrowka with [[Peter B. Kronheimer]] received 2011 [[Doob Prize]] for their book ''Monopoles and Three-Manifolds'' ([[Cambridge University Press]], 2007).<ref>[http://www.ams.org/news/ams-news-releases/ams-news-releases Kronheimer and Mrowka Receive 2011 Doob Prize]</ref>


==References==
==References==
* [http://www-math.mit.edu/people/profiles/mrowka-tomasz.html Tomasz Mrowka at MIT Mathematics]
* [http://web.mit.edu/newsoffice/2007/mrowka-0207.html MIT news]
* [http://www.ams.org/notices/200704/comm-veblen-web.pdf 2007 Veblen Prize]
{{Reflist}}
{{Reflist}}


Revision as of 18:43, 18 September 2015

Tomasz Mrowka
Mrowka in Aarhus, 2011.
BornSeptember 8, 1961 (1961-09-08) (age 63)
State College, Pennsylvania, U.S.
NationalityUnited States
Alma materUniversity of California
AwardsVeblen Prize (2007)
Doob Prize (2011)
Scientific career
FieldsMathematics
InstitutionsMIT
Doctoral advisorClifford Taubes
Robion Kirby
Doctoral studentsLarry Guth
Christopher Herald
Maksim Lipyansky
Lenhard Ng
Yongbin Ruan
Aleksey Zinger

Tomasz Mrowka (born September 8, 1961) is an American mathematician specializing in differential geometry and gauge theory. He is the Singer Professor of Mathematics and head of the Department of Mathematics at Massachusetts Institute of Technology.

Mrowka is married to MIT mathematics professor Gigliola Staffilani.[1]

Career

A 1983 graduate of MIT, he received the PhD from University of California, Berkeley in 1988 under the direction of Clifford Taubes and Robion Kirby. He joined the MIT mathematics faculty as professor in 1996, following faculty appointments at Stanford and at Caltech (professor 1994–96).[2] At MIT, he was the Simons Professor of Mathematics from 2007-2010, and was named the Simons Professor of Mathematics in 2010. He was named head of the Department of Mathematics in 2014.[3]

A prior Sloan fellow and Young Presidential Investigator, he was selected for a Clay Mathematics Visiting Professorship in 1995. In 2007, he received the Oswald Veblen Prize in Geometry from the AMS jointly with Peter Kronheimer, "for their joint contributions to both three- and four-dimensional topology through the development of deep analytical techniques and applications."[4] He was named a Guggenheim Fellow in 2010, and in 2011 received the Doob Prize with Peter B. Kronheimer for their book Monopoles and Three-Manifolds (Cambridge University Press, 2007).[5] He is a Fellow of the American Academy of Arts & Sciences.

Research

Mrowka’s work combines analysis, geometry, and topology, specializing in the use of partial differential equations, such as the Yang-Mills equations from particle physics to analyze low-dimensional mathematical objects.[3] Jointly with Robert Gompf, he discovered four-dimensional models of space-time topology.[6]

In joint work with Peter Kronheimer, Mrowka settled many long-standing conjectures, three of which earned them the 2007 Veblen Prize. The award citation mentions three papers that Mrowka and Kronheimer wrote together. The first paper in 1995 deals with Donaldson's polynomial invariants and introduced Kronheimer–Mrowka basic class, which have been used to prove a variety of results about the topology and geometry of 4-manifolds, and partly motivated Witten's introduction of the Seiberg–Witten invariants.[7] The second paper proves the so-called Thom conjecture and was one of the first deep applications of the then brand new Seiberg–Witten equations to four-dimensional topology.[8] In the third paper in 2004, Mrowka and Kronheimer used their earlier development of Seiberg–Witten monopole Floer homology to prove the Property P conjecture for knots.[9] The citation says: "The proof is a beautiful work of synthesis which draws upon advances made in the fields of gauge theory, symplectic and contact geometry, and foliations over the past 20 years."[4]

In further recent work with Kronheimer, Mrowka showed that a certain subtle combinatorially-defined knot invariant introduced by Mikhail Khovanov can detect “knottedness.”[10]

References

  1. ^ Baker, Billy (April 28, 2008), "A life of unexpected twists takes her from farm to math department", Boston Globe. Archived by the Indian Academy of Sciences, Women in Science initiative.
  2. ^ "Tomasz Mrowka | MIT Mathematics". math.mit.edu. Retrieved September 18, 2015.
  3. ^ a b "Tomasz Mrowka named head of the Department of Mathematics". Retrieved September 18, 2015.
  4. ^ a b "2007 Veblen Prize" (PDF). American Mathematical Society. April 2007.
  5. ^ Kronheimer and Mrowka Receive 2011 Doob Prize
  6. ^ Gompf, Robert E.; Mrowka, Tomasz S. (July 1, 1993). "Irreducible 4-Manifolds Need not be Complex". Annals of Mathematics. Second Series. 138 (1): 61–111. doi:10.2307/2946635.
  7. ^ Kronheimer, Peter; Mrowka, Tomasz (1995). "Embedded surfaces and the structure of Donaldson's polynomial invariants" (PDF). J. Differential Geom. 41 (3): 573–34.
  8. ^ Kronheimer, P. B.; Mrowka, T. S. (January 1, 1994). "The Genus of Embedded Surfaces in the Projective Plane". Mathematical Research Letters. 1 (6). doi:10.4310/mrl.1994.v1.n6.a14.
  9. ^ Kronheimer, Peter B; Mrowka, Tomasz S (January 1, 2004). "Witten's conjecture and Property P". Geometry & Topology. 8 (1). doi:10.2140/gt.2004.8.295.
  10. ^ Kronheimer, P. B.; Mrowka, T. S. (February 11, 2011). "Khovanov homology is an unknot-detector". Publications mathématiques de l'IHÉS. 113 (1): 97–208. doi:10.1007/s10240-010-0030-y. ISSN 0073-8301.

Template:Persondata

Retrieved from "https://en.wikipedia.org/w/index.php?title=Tomasz_Mrowka&oldid=681673391"