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Kevin Hutchinson

Lecturer/Assistant Professor

School Of Mathematics & Statistics
Science Centre - North
Belfield
Dublin 4

Tel: +353 1 7162577
Email: kevin.hutchinson@ucd.ie

Biography

Member, Irish Mathematical Society
Member, European Mathematical Society
Member, American Mathematical Society
Reviewer, Mathematical Reviews
Dr Hutchinson is the Principal Investigator of a project entitled `K-theory, Quadratic Forms and Central Simple Algebras', funded by IRCSET (Research Project R8690), October 2002 to October 2005.
He was also a member of the UCD node of the EU RTN network on K-Theory and Linear Algebraic Groups. (2001-2005)

Professional

         

Conference Contributions

Kevin Hutchinson (2011) Conference in honour of Jean-Louis Cathelineau. [Invited Lecture], Seminaire Mediteraneen d'Algebre et Topologie, University of Nice , 14-JUN-12 - 16-JUN-12.
Kevin Hutchinson; (2011) Conference in Honour of Professor A O Kuku. [Invited Lecture], Algebraic K-theory and its Applications, Nanjing University, Nanjing China , 17-MAR-11 - 21-MAR-11.
Kevin Hutchinso n (2012) Conference in honour of Jurgen Hurrelbrink. [Invited Lecture], Algebraic K-theory and Arithmetic, Banach Centre, Bedlewo, Poland , 22-JUL-12 - 28-OCT-12.
Kevin Hutchinson; (2009) A research conference in number theory. [Invited Lecture], UCD/Nottingham Number Theory Meeting, University of Nottingham, UK , 02-MAY-09 - 02-MAY-09.

Committees

Committee : Irish Mathematical Society
Committee : National SubCommission on Mathematical Instruction
Committee : Graduate Taught Programmes Board, EMPS

Employment

Employer: University College Dublin
Position: Lecturer
Employer: Haverford College
Position: Visiting Assistant Professor
Employer: University of Pennyslyvania
Position: Assistant Professor

Education

Year 1981 Institution: University College Dublin
Qualification: BA Subject:
Year 1982 Institution: University College Dublin
Qualification: MA Subject:
Year 1984 Institution: Cornell University
Qualification: MSc Subject: --none--
Year 1987 Institution: Cornell University, NY, USA
Qualification: PhD Subject:
       

Other Activities

Invited Seminar : Relations between elementary matrices, and number theroy (to Queen's University Belfast) 02/12/2005

Invited Seminar Talk: DCU School of Mathematical Sciences Seminar, February 28th, 2008.

Title: "Quadratic Forms and Geometry"

Invited Seminar:  Hausdorff Centre for Mathematics, Bonn, Algebra Seminar, 25th November 2008

Talk Title: Homology of the Special Linear Group and Milnor-Witt K-theory

Publications

     

Peer Reviewed Journals

Kevin Hutchinson and Matthias Wendt (2015) 'On the third homology of SL_2 and weak homotopy invariance'. Transactions of the American Mathematical Society, 367 (10):7481-7513. Link to full text [Details]
Kevin Hutchinson (2016) 'The second homology of SL_2 of S-integers'. Journal of Number Theory, 159 :223-272. Link to full text [Details]
Kevin Hutchinson (2015) 'On the low-dimensional homology of SL_2(k[t,1/t])'. Journal of Algebra, 425 :324-366. [DOI] Link to full text [Details]
Kevin Hutchinson (2013) 'A refined Bloch group and the third homology of SL_2 of a field'. Journal of Pure and Applied Algebra, 217 (11):2003-2035. Link to full text [Details]
Kevin Hutchinson (2013) 'A Bloch-Wigner sequence for SL_2'. K-Theory, 12 :15-68. [DOI] Link to full text [Details]
Kevin Hutchinson, Liqun Tao (2013) 'Milnor-Witt K-theory and tensor powers of the augmentation ideal of Z[F^*]'. Algebra Colloquium, 20 (3):515-522. [Details]
Hutchinson, K. and Tao, L.; (2010) 'Homology stability for the special linear group of a field and Milnor-Witt K-theory'. Documenta Mathematica, special volume dedicated to A. A. Suslin :245-293. Link to full text [Details]
Hutchinson, K. and Tao, L.; (2009) 'The third homology of the special linear group of a field'. Journal of Pure and Applied Algebra, 213 (9):1665-1680. Available Online [Details]
Hutchinson, K.; (2008) ''A Note on Milnor-Witt K-theory and a Theorem of Suslin'. Communications in Algebra, 36 (7):2710-2718. Available Online Link to full text [Details]
Hutchinson, K.; (2006) 'Etale wild kernels of exceptional number fields'. JOURNAL OF NUMBER THEORY, 120 :47-71. [Details]
Hutchinson, K.; (2004) 'On Tame and Wild Kernels of Special Number Fields'. Journal of Number Theory, 107 :368-391. [Details]
Hutchinson, Kevin; Ryan, Dermot; (2004) 'Hilbert symbols as maps of functors'. Acta Arithmetica, 114 (4):349-368. [Details]
Hutchinson, K.; (2001) 'The 2-Sylow subgroup of the wild kernel of exceptional number fields'. Journal of Number Theory, 87 (2):222-238. [Details]
Hutchinson, K; (2001) 'The 2-Sylow subgroup of the wild kernel of exceptional number fields'. Journal of Number Theory, 87 :222-238. [Details]
Boland, PJ; Hutchinson, K; ; (2000) 'Student selection of random digits'. Journal of the Royal Statistical Society Series D-The Statistician, 49 (NA):519-529. [Details]
Boland, P.J. and Hutchinson, K.; (2000) 'Student Selection of Random Digits'. The Statistician, 49 (4):519-529. [Details]
Hutchinson, K.; (1999) 'Conditions under which K2 is not generated by Dennis-Stein symbols'. Acta Arithmetrica, LXXXXIX :189-199. [Details]
Hutchinson, K.; (1996) 'Hecke Actions on the K-Theory of Commutative Rings'. Journal of Pure and Applied Algebra, 111 :181-198. [Details]
Hutchinson, K.; (1995) 'On relative integral bases for unramified extensions'. Acta Arithmetrica, :279-286. [Details]
HUTCHINSON, K; (1995) 'NORM GROUPS OF GLOBAL FIELDS'. Journal of Number Theory, 50 :323-328. [Details]
HUTCHINSON, K; (1995) 'ON RELATIVE INTEGRAL BASES FOR UNRAMIFIED EXTENSIONS'. Acta Arithmetica, 70 :279-286. [Details]
Hutchinson, K.; (1995) 'Norm Groups of Global Fileds'. Journal of Number Theory, 50 (2):323-328. [Details]
Hutchinson, K.; (1990) 'A New Approach to Matsumoto's Theorem'. K-Theory, 4 :181-200. [Details]
 

Conference Publications

Kevin Hutchinson and Masha Vlasenko (2010) Lines crossing a tetrahedron and the Bloch group . In: Piotr Pragacz eds. IMPANGA Conference on Algebraic Geometry Banach Centre, Bedlewo, , 04-JUL-11 - 10-JUL-11 , pp.297-303 [Details]
                                                                                                                                       

Research

Research Interests

Dr Hutchinson's main research interests concern algebraic K-theory and its applications to number theory. Algebraic K-theory is a powerful machine for constructing useful algebraic invariants of mathematical objects, which often turn out to reveal unexpected connections between apparently unrelated parts of mathematics; in particular, between geometry and algebra. This machine can be applied to the objects of fundamental interest in algebraic number theory: the rings of algebraic integers in number fields. When this is done, many classical invariants are recovered as special cases; ideal class groups, groups of units, reciprocity laws. But new invariants and new connections with geometry and topology are also revealed by this approach. For example, the values at integers of zeta functions associated to the number field are closely related to these K-theoretic invariants.


Dr Hutchinson's early work studied the K_2 and K_3 of fields. In particular, he provided a new approach, via homological algebra, to proving and understanding Matsumoto's Theorem describing K_2 of fields. Since coming to UCD, however, his research has concentrated increasingly on the K-theory of number fields and the connections with Galois cohomology and Iwasawa theory. He has published several papers on the K_2 of rings of integers in number fields (`tame kernels'). He has studied and written on the the connections between the two-primary structure of these groups and the 2-cyclotomic tower of the number field. . Dr Hutchinson has been working recently on  a project exploring the connection between the K-theory of a field, the Witt ring of quadratic forms, and the geometry of projective space over the field. With his PhD student, L. Tao, this has led to results about the precise relationship of homology of special linear groups of fields to Milnor-Witt K-theory, answering a question of Jean Barge and Fabien Morel and resolving a conjecture of C-H. Sah about homology stability for this class of linear groups.

 Homological Algebra, K-theory, Algebraic Number Theory


I am the Principal Investigator supervising  the IRCSET  Postdoctoral project `Structure of K-theory of Rings of Integers' from November 1st 2008 to October 31st 2010 (R11131).

I was the Principal Investigator of a project entitled K-theory, Quadratic Forms
and Central Simple Algebras, funded by IRCSET (Research Project R8690), October
2002 to October 2005.
I was the Principal Investigator of a project entitled Geometric Interpretations of
the Witt Ring of a Field, funded by SFI RFP05 (Research Project R9609), October
2005 to September 2008.
I was a member of the ‘Dublin team' of the EU RTN network on K-Theory and
Linear Algebraic Groups, 2002-2006.

Research Projects

Sponsor : Irish Research Council for Science Engineering and Technology (IRCSET)
Title : Structure of K-groups of Rings of Integers
Start Date / End Date : 01-NOV-08 / 31-OCT-10
Sponsor : Science Foundation Ireland (SFI)
Title : Geometric Interpretations of the Witt Ring of a Field
Start Date / End Date : 01-SEP-05 / 31-JAN-09
Sponsor : Irish Research Council for Science Engineering and Technology (IRCSET)
Title : Quadratic Forms, Algebraic K-Theory and Central Simple Algebras
Start Date / End Date : 01-OCT-02 / 30-SEP-05