Algebra and Number Theory in UCD

Algebra is one of the oldest and most vibrant branches of mathematics. Historically, the former Department of Mathematics at UCD was one of the catalysts for the expansion of mathematical research activity in Ireland. For example, weekly research seminars in Algebra began in the 1970's and have regularly attracted international speakers of the highest caliber over the last 30 years. Also, EU research training networks and several international conferences in Matrix Theory, Quadratic Forms, K-theory and Algebraic Groups were held at UCD.

Currently, the areas of research of the group include Algebraic K-theory, Matrix Theory, Quadratic Forms, Number Theory, and Information Theory and Coding. Between 2004 and 2007 alone, the group published some 40 refereed articles and attracted research funding in the order of €925,000. Recently, the K-theory, Quadratic Forms, and Number Theory Seminar was introduced. During 2004-2007, over 40 international visitors from Belgium, England, China, Germany, India, France, and the U.S. have given talks in this seminar. 

Members

Members of the Algebra and Number Theory group at UCD include:

Staff	Postdoctoral Fellows	PhD Students
Dr Vincent Astier Dr Russell Higgs Dr Kevin Hutchinson Prof Thomas J. Laffey (Emeritus) Prof David W. Lewis (Emeritus) Dr Robert Osburn Dr Helena Šmigoc Dr Thomas Unger	Dr James O'Shea	Anthony Cronin Ronan Flatley

Seminars

The K-Theory, Quadratic Forms and Number Theory Seminar usually takes place during term on Wednesday afternoons at 3pm. We maintain a schedule of upcoming and past seminars.

Funded Research Projects

• Hutchinson and Lewis, "Quadratic Forms, Algebraic K-theory and Central Simple Algebras", IRCSET Basic Research Grant, 2002-2005.
• Hutchinson, "Geometric Interpretations of the Witt Ring of a Field", SFI RFP, 2005-2008.
• Hutchinson, "Structure of K-groups of rings of integers", IRCSET Postdoctoral Fellowship Scheme, 2008-2010.


• Laffey, IRCSET Postdoctoral Fellowship Scheme, 2006-2008.
• Laffey, "Nonnegative matrices", SFI RFP 2005-2008.
• Laffey, IRCSET Postgraduate Research Scholarship, 2004-2008.


• Lewis, "Algebraic K-theory, Linear Algebraic Groups and Related Structures", European Union RTN, 2002-2006.


• Osburn, "Dyson's rank and overpartitions", UCD Seed Funding 2007-2008.
• Osburn, "Arithmetic properties of coefficients of modular forms", SFI RFP, 2008-2011.
• Osburn, "Ramanujan-type congruences for overpartitions and overpartition pairs", IRCSET/IRCHSS Ulysses programme, 2007-2008.
• Osburn, "Two-dimensional lattices with few distances", UCD Seed Funding, 2006-2007.
• Osburn, "Variations of Kummer's conjecture", IRCSET Postdoctoral Fellowship Scheme, 2007-2009.


• Unger, "Levels of quaternion and octonion algebras", IRCSET Postgraduate Research Scholarship, 2002-2006.
• Unger, "Weakly hyperbolic involutions and hermitian forms", UCD Seed Funding, 2006-2007.
• Unger, "The Hasse principle for weak isotropy of central simple algebras with an involution of the second kind", SFI RFP 2007-2010.
• Unger, "Isotropy of quadratic forms and algebras with involution", IRCSET Postdoctoral Fellowship Scheme - Inspire, 2009-2012.