# Professor Roger Behrend

Professor

- behrendr@cardiff.ac.uk
- +44 (0)29 2087 5543
- M/2.45, Maths and Education Building , Senghennydd Road, Cardiff, CF24 4AG

## Overview

### News

- A research grant has been awarded by The Leverhulme Trust for a project directed by Roger Behrend entitled
*The combinatorics of alternating sign matrices and plane partitions*. - Roger Behrend, Ilse Fischer and Matjaž Konvalinka have been awarded the American Mathematical Society's 2019 David P. Robbins Prize. For more information, see the announcement, Notices of the American Mathematical Society, prize ceremony booklet or prize ceremony video and photos.

### Current research

- Combinatorics, including alternating sign matrices, graphs, lattice paths, plane partitions and polytopes.

### Current teaching

- MA1008 Linear Algebra I.
- MA3004 Combinatorics.

### Current supervision

- Hassan Izanloo, PhD.

### Professional memberships

- American Mathematical Society.
- Institute of Physics.
- London Mathematical Society.

## Biography

### Qualifications

- BSc, University of Melbourne, Australia.
- MSc, Imperial College London, UK.
- PhD, University of Melbourne, Australia.

### Previous positions

- Research Fellow, University of Bonn, Germany.
- Research Fellow, State University of New York, Stony Brook, USA.

## Publications

### 2020

- Ayyer, A., Behrend, R. E. and Fischer, I. 2020. Extreme diagonally and antidiagonally symmetric alternating sign matrices of odd order. Advances in Mathematics 367, article number: 107125. (10.1016/j.aim.2020.107125)

### 2019

- Ayyer, A. and Behrend, R. E. 2019. Factorization theorems for classical group characters, with applications to alternating sign matrices and plane partitions. Journal of Combinatorial Theory, Series A 165, pp. 78-105. (10.1016/j.jcta.2019.01.001)

### 2018

- Behrend, R. 2018. An update on matters discussed at Oberwolfach by Ian Macdonald in May 1977 and David Robbins in May 1982. Presented at: Oberwolfach Workshop 1820, Oberwolfach, 13 - 19 May 2018Enumerative Combinatorics, Vol. 15. Oberwolfach Reports Vol. 23. European Mathematical Society pp. 1416-1418., (10.4171/OWR/2018/23)

### 2017

- Behrend, R. E., Fischer, I. and Konvalinka, M. 2017. Diagonally and antidiagonally symmetric alternating sign matrices of odd order. Advances in Mathematics 315, pp. 324-365. (10.1016/j.aim.2017.05.014)

### 2016

- Behrend, R. E., Fischer, I. and Konvalinka, M. 2016. Diagonally and antidiagonally symmetric alternating sign matrices of odd order. Discrete Mathematics and Theoretical Computer Science BC, pp. 131-142.

### 2015

- Behrend, R. E., O, S. and West, D. B. 2015. Sharp lower bounds on the fractional matching number. Discrete Applied Mathematics 186, pp. 272-274. (10.1016/j.dam.2015.01.014)

### 2014

- Behrend, R. E. 2014. Alternating sign matrix enumeration involving numbers of inversions and -1's, and positions of boundary 1's. RIMS Kokyuroku 1913, pp. 1-21., article number: 1.

### 2013

- Behrend, R. E. 2013. Fractional perfect b-matching polytopes I: General theory. Linear Algebra and its Applications 439(12), pp. 3822-3858. (10.1016/j.laa.2013.10.001)
- Behrend, R. E. 2013. Multiply-refined enumeration of alternating sign matrices. Advances in Mathematics 245, pp. 439-499. (10.1016/j.aim.2013.05.026)
- Behrend, R. E., Di Francesco, P. and Zinn-Justin, P. 2013. A doubly-refined enumeration of alternating sign matrices and descending plane partitions. Journal of Combinatorial Theory, Series A 120(2), pp. 409-432. (10.1016/j.jcta.2012.09.004)

### 2012

- Behrend, R. E., Di Francesco, P. and Zinn-Justin, P. 2012. On the weighted enumeration of alternating sign matrices and descending plane partitions. Journal of Combinatorial Theory, Series A 119(2), pp. 331-363. (10.1016/j.jcta.2011.09.004)

### 2008

- Behrend, R. E. 2008. Osculating paths and oscillating tableaux. Electronic Journal of Combinatorics 15(1), article number: R7.

### 2007

- Behrend, R. E. and Knight, V. A. 2007. Higher spin alternating sign matrices. Electronic Journal of Combinatorics 14(1), article number: R83.

### 2004

- Behrend, R. E. and Evans, D. E. 2004. Integrable lattice models for conjugate An(1). Journal of Physics A Mathematical and General 37(8), pp. 2937-2947. (10.1088/0305-4470/37/8/006)

### 2001

- Behrend, R. E. and Pearce, P. A. 2001. Integrable and conformal boundary conditions for sl(2) A-D-E lattice models and unitary minimal conformal field theories. Journal of Statistical Physics 102(3/4), pp. 577-640. (10.1023/A:1004890600991)

### 2000

- Behrend, R. E.et al. 2000. Boundary conditions in rational conformal field theories. Nuclear Physics B 579(3), pp. 707-773. (10.1016/S0550-3213(00)00225-X)

### 1998

- Behrend, R. E., Pearce, P. A. and Zuber, J. B. 1998. Integrable boundaries, conformal boundary conditions and A-D-E fusion rules [Letter]. Journal of Physics A: Mathematical and General 31(50), pp. L763-L770. (10.1088/0305-4470/31/50/001)
- Behrend, R. E.et al. 1998. On the classification of bulk and boundary conformal field theories. Physics Letters B 444(1-2), pp. 163-166. (10.1016/S0370-2693(98)01374-4)

### 1997

- Behrend, R. E. and Pearce, P. A. 1997. Boundary weights for Temperley-Lieb and dilute Temperley-Lieb models. International Journal of Modern Physics B 11(23), pp. 2833-2847. (10.1142/S0217979297001386)

### 1996

- Behrend, R. E. and Pearce, P. A. 1996. A construction of solutions to reflection equations for interaction-round-a-face models. Journal of Physics A: Mathematical and General 29(24), pp. 7827-7835. (10.1088/0305-4470/29/24/009)
- Behrend, R. E. and Pearce, P. A. 1996. Reflection equations and exactly solvable lattice spin models. Czechoslovak Journal of Physics 46(12), pp. 1179-1187. (10.1007/BF01690331)
- Behrend, R. E., Pearce, P. A. and O'Brien, D. L. 1996. Interaction-round-a-face models with fixed boundary conditions: The ABF fusion hierarchy. Journal of Statistical Physics 84(1-2), pp. 1-48. (10.1007/BF02179576)

## Teaching

### Modules taught

- MA0017 Elementary Mathematical Methods I.
- MA0122 Algebra I.
- MA1008 Linear Algebra I.
- MA1700 Numerical Analysis I.
- MA0213 Groups.
- MA2700 Numerical Analysis II.
- MA0323 Statistical Mechanics.
- MA3003 Groups, Rings and Fields.
- MA3004 Combinatorics.
- MA4901 Reading Module.

### Teaching-related roles

- Chair of Year Two Examination Board.
- Member of Extenuating Circumstances Panel.
- Undergraduate Open Day Speaker.

### Teaching award

- Lecturer of the Year, 2016–2017.

### Research areas

- Combinatorics, including alternating sign matrices, graphs, lattice paths, plane partitions and polytopes.
- Mathematical physics, including conformal field theory and integrable statistical mechanical models.

### Selected conference talks

- Algorithmic and Enumerative Combinatorics Special Research Programme Colloquium, 15 June 2018, Johannes Kepler University Linz, Austria.
- Workshop on Enumerative Combinatorics, 13–19 May 2018, Mathematics Research Institute, Oberwolfach, Germany.
- Algorithmic and Enumerative Combinatorics Special Research Programme Colloquium, 16 March 2018, University of Vienna, Austria.
- Algebraic and Enumerative Combinatorics in Okayama, 19–23 February 2018, Okayama University, Japan.
- Programme on Algorithmic and Enumerative Combinatorics, 16 October – 24 November 2017, Erwin Schrödinger International Institute for Mathematics and Physics, Vienna, Austria.
- Programme on Statistical Mechanics, Integrability and Combinatorics, 11 May – 3 July 2015, Galileo Galilei Institute for Theoretical Physics, Florence, Italy.
- Programme on Combinatorics, Geometry and Physics, 2 June – 31 July 2014, Erwin Schrödinger International Institute for Mathematics and Physics, Vienna, Austria.
- Workshop on Algebraic Combinatorics Related to Young Diagrams and Statistical Physics, 6–10 August 2012, International Institute for Advanced Studies, Kyoto, Japan.
- 68th Séminaire Lotharingien de Combinatoire, 25–28 March 2012, Domaine Saint-Jacques, France.
- StatPhys24 Satellite Meeting on Combinatorics and Mathematical Physics, 12–14 July 2010, University of Queensland, Brisbane, Australia.
- Coimbra Meeting on 0-1 Matrix Theory and Related Topics, 17–19 June 2010, University of Coimbra, Portugal.
- Programme on Combinatorics and Statistical Physics, 1 February – 15 June 2008, Erwin Schrödinger International Institute for Mathematics and Physics, Vienna, Austria.
- Programme on Combinatorics and Statistical Mechanics, 14 January – 4 July 2008, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK.
- 6th International Conference on Lattice Path Combinatorics and Applications, 12–14 July 2007, East Tennessee State University, Johnson City, USA.
- 5th Permutation Patterns Conference, 11–15 June 2007, University of St Andrews, UK.
- Gregynog Mathematics Colloquium, 21–23 May 2007, Gregynog, UK.
- Workshop on Combinatorial Problems Raised by Statistical Mechanics, 19–23 February 2007, Centre de Recherches Mathématiques, Montréal, Canada.
- 6th Bologna Workshop on Conformal Field Theories and Integrable Models, 22–25 September 2004, University of Bologna, Italy.

### Selected departmental talks

- Chalmers University of Technology and University of Gothenburg, Sweden, Department of Mathematical Sciences, 11 June 2019.
- Cardiff University, UK, School of Mathematics, 20 March 2019.
- University of Queensland, Australia, School of Mathematics and Physics, 14 August 2018.
- City University of London, UK, Department of Mathematics, 21 March 2017.
- University of South Wales, UK, School of Computing and Mathematics, 26 October 2016.
- University of Melbourne, Australia, Department of Mathematics and Statistics, 11 August 2016.
- Queen Mary University of London, UK, School of Mathematical Sciences, 11 March 2016.
- University of Glasgow, UK, School of Mathematics and Statistics, 18 February 2016.
- Maxwell Institute for Mathematical Sciences, UK, 17 February 2016.
- Royal Holloway University of London, UK, Department of Mathematics, 2 December 2014.
- University of Glasgow, UK, School of Mathematics and Statistics, 13 November 2012.
- University of Kent, UK, School of Mathematics, Statistics and Actuarial Science, 12 June 2012.
- University of Melbourne, Australia, Department of Mathematics and Statistics, 16 & 17 May 2011.
- Pierre and Marie Curie University, France, Theoretical and High Energy Physics Laboratory, 24 March 2011.
- Swansea University, UK, Mathematics Department, 6 November 2007.
- University of Melbourne, Australia, Department of Mathematics and Statistics, 6 September 2007.
- Open University, UK, Mathematics Department, 8 December 2005.
- University of Edinburgh, UK, School of Mathematics, 8 December 2004.
- University of York, UK, Department of Mathematics, 26 June 2003.
- University of Oxford, UK, Mathematical Institute, 26 February 2002.

### Visiting research positions

- Faculty of Mathematics, University of Vienna, Austria, 1 September 2017 – 31 August 2018.
- Galileo Galilei Institute for Theoretical Physics, Florence, Italy, 14 May – 6 June 2015.
- Erwin Schrödinger International Institute for Mathematics and Physics, Vienna, Austria, 8–21 June 2014.
- Erwin Schrödinger International Institute for Mathematics and Physics, Vienna, Austria, 8 May – 13 June 2008.
- Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, 14 January – 25 April 2008.

### Research-related roles

- Reviewer for journals and funding agencies.
- PhD examiner.
- Treasurer of Mathematical and Theoretical Physics Group, Institute of Physics, 2012–2016.
- Isaac Newton Institute Correspondent, 2012–2017.

### Conference organisation

- 31st International Conference on Formal Power Series and Algebraic Combinatorics, University of Ljubljana, Slovenia, 1–5 July 2019.
- 29th International Conference on Formal Power Series and Algebraic Combinatorics, Queen Mary University of London, UK, 9–13 July 2017.
- Workshop on Combinatorial Physics, Cardiff University, UK, 17–19 December 2013.