Professor Joseph Grotowski completed his Bachelor of Science with Honours in Mathematics at the Australian National University in 1985. He then moved to New York for postgraduate studies in Mathematics, and completed an MS in 1987 and a PhD in 1990 at the Courant Institute, NYU.
He held a number of positions in Germany, and completed his Habilitation at the Friedrich-Alexander Universitaet Erlangen-Nuernberg in 2001. He took up a position as an Associate Professor at the City College of New York of the City University of New York in 2003, and returned to Australia to take up a position as a Senior Lecturer at UQ in 2005. He was promoted to Associate Professor from 2010, and Full Professor from 2013.
He served as Head of the Mathematics Discipline from 1 January 2010 until 30 April 2014. From 1 May 2014 he has been Head of the School of Mathematics and Physics.
He is currently on the Board of the Australian Mathematical Sciences Institute, and serves on the advisory Board of the MATRIX Research Insitute. He has been active in CSIRO Mathematicians in Schools for a number of years.
Journal Article: Weak martingale solutions to the stochastic Landau–Lifshitz–Gilbert equation with multi-dimensional noise via a convergent finite-element scheme
Goldys, Beniamin, Grotowski, Joseph F. and Le, Kim-Ngan (2019). Weak martingale solutions to the stochastic Landau–Lifshitz–Gilbert equation with multi-dimensional noise via a convergent finite-element scheme. Stochastic Processes and their Applications, 130 (1), 232-261. doi: 10.1016/j.spa.2019.02.011
Journal Article: High specific strength and stiffness structures produced using selective laser melting
Challis, Vivien J., Xu, Xiaoxue, Zhang, Lai Chang, Roberts, Anthony P., Grotowski, Joseph F. and Sercombe, Timothy B. (2014). High specific strength and stiffness structures produced using selective laser melting. Materials & Design, 63, 783-788. doi: 10.1016/j.matdes.2014.05.064
Journal Article: High resolution topology optimization using graphics processing units (GPUs)
Challis, Vivien J., Roberts, Anthony P. and Grotowski, Joseph F. (2014). High resolution topology optimization using graphics processing units (GPUs). Structural and Multidisciplinary Optimization, 49 (2), 315-325. doi: 10.1007/s00158-013-0980-z
(2017–2019) University of Western Australia
Inspiring mathematics and science in teacher education
(2014–2017) OLT Enhancing the Training of Mathematics and Science Teachers Program (ETMST)
(2012–2014) University of Sydney
Critical O(d)-Equivariant Biharmonic Maps
(2016) Doctor Philosophy
Regularity Results for Nonlinear Elliptic Systems
(2016) Doctor Philosophy
A degree-theoretic approach to geometric equations on manifolds with symmetries
(2019) Doctor Philosophy
The Keller Segel system and extensions
This project relates to analytic aspects of a mathematical model for Chemotaxis.
Topology Optimisation
We are currently working in an exciting new area of mathematics called Topology optimisation. Our aim is to develop the tools to optimize the shape and topology of porous and composite materials to perform specific tasks. In particular we have a current ARC Discovery grant that will provide funding for APA top-ups and research costs for projects relating to optimal design of bone implants. Specific projects involve research in a range of fields from applied mathematics, as well as computational science. There is also scope for projects with an emphasis on pure mathematics (geometric evolution equations).
Projects to be supervised by me and/or Dr. Tony Roberts
Optimal regularity results via A-harmonic approximation
Duzaar, F., Grotowski, J. and Steffen, K. (2003). Optimal regularity results via A-harmonic approximation. Geometric analysis and nonlinear partial differential equations. (pp. 265-296) edited by S. Hildebrandt and H. Karcher. Berlin: Springer Verlag.
Goldys, Beniamin, Grotowski, Joseph F. and Le, Kim-Ngan (2019). Weak martingale solutions to the stochastic Landau–Lifshitz–Gilbert equation with multi-dimensional noise via a convergent finite-element scheme. Stochastic Processes and their Applications, 130 (1), 232-261. doi: 10.1016/j.spa.2019.02.011
High specific strength and stiffness structures produced using selective laser melting
Challis, Vivien J., Xu, Xiaoxue, Zhang, Lai Chang, Roberts, Anthony P., Grotowski, Joseph F. and Sercombe, Timothy B. (2014). High specific strength and stiffness structures produced using selective laser melting. Materials & Design, 63, 783-788. doi: 10.1016/j.matdes.2014.05.064
High resolution topology optimization using graphics processing units (GPUs)
Challis, Vivien J., Roberts, Anthony P. and Grotowski, Joseph F. (2014). High resolution topology optimization using graphics processing units (GPUs). Structural and Multidisciplinary Optimization, 49 (2), 315-325. doi: 10.1007/s00158-013-0980-z
Challis, Vivien J., Guest, James K., Grotowski, Joseph F. and Roberts, Anthony P. (2012). Computationally generated cross-property bounds for stiffness and fluid permeability using topology optimization. International Journal of Solids And Structures, 49 (23-24), 3397-3408. doi: 10.1016/j.ijsolstr.2012.07.019
Roberts, A. P., Grayson, G., Challis, V. J., Zhang, L. C., Grotowski, J. F., Schaffer, G. B. and Sercombe, T. B. (2011). Elastic moduli of sintered powders with application to components fabricated using selective laser melting. Acta Materialia, 59 (13), 5257-5265. doi: 10.1016/j.actamat.2011.05.002
On radial solutions of the Schrodinger type equation
Chabrowski, Jan H. and Grotowski, Joseph F. (2011). On radial solutions of the Schrodinger type equation. Advanced Nonlinear Studies, 11 (2), 295-310. doi: 10.1515/ans-2011-0204
Challis, VJ, Roberts, AP, Grotowski, JF, Zhang, LC and Sercombe, TB (2010). Prototypes for bone implant scaffolds designed via topology optimization and manufactured by solid freeform fabrication. Advanced Engineering Materials, 12 (11), 1106-1110. doi: 10.1002/adem.201000154
Kernel density estimation via diffusion
Botev, Z. I., Grotowski, J. F. and Kroese, D. P. (2010). Kernel density estimation via diffusion. Annals of Statistics, 38 (5), 2916-2957. doi: 10.1214/10-AOS799
The influence of non-coaxiality on shear banding in viscous-plastic materials
Muhlhaus, Hans, Moresi, Louis, Gross, Lutz and Grotowski, Joseph (2010). The influence of non-coaxiality on shear banding in viscous-plastic materials. Granular Matter, 12 (3), 229-238. doi: 10.1007/s10035-010-0176-9
Geometric evolution equations in critical dimensions
Grotowski, J. F. and Shatah, J. (2007). Geometric evolution equations in critical dimensions. Calculus of Variations and Partial Differential Equations, 30 (4), 499-512. doi: 10.1007/s00526-007-0100-2
Heat kernels in geometric evolution equations
Grotowski, Joseph F. (2006). Heat kernels in geometric evolution equations. Contemporary Mathematics, 398, 193-201.
Regularity of almost minimizers of quasi-convex variational integrals with subquadratic growth
Duzaar, Frank, Grotowski, Joseph F. and Kronz, Manfred (2005). Regularity of almost minimizers of quasi-convex variational integrals with subquadratic growth. Annali Di Matematica Pura Ed Applicata, 184 (4), 421-448. doi: 10.1007/s10231-004-0117-5
Removable singularities for p-harmonic maps: The subquadratic case
Gastel, Andreas, Grotowski, Joseph F. and Kronz, Manfred (2005). Removable singularities for p-harmonic maps: The subquadratic case. Advances in Geometry, 5 (3), 469-483. doi: 10.1515/advg.2005.5.3.469
Minimizing conformal energies in homotopy classes
Grotowski, Joseph F. and Kronz, Manfred (2004). Minimizing conformal energies in homotopy classes. Forum Mathematicum, 16 (6), 841-864. doi: 10.1515/form.2004.16.6.841
Book Review : Harmonic maps, conservation laws and moving frames / F. Helein
Grotowski, Joseph (2004). Book Review : Harmonic maps, conservation laws and moving frames / F. Helein. Jahresbericht der Deutschen Mathematiker-Vereinigung (196), 3-5.
Partial and full boundary regularity for minimizers of functionals with nonquadratic growth
Duzaar, Frank, Grotowski, Joseph F. and Kronz, Manfred (2004). Partial and full boundary regularity for minimizers of functionals with nonquadratic growth. Journal of Convex Analysis, 11 (2), 437-476.
Boundary Regularity for quasilinear elliptic systems
Grotowski, Joseph F. (2002). Boundary Regularity for quasilinear elliptic systems. Communications In Partial Differential Equations, 27 (11-12), 2491-2512. doi: 10.1081/PDE-120016165
Boundary regularity for nonlinear elliptic systems
Grotowski, J. F. (2002). Boundary regularity for nonlinear elliptic systems. Calculus of Variations And Partial Differential Equations, 15 (3), 353-388. doi: 10.1007/s005260100131
Grotowski, J. F., Huntley, J. and Jorgenson, J. (2001). Asymptotic behavior of, small eigenvalues, short geodesics and period matrices on degenerating hyperbolic Riemann surfaces. Forum Mathematicum, 13 (6), 729-740. doi: 10.1515/form.2001.031
Finite time blow-up for the Yang-Mills heat flow in higher dimensions
Grotowski, J. F. (2001). Finite time blow-up for the Yang-Mills heat flow in higher dimensions. Mathematische Zeitschrift, 237 (2), 321-333. doi: 10.1007/PL00004871
On the Gribov copy problem for the Coulomb gauge
Grotowski, J. F. and Schirmer, P. P. (2001). On the Gribov copy problem for the Coulomb gauge. Communications In Mathematical Physics, 216 (1), 179-193. doi: 10.1007/s002200000337
Optimal partial regularity for nonlinear elliptic systems of higher order
Duzaar, F., Gastel, A. and Grotowski, J. F. (2001). Optimal partial regularity for nonlinear elliptic systems of higher order. Journal of Mathematical Sciences, 8, 463-499.
Duzaar, F and Grotowski, JF (2000). Optimal interior partial regularity for nonlinear elliptic systems: the method of A-harmonic approximation. Manuscripta Mathematica, 103 (3), 267-298. doi: 10.1007/s002290070007
Partial regularity for almost minimizers of quasi-convex integrals
Duzaar, F., Gastel, A. and Grotowski, J. F. (2000). Partial regularity for almost minimizers of quasi-convex integrals. Siam Journal On Mathematical Analysis, 32 (3), 665-687. doi: 10.1137/S0036141099374536
Existence and regularity for higher-dimensional H-systems
Duzaar, F and Grotowski, JF (2000). Existence and regularity for higher-dimensional H-systems. Duke Mathematical Journal, 101 (3), 459-485. doi: 10.1215/S0012-7094-00-10133-0
On variational models for quasi-static Bingham fluids
Fuchs, M, Grotowski, JF and Reuling, J (1996). On variational models for quasi-static Bingham fluids. Mathematical Methods in the Applied Sciences, 19 (12), 991-1015. doi: 10.1002/(SICI)1099-1476(199608)19:12<991::AID-MMA810>3.0.CO;2-R
Partial and full regularity for restricted classes of p-harmonic maps
Grotowski, JF (1996). Partial and full regularity for restricted classes of p-harmonic maps. Nonlinear Analysis-Theory Methods & Applications, 26 (3), 429-442. doi: 10.1016/0362-546X(94)00288-S
A mixed boundary value problem for energy minimizing harmonic maps
Duzaar, F and Grotowski, JF (1996). A mixed boundary value problem for energy minimizing harmonic maps. Mathematische Zeitschrift, 221 (1), 153-167. doi: 10.1007/PL00004503
On Various Classes of Harmonic Maps
Grotowski, JF, Shen, Y and Yan, S (1995). On Various Classes of Harmonic Maps. Archiv der Mathematik, 64 (4), 353-358. doi: 10.1007/BF01198092
Energy Minimizing Harmonic Maps with An Obstacle At the Free-Boundary
Duzaar, F and Grotowski, JF (1994). Energy Minimizing Harmonic Maps with An Obstacle At the Free-Boundary. Manuscripta Mathematica, 83 (3-4), 291-314. doi: 10.1007/BF02567615
Finite-Time Blow-Up for the Harmonic Map Heat-Flow
Grotowski, JF (1993). Finite-Time Blow-Up for the Harmonic Map Heat-Flow. Calculus of Variations and Partial Differential Equations, 1 (2), 231-236. doi: 10.1007/BF01191618
Concentrated Boundary Data and Axially-Symmetrical Harmonic Maps
Grotowski, JF (1993). Concentrated Boundary Data and Axially-Symmetrical Harmonic Maps. Journal of Geometric Analysis, 3 (3), 279-292. doi: 10.1007/BF02921394
Harmonic Map Heat-Flow for Axially Symmetrical Data
Grotowski, JF (1991). Harmonic Map Heat-Flow for Axially Symmetrical Data. Manuscripta Mathematica, 73 (2), 207-228. doi: 10.1007/BF02567639
The influence of non-coaxiality on shear banding in viscous-plastic materials
Muhlhaus, Hans B., Moresi, L., Gross, Lutz and Grotowski, Joseph (2010). The influence of non-coaxiality on shear banding in viscous-plastic materials. Scientific Conference on From Shear Bands to Rapid Flow, Monte Verita, Switzerland, 22-27 Februray, 2009. Berlin, Germany: Springer. doi: 10.1007/s10035-010-0176-9
Grotowski, JF (1991). Heat-Flow for Harmonic Maps. Nato Advanced Research Workshop On Defects, Singularities and Patterns in Nematic Liquid Crystals : Mathematical and Physical Aspects, Orsay France, May 28-Jun 01, 1990. DORDRECHT: KLUWER ACADEMIC PUBL.
(2017–2019) University of Western Australia
Inspiring mathematics and science in teacher education
(2014–2017) OLT Enhancing the Training of Mathematics and Science Teachers Program (ETMST)
(2012–2014) University of Sydney
(2011–2019) University of Western Australia
(2011–2012) UWA-UQ Bilateral Research Collaboration Award
(2011–2012) ARC LIEF Collaborating/Partner Organisation Contributions
New-generation parallel-computing cluster for the mathematical and physical sciences
(2011) UQ Major Equipment and Infrastructure
The Influence of particle shape fragmentation and compaction on 3D hopper flow
(2009–2011) ARC Discovery Projects
(2008–2010) University of Western Australia
A new enabling technology for learning and teaching quantitative skills
(2006–2008) Carrick Competitive Grants
Existence of solutions for the Ericksen-Leslie system.
Doctor Philosophy — Associate Advisor
Other advisors:
Critical O(d)-Equivariant Biharmonic Maps
(2016) Doctor Philosophy — Principal Advisor
Other advisors:
Regularity Results for Nonlinear Elliptic Systems
(2016) Doctor Philosophy — Principal Advisor
Other advisors:
A degree-theoretic approach to geometric equations on manifolds with symmetries
(2019) Doctor Philosophy — Associate Advisor
Other advisors:
Synchronisation of Nanomechanical Oscillators
(2017) Doctor Philosophy — Associate Advisor
Other advisors:
The Bianchi Identity and the Ricci Curvature Equation
(2016) Doctor Philosophy — Associate Advisor
Other advisors:
(2014) Doctor Philosophy — Associate Advisor
Existence results in nonlinear ordinary differential equations: boundary value problems
(2014) Doctor Philosophy — Associate Advisor
(2011) Doctor Philosophy — Associate Advisor
Other advisors:
(2010) Doctor Philosophy — Associate Advisor
Other advisors:
(2010) Doctor Philosophy — Associate Advisor
Other advisors:
EXISTENCE OF SOLUTIONS TO CONTINUOUS AND DISCRETE BOUNDARY VALUE PROBLEMS FOR SYSTEMS OF FIRST-ORDER EQUATIONS
(2007) Doctor Philosophy — Associate Advisor
Note for students: The possible research projects listed on this page may not be comprehensive or up to date. Always feel free to contact the staff for more information, and also with your own research ideas.
The Keller Segel system and extensions
This project relates to analytic aspects of a mathematical model for Chemotaxis.
Topology Optimisation
We are currently working in an exciting new area of mathematics called Topology optimisation. Our aim is to develop the tools to optimize the shape and topology of porous and composite materials to perform specific tasks. In particular we have a current ARC Discovery grant that will provide funding for APA top-ups and research costs for projects relating to optimal design of bone implants. Specific projects involve research in a range of fields from applied mathematics, as well as computational science. There is also scope for projects with an emphasis on pure mathematics (geometric evolution equations).
Projects to be supervised by me and/or Dr. Tony Roberts