Dr Susana Gutierrez BSc, PhD

Dr Susana Gutierrez

School of Mathematics
Senior Lecturer

Contact details

Telephone
+44 (0) 121 414 2915
Fax
+44 (0) 121 414 3389
Email
s.gutierrez@bham.ac.uk
View my research portal
Address
School of Mathematics
Watson Building
University of Birmingham
Edgbaston
Birmingham
B15 2TT
UK

Susana Gutierrez is a Senior Lecturer and a member of the Mathematical Analysis Research Group in the School of Mathematics.

Susana’s research interests lie in a variety of aspects of euclidean harmonic analysis, with particular emphasis on applications to partial differential equations of mathematical physics. Susana has received funding for her research from the EPSRC.

Qualifications

  • PhD in Mathematics, University of the Basque Country (Spain), 2000
  • MSc in Mathematics, University of the Basque Country (Spain), 1998
  • BSc in Mathematics, University of the Basque Country (Spain), 1995

Biography

Susana Gutierrez studied Mathematics in Bilbao (Spain). She qualified with a Masters degree in Mathematics from the University of the Basque Country (Bilbao, Spain) in 1998, and received her PhD in Mathematics from the same institution in 2000. After completing her PhD, Susana held postdoctoral positions at the Universidad Complutense de Madrid (Spain), University of Edinburgh (UK), École Normale Supérieure (ENS) (Paris, France) and University of Nottingham (UK). Susana joined the School of Mathematics here at Birmingham in 2007.

 

Teaching

  • Single Honours Mathematics (G100, G103, G141)
  • Mathematics Majors: Mathematics with Business Management (G1N2); Mathematics with Engineering (J920); Mathematics with Philosophy (G1V5)
  • Joint Honours Mathematics: Mathematics & Computer Science (GG14); Pure Mathematics & Computer Science (GGC4); Mathematics & Sport Science (GC17); Mathematics & Music (GW13); Mathematics & Philosophy (GV15)
  • Theoretical Physics and Applied Mathematics (FG31)
  • Mathematics Minors: French Studies and Mathematics (GR11); German Studies and Mathematics (GR12)
  • Natural Sciences (CFG0, FCG0)

Research

RESEARCH THEMES

  • Euclidean Harmonic Analysis
  • Partial Differential Equations
  • Singularity Formation Phenomena.

RESEARCH ACTIVITY

Susana’s research concerns the rigorous analytical study of qualitative and quantitative properties of partial differential equations motivated by models of well-known physical processes. A recurring theme in her research is the application of techniques and perspectives from euclidean harmonic analysis and dispersive PDEs.

Susana has worked on developing the theory of singularity formation phenomena in the setting of nonlinear Schrodinger equations and intimately related geometric flows. These include the so-called Localized Induction Approximation for the evolution of vortex filaments in classical fluids, and more recently the family of Landau-Lifshitz-Gilbert equations describing the dynamics for the spin in ferromagnetic materials.  Susana has also contributed to the understanding of the properties of kinetic transport equations and certain nonlinear kinetic models of chemotaxis.

Other activities

  • Editor of the Proceedings of the Royal Society of Edinburgh Section A, Mathematics, 2020 – present.
  • Member of the LMS Research Policy Committee, 2021 – present.
  • External member of the Scottish Mathematical Sciences Training Centre (SMSTC), 2019 – pre-sent.

Publications

Selected:

S. Gutierrez and A. de Laire (2021), Self-similar shrinkers of the one-dimensional Landau–Lifshitz–Gilbert equation, Journal of Evolutions Equations 21 (1), 473–501.

S. Gutierrez and A. de Laire (2019), The Cauchy problem for the Landau-Lifshitz-Gilbert equation in BMO and self-similar solutions, Nonlinearity 32 (7), 2522–2563.

J. Bennett, N. Bez, T. C. Flock, S. Gutierrez and M. Iliopoulou (2018), A sharp k-plane Strichartz in-equality for the Schroedinger equation, Transactions of the American Mathematical Society 370, 5617-5633.

J. Bennett, N. Bez, S. Gutierrez and S. Lee (2018), Estimates for the kinetic transport equation in hyperbolic Sobolev spaces, Journal de Mathematiques Pures et Appliquees 114, 1–28.

S. Gutierrez and A. de Laire (2015), Self-similar solutions of the one-dimensional Landau-Lifshitz-Gilbert equation, Nonlinearity, Volume 28, no. 5, (2015), 1307-1350.

J. Bennett, N. Bez, S. Gutierrez and S. Lee (2014), On the Strichartz estimates for the kinetic transport equation, Communications in Partial Differential Equations, Volume 39, no. 10, 1821-1826.

J. Bennett, N. Bez  and S. Gutierrez (2014), Transversal multilinear Radon-like transforms: local and global estimates, Revista Matematica Iberoamericana, Volume 29, no. 3, 765-788.

J.A. Barcelo, L. Fanelli, S. Gutierrez, A. Ruiz and M. C. Vilela (2013), Hardy uncertainty principle and unique continuation properties of covariant Schrodinger flows, Journal of Functional Analysis, Volume 264, no. 10, 2386-2415.

S. Gutierrez and L. Vega (2013), On the stability of self-similar solutions of 1D cubic Schrodinger equations, Mathematische Annalen, Volume 356, no. 1, 259-300.

N. Bournaveas and S. Gutierrez (2008), Averages over spheres for kinetic transport equations with velocity derivatives in the right-hand side, SIAM Journal on Mathematical Analysis, SIMA, Volume 40, no. 2, 653-674.. 

N. Bournaveas, V. Calvez, S. Gutierrez and B. Perthame (2008), Global existence for a kinetic model of chemotaxis via dispersion and Strichartz estimates, Communications in Partial Differential Equations, Volume 33, no. 1, 79-95.

N. Bournaveas and S. Gutierrez (2007), On the regularity of the averages over spheres for kinetic transport equations in hyperbolic Sobolev spaces, Revista Matematica Iberoamericana, Volume 23, no. 2, 481-512.

S. Gutierrez and L. Vega (2004), Self-similar solutions of the localized induction approximation: singularity formation, Nonlinearity, Volume 17, no.  6, 2091-2136.

S. Gutierrez (2004), Non trivial Lq solutions to the Ginzburg-Landau equation, Mathematische Annalen, Volume 328, no. 1&2, 1-25.

S. Gutierrez, J. Rivas and L. Vega (2003), Formation of singularities and self-similar vortex motion under the localized induction approximation, Communications in Partial Differential Equations, Volume 28, no. 5&6, 927-968.

S. Gutierrez (2000), A note on restricted weak-type estimates for Bochner Riesz operators with negative index in Rn, n≥2, Proceedings Amer. Math. Soc., Volume 128, no. 2, 495-501.

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