Dr Susana Gutierrez BSc MSc PhD

Dr Susana Gutierrez

School of Mathematics
Senior Lecturer

Contact details

Telephone
+44 (0) 121 414 2915
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 Master's 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

Semester 1

LH Metric Spaces and Topology

Semester 2

LI/LH Real and Complex Analysis

Postgraduate supervision

Susana is interested in supervising doctoral research students in Euclidean Harmonic Analysis and Partial Differential Equations.

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 non-linear Schrödinger 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 – present.

Publications

Recent publications

Article

Gutiérrez, S & Laire, AD 2020, 'Self-similar shrinkers of the one-dimensional Landau-Lifshitz-Gilbert equation', Journal of Evolution Equations. https://doi.org/10.1007/s00028-020-00589-8

Gutiérrez, S & De Laire, A 2019, 'The Cauchy problem for the Landau-Lifshitz-Gilbert equation in BMO and self-similar solutions', Nonlinearity, vol. 32, no. 7, pp. 2522-2563. https://doi.org/10.1088/1361-6544/ab1296

Bennett, J, Bez, N, Flock, TC, Gutiérrez, S & Iliopoulou, M 2018, 'A sharp k-plane Strichartz inequality for the Schrödinger equation', Transactions of the American Mathematical Society, vol. 370, no. 8, pp. 5617-5633 . https://doi.org/10.1090/tran/7309

Bennett, J, Bez, R, Gutierrez, S & Lee, S 2018, 'Estimates for the kinetic transport equation in hyperbolic Sobolev spaces', Journal de Mathematiques Pures et Appliquees , vol. 114, pp. 1-28. https://doi.org/10.1016/j.matpur.2018.03.007

Gutierrez, S & De Laire, A 2015, 'Self-similar solutions of the one-dimensional Landau–Lifshitz–Gilbert equation', Nonlinearity, vol. 28, no. 5, pp. 1307-1350. https://doi.org/10.1088/0951-7715/28/5/1307

Bennett, J, Bez, N, Gutierrez, S & Lee, S 2014, 'On the Strichartz estimates for the kinetic transport equation', Communications in Partial Differential Equations, vol. 39, no. 10, pp. 1821-1826. https://doi.org/10.1080/03605302.2013.850880

Bennett, J, Bez, N & Gutiérrez, S 2013, 'Global Nonlinear Brascamp–Lieb Inequalities', Journal of Geometric Analysis, vol. 23, no. 4, pp. 1806-1817. https://doi.org/10.1007/s12220-012-9307-3

Antonio Barcelo, J, Fanelli, L, Gutierrez, S, Ruiz, A & Cruz Vilela, M 2013, 'Hardy uncertainty principle and unique continuation properties of covariant Schrödinger flows', Journal of Functional Analysis, vol. 264, no. 10, pp. 2386-2415. https://doi.org/10.1016/j.jfa.2013.02.017

Gutierrez, S & Vega, L 2013, 'On the stability of self-similar solutions of 1D cubic Schrödinger equations', Mathematische Annalen, vol. 356, no. 1, pp. 259-300. https://doi.org/10.1007/s00208-012-0847-4

Bennett, J, Bez, N & Gutiérrez, S 2013, 'Transversal multilinear Radon-like transforms: Local and global estimates', Revista Matematica Iberoamericana, vol. 29, no. 3, pp. 765-788. https://doi.org/10.4171/RMI/739

Gutiérrez, S 2011, 'Vortex filaments and ID cubic Schrödinger equations: Singularity formation', Communications in Applied Analysis, vol. 15, no. 2-4, pp. 457-474.

Bournaveas, N & Gutierrez, S 2008, 'Averages over Spheres for Kinetic Transport Equations with Velocity Derivatives in the Right-Hand Side', SIAM Journal on Mathematical Analysis, vol. 40, no. 2, pp. 653-674. https://doi.org/10.1137/070698415

Bournaveas, N, Calvez, V, Gutierrez, S & Perthame, B 2008, 'Global Existence for a Kinetic Model of Chemotaxis via Dispersion and Strichartz Estimates', Communications in Partial Differential Equations, vol. 33, no. 1, pp. 79-95. https://doi.org/10.1080/03605300601188474

Bournaveas, N & Gutierrez, S 2007, 'On the regularity of the averages over spheres for kinetic transport equations in hyperbolic Sobolev spaces', Revista Matematica Iberoamericana, vol. 23, no. 2, pp. 481-512.

Preprint

Bennett, J, Gutierrez, S, Nakamura, S & Itamar, O 2024 'A phase-space approach to weighted Fourier extension inequalities' arXiv. https://doi.org/10.48550/arXiv.2406.1488

View all publications in research portal