*Six Questions with: Dr Latifa Debbi*

Dr Debbi is researcher in the Laboratory of Applied Mathematics at the Université Ferhat Abbas Setif and was a Visiting Fellow on the Stochastic Partial Differential Equations programme in 2010.

**When did you become first interested in mathematics and what keeps your interest fresh?**

I have been interested in mathematics since I was a child. Before going to primary school, I used to ask myself questions such as: why 'one' is written as '1' and not as '2'? Why is the colour blue called 'blue', not 'red' or 'green'? In primary school, I studied arithmetic and geometry and I enjoyed writing problems for myself and solving them, since I found the exercises given in school were very easy for me. The first time I heard the word 'mathematics', it was used by people who tried to frighten me as they said it was a very difficult science which is studied in -middle school. I spent a long time thinking about 'mathematics' and became very curious about it and developed a yearning to study it. Later, the challenge became a pleasure thanks to my school teachers. I keep my interest fresh because in every step of my mathematical life I discover beautiful things. It is wonderful to meet talented mathematicians and I use mathematics to solve many religious, philosophical and daily problems.

**Could you tell us a little about your career path so far and what your current research involves? **

Whilst I was an undergraduate student there was political trouble in Algeria. The situation was very difficult and many professors left and all exchanges with foreign universities were stopped. I was accepted to do a PhD in Orsay (Paris X) with a grant after the second year, but the political situation did not allow me to go. The project was to have been supervised by R. Temam and it was on numerical approximation of the Navier-Stokes equations. Instead of a PhD I completed a Masters in Algeria and I got a position of lecturer (Maître assistant) in the University, but I still wanted to do my PhD. I was looking for the topic and for the subject of my PhD research by myself. I had the opportunity to visit Paris VI twice for one month each. I attended talks in Paris VI, Paris X and in the Henri Poincaré Institute.During my second visit, I met Professor M. Yor from Paris VI, to whom I am very grateful for his help, since, it was thanks to him, that I found my way in mathematical research. Later, after the partial stability in my country, I got a grant to do my PhD in the University of Henri Poincaré in Nancy. I finished the scientific part of my PhD thesis in two and a half years and returned to Algeria. I got a position of Assistant Professor (Maître de conferences). In August, I will move to Montan Universitat for a short post-doc position.

My current topic of research is stochastic partial differential equations driven by fractional operators and perturbed by cylindrical, fractional or Levy noises. These kinds of equations emerge in many applications in physics and in mechanics where the anomalous diffusion can be countered. I am interested in the existence, uniqueness, regularity, ergodic properties and numerical approximations of the solutions.

**What achievements are you most proud of? **

My joint paper with Z. Brzezniak, [1], was a pleasure for me and I have learnt a lot from my coauthor. We have been interested in the existence and uniqueness of the solution of the Burgers equation driven by fractional operator and perturbed by cylindrical noise. We have been motivated by the three interactions between the small dissipation effect given by the fractional Laplacian the steepening effect given by the nonlinear term and the random perturbation given by the random noise. I enjoyed the time I have spent in looking for some estimations in delicate Sobolev spaces. In my first paper [2], my supervisor, L. Abbaoui and myself, were answering a question which remained open for 10 years. It was about the correlative representation of stochastic processes and stochastic fields considered as curves and as surfaces in Hilbert spaces. We have considered fields for which at least one of the operators is non self-adjoint with nondegenerate real spectrum. The paper has been published again 10 years later. I am also proud of my papers [3] and [4]. The questions treated in both papers motivated people to study many related questions. In [3], I gave a probabilistic representation to the solution of high-order fractional heat type equation. In [4], I have been interested in the existence, uniqueness and regularity of the solution of stochastic partial differential equations driven by fractional operator. It is joint work with M. Dozzi.

**How do you achieve a balance between your work and homelife?**

Growing up as a woman in Algeria has involved many difficulties for me because women are underestimated by society and by the law. Intellectual women can be the victims of threats and aggressive acts. It is very difficult for women to gain support for their ideas or academic research. As a mathematician, believing in proofs and justice, I have spent a great deal of time and energy fighting for gender equality and to create some balance, but it is really hard!

**What advice would you offer to young women who are just starting their careers in the mathematical sciences? **

Mathematics is a science and an art. It is related to your intelligence and your feelings of the beauty and elegance of mathematics. Mathematics is for everyone - not just for men.

**Has your visit to the Newton Institute been fruitful?**

Yes it was. In fact, The Newton Institute gave me the opportunity to meet some of my coauthors and hence to make progress in my projects, to begin new research and to attend talks of high-level that are related to my area of research. The Institute provides a scientifically active and friendly atmosphere for the visiting researchers. I would like to thank the staff for their kind hospitality.

##### References

[1] Brzezniak, Zdzislaw; Debbi, Latifa. On stochastic Burgers equation driven by a fractional Laplacian and space-time white noise. *Stochastic differential equations: theory and applications*, 135--167, Interdiscip. Math. Sci., 2, World Sci. Publ., Hackensack, NJ, 2007.

[2] Abbaoui, Lyazid; Debbi, Latifa. An application of the non-self adjoint operators theory in the study of stochastic processes. *J. Appl. Math. Stoch. Anal.* 2004, no. 2, 149--157.

[3] Debbi, Latifa. Explicit solutions of some fractional partial differential equations via stable subordinators. *J. Appl. Math. Stoch. Anal. 2006*, Art. ID 93502, 18 pp.

[4] Debbi, Latifa; Dozzi, Marco. On the solutions of nonlinear stochastic fractional partial differential equations in one spatial dimension. *Stochastic Process. Appl.* 115 (2005), no. 11, 1764--1781.