My research interests are the following:
- Stochastic Integrable systems
- Random matrix theory
- Macdonald processes
- Macdonald polynomials
I'm also interested in Geometric Analysis and Stochastic Analysis.
2014-2015 Postgraduate award (Parts 1 and 2), in Introduction to Academic and Professional Practice for Postgraduates who teach, Learning and Development Centre, University of Warwick, UK.
Tutor: Dr. Elke Thönnes
2010-2012 M.Sc. by Research in Mathematics, Department of Mathematics, University of Warwick, UK.
Supervisor Prof. K. David Elworthy.
Thesis title Derivative formula on the Heisenberg Lie group.
2008-2010 M.Sc. in Mathematics, Institute of Mathematics, Statistics and Scientific Computing,
State University of Campinas, IMECC/UNICAMP, Campinas, São Paulo, Brazil.
Supervisor Dr. Pedro Catuogno.
Thesis title Stochastic Calculus and Parallel Translation.
2005-2008 B. Sc. in Mathematics, Department of Mathematics, Centre for Natural and Exact Sciences,
Federal University of Pernambuco, CCEN/UFPE, Recife, Pernambuco, Brazil.
Supervisors Dr. Antônio Carlos Monteiro and Prof. Manoel Lemos.
Topics in Number Theory and Cryptography.
- I am focusing on topics related to random matrices and stochastic integrable systems. The seminars and talks at Warwick are giving me ideas and I am writing notes about it.
- I’m also interested in topics related to Geometric RSK correspondence and Whittaker functions.
- Coalescent processes
I wrote some notes about coalescent processes and also exchangeable random partitions in my 9 months report. They are mainly based on Pitman, Gnedin, and Möhle papers.
- M.Sc. by Research thesis
I considered a left invariant stochastic differential equation defined on the 3-dimensional Heisenberg Lie group. This SDE is associated to a hypoelliptic operator. I proved the integration by parts formula for this special case and I also calculated a Bismut type formula which I extended to the general case of a n-dimensional Lie group.
I worked with the Malliavin covariance matrix which turned out to be a 3x3 matrix with entries described as sums of integrals of Brownian motions and squared Brownian motions. The appropriate rescaling on the time variable turned out to be important to conclude that the determinant is positive which allowed me to calculate the inverse matrix and then arrived in a Bismut type formula. I also applied the adjoint of the derivative of the Itô map to perform these calculations.
During the period of work on this project I was interested in investigating the infinite-dimensional case.
- Large Deviations
I wrote some notes on large deviations for validation on the TCC course and I received grade A for it. It consists of a generalization (from a nontopological point of view) of the classical large deviation principle for Gaussian measures. It is based on the notes "Isoperimetry and Gaussian analysis" by Michel Ledoux (St Flour course 1994).
- Fragmentation processes
I wrote some notes on fragmentation processes based on the book “Random Fragmentation and Coagulation Processes” by F. Bertoin. After my 9-months presentation I received a question about those processes and I decided to learn more about them in order to answer this question and other questions in the future.
Conferences and presentations
- École d'hiver sur les marches aléatoires et les processus de Dunkl, Laboratoire de Mathématiques et Physique Théorique, Universite Francois Rabelais de Tours, project MADACA, 5-9 January, 2015.
- Advances in Probability: Integrability, Universality and Beyond, Clay Mathematics Institute, University of Oxford, 28-02 October 2014.
- UK-Japan Stochastic Analysis School, University of Warwick, 1-5 September 2014.
- School and Workshop on Random Interacting Systems, University of Bath, 23-27 June 2014.
- Young Women in Probability, University of Bonn, 26-28 May 2014. Poster presented.
- CRiSM Council PhD Day, University of Warwick, 20 May 2014. Poster presented.
- Probability, Analysis and Dynamics, University of Bristol, 22-25 April 2014.
- Stochastic Growth Models (MiR@W day), University of Warwick, 21 October 2013.
- XVII Brazilian School of Probability, Mambucaba, 04-10 August, 2013. Poster presented.
- Academy for PhD Training in Statistics: Applied Stochastic Processes (lectured by Dr. Christina Goldschmidt), University of Warwick, 29-03 August, 2013.
- Young Researchers Meeting, University of Warwick, 21 May 2013. Talk given.
- Models and Inference in Population Genetics (MiR@W day), University of Warwick, 15 October 2012.
- XVI Brazilian School of Probability, Recife, 6-11 August, 2012.
- Stochastic Analysis and Stochastic PDEs, University of Warwick, 16-20 April, 2012.
- 2012 UK Easter Probability Meeting, University of Warwick, 26-30 March, 2012.
- Multiscale Systems: Theory and Applications, University of Warwick, 12-16 December, 2011.
- 5th International Conference on Stochastic Analysis and its Applications, University of Bonn, 5-9 September, 2011.
- Young Researchers in Mathematics 2011, University of Warwick, 14-16 April, 2011.
- Young Women in Probability, University of Bonn, 11-21 May, 2011.
- 2014/2015 (Term 2): ST115 Introduction to Probability (Lecturer: Dr. Jon Warren).
- 2014/2015 (Term 1): ST208 Mathematical Methods (Lecturer: Dr. David Croydon).
- 2013/2014 (Term 2): ST115 Introduction to Probability (Lecturer: Dr. Jon Warren).
- 2013/2014 (Term 1): ST202 Stochastic Processes (Lecturer: Dr. Krys Łatuszyński).
- 2012/2013 (Term 2): ST111/ST112 Probability A/B (Lecturer: Dr. Nikos Zygouras).
- Teaching training event on Giving feedback (with Dr. Crossman and Dr. Thonnes), Department of Statistics, University of Warwick, 8th May 2015.
- Maths/Stats PCAPP programme. Teaching Forum (with Dr. Jon Warren and Dr. David Wood), Department of Statistics and Department of Mathematics, University of Warwick, 21 January 2015.
- Maths/Stats PCAPP programme. Teaching training session on A-level Mathematics, Department of Statistics and Department of Mathematics, University of Warwick, 27 October 2014.
- Postgraduate teaching training session in teaching support, Department of Statistics, Deparment of Mathematics, and the Learning and Development Centre, University of Warwick, 8th October 2014.
- Teaching training session on A-level Mathematics, Department of Statistics, University of Warwick, 22 September 2014.
- International Communication Workshop, Department of Statistics, University of Warwick, 5 June 2014.
- Teaching training session on mathematical thinking, Department of Statistics, University of Warwick, 23 September 2013.
- Workshop for Posgraduate Students who Teach, Higher Education Academy, University of Leicester, 14 November 2012.
-Postgradute Award: Teaching and Learning in Higher Education
The following workshops are part of the programme:
- 'Reflecting on your teaching and reflective writing', 3 hrs, 8 July 2014.
- 'Introduction to E-learning', 2 hrs, 10 June 2014.
- 'Teaching inclusively', 3 hrs, 2 June 2014.
- 'What does it mean to teach', 3hrs, 23 May 2014.
- 'Lecturing, Assessment and research based learning', 5hrs, 21 May 2014.
- 'Reflecting on your teaching and reflective writing', 3 hrs, 15 May 2014.
- 'Motivating students beyond classroom', 3 hrs, 9 May 2014.
- 'Enhancing skills in small group teaching', 5hrs, 25 April 2014.
Courses and reading groups
- 2014/2015 (Term 1, Term 2): Mathematical physics and probability reading seminar.
- 2013/2014 (Term 1, Term 2 and Term 3): Mathematical physics and probability reading seminar.
- 2012/2013 (February-June): Measure-valued process reading group.
- 2012/2013 (Term 1): An Invitation to Graduate Probability, MASDOC program.
- 2012/2013 (Term 1): Advanced Topics in Biostatistics, Component 3 only: Diffusion processes.
- Past courses at Warwick: Large deviations (TTC course, Dr. Hendrik Weber), An introduction to Stochastic PDEs (TTC course, Prof. Martin Hairer), Topics in Stochastic Analysis (Prof. David Elworthy), Stochastic Analysis, Brownian Motion, Functional Analysis II, Advance PDE.
- 2013/2014 (Term 1, Term 2): In-sessional English 'Speaking & Listening' with Nigel Prentice, University of Warwick, UK.
- 2012/2013 (Summer), and 2013/2014 (Term 1): Research academic coaching (part of Academic Writing Programme), My Advantage, University of Warwick, UK.
- 2012/2013 (Term 3): Dissertation Writing, Centre for Applied Linguistics, University of Warwick, UK.
- Past activities at Warwick: Spanish (Beginner) and German (Beginner), Lifelong Language Learning, The Language Centre.
Seminars at Warwick
I regularly attend some talks of the following seminars:
- Mathematical physics and probability reading seminar.
- Probability Seminar
- Mathematics Colloquium
- East Midlands Stochastic Analysis Seminar
- Statistical Mechanics Seminar
- Midlands Probability Theory
I'm from Recife, Pernambuco, Brazil. It is located in the northeast part of Brazil and it boasts a beautiful archipelago called Fernando de Noronha nearby. The temperature is around 25-30 celsius all year long and people are extremely kind.
I love reading novels and poetry.
-Women in academia
- Mathematics: The right choice? by Frances Kirwan (Mathematics: Frontiers and Perspectives).
Department of Statistics
University of Warwick
Coventry CV4 7AL
email: r <dot> r <dot> albuquerque <at> warwick.ac.uk