I spent 10 years of my life (2007-2017) first studying and then teaching and doing research in mathematics in the Mathematics Department of Universidad Autónoma de Madrid. Nowadays I only do any research in mathematics very rarely, but I’m quite fond of this period of my life. Here you can find some of my work from those years.

###### PhD thesis

K-spectral sets, operator theory and related function theory, February 2017

###### MSc thesis

Complex analysis techniques in the spectral theory of linear operators, September 2013

This includes a self-contained introduction to the Sz.-Nagy–Foias theory of dilations and Ando’s theorem about the dilation of pairs of commuting contractions. I am particularly happy about the way that the analytic model for \(C_{\cdot 0}\) contractions is written, and I think it provides a good alternative exposition to the Sz.-Nagy–Foias book. Perhaps this can be useful to postgraduate students interested in these topics.

MSc thesis defense slides (in Spanish).

###### Teaching Statement

Clearly, my favourite activity during my PhD studies was teaching. I enjoyed a lot helping the students and finding unconventional ways of explaining things and getting the students engaged. Life has now taken me through other paths and I don’t teach maths any longer (except for the odd exceptional private class). Now I’m well busy with other things that are perhaps more intelectually challenging, but probably not so emotionally rewarding as teaching. Certainly I miss teaching, but who knows what will happen in the future.

As an example of my style of teaching (and for some anecdotes), you can read my Teaching Statement, which I wrote in Spring 2017.

(If any of my former students finds themselves reading this, please drop me a line. I would love to know how are you doing.)

###### Articles

- M. Dritschel, D. Estévez, D. Yakubovich, Resolvent criteria for similarity to a normal operator with spectrum on a curve, J. Math. Anal. Appl. 463 (2018), no. 1, 345-364. (also in arXiv).
- M. Dritschel, D. Estévez, D. Yakubovich, Tests for complete K-spectral sets, J. Functional Anal. 273 (2017), no. 3, 984-1019. (also in arXiv).
- M. Dritschel, D. Estévez, D. Yakubovich, Traces of analytic uniform algebras on subvarieties and test collections, J. London Math. Soc. 95 (2017), no. 2, 414-440. (also in arXiv).
- D. Estévez, Explicit traces of functions on Sobolev spaces and quasi-optimal linear interpolators, Math. Ineq. Appl. 20 (2017), no. 2, 441-457. (also in arXiv).
- D. Estévez, D.V. Yakubovich, Decay rate estimations for linear quadratic optimal regulators, Linear Algebra Appl. 439 (2013), no. 11, 3332-3358. (also in arXiv).

###### Miscellaneous works

The Hodge decomposition theorem, January 2013. A self-contained proof of the Hodge decomposition theorem. This was done for an MSc course in differential geometry given by Gabino González.

Interpolación en espacios de Hardy, December 2011 (in Spanish). A self-contained proof of the Shapiro-Shields theorem about weighted interpolation in \(H^p(\mathbb{D})\), with an application to the study of eigenvectors of the model operator \(T = P_KM_z|K\), where \(K = H^2 \ominus BH^2\). This was done for an undergraduate course in complex analysis given by Ana Vargas.

###### Trivia

Erdös number: 3 (co-authored with M. Dritschel, who co-authored with J.M. Anderson, who co-authored with Erdös)

###### Talks

- April 2017, Conjuntos K-espectrales y tuplas de operadores, Analysis and Applications Seminar, Universidad Autónoma de Madrid.
- April 2017, Conjuntos K-espectrales y tuplas de operadores, Seminario Rubio de Francia, Universidad de Zaragoza.
- February 2017, Generación de álgebras de funciones analíticas y separación de singularidades, Complex Analysis Seminar, Universidad Autónoma de Madrid.
- June 2016, Conditions for similarity to a normal operator involving resolvent estimates, Operator Theory 26th international conference, West University, Timisoara (Romania).
- October 2015, Generation of algebras and separation of singularities, Analysis Seminar, Newcastle University (United Kingdom).
- July 2015, Separation of singularities, generation of algebras and complete K-spectral sets, IWOTA 2015, Ivane Javakhishvili Tbilisi State University, Tbilisi (Georgia).
- May 2015, Separación de singularidades, generación de álgebras y conjuntos completamente K-espectrales, XVI Encuentro de Análisis Real y Complejo, Carmona, Sevilla.
- July 2014, Separating structures and operator vessels, IWOTA 2014, VU University, Amsterdam (The Netherlands)
- June 2014, Separation of singularities, generation of algebras and complete K-spectral sets, 11th Advanced Course in Operator Theory and Complex Analysis, Universidad de Sevilla.
- September 2013, Complex analysis techniques in the spectral theory of operators, Workshop of Young Researchers in Mathematics, Universidad Complutense de Madrid.
- May 2013, The extension problem in Sobolev spaces and quasi-optimal interpolators, Hilbert Function Spaces 2013 conference, Gargnano (Italy).
- March 2013, El problema de extensión en espacios de Sobolev e interpoladores quasi-óptimos, Analysis and Applications Seminar, Universidad Autónoma de Madrid.
- June 2011, Localización de ceros de funciones raciones y el estudio la calidad de un regulador lineal cuadrático óptimo, Complex Analysis Seminar, Universidad Autónoma de Madrid.