# Miruna-Ştefana Sorea

Emails: mirunastefana.sorea(at)ulbsibiu(dot)ro miruna.stefana.sorea2022(at)gmail(dot)com

I am a Lecturer and Researcher in the Department of Mathematics and Computer Science, the Faculty of Sciences, „Lucian Blaga” University of Sibiu, Romania.

I am also a member of the Research Center in Mathematics and Applications, which is part of the Faculty of Sciences, „Lucian Blaga” University of Sibiu, in the Numerical Methods and Approximation Theory Group.

Between October 2020 and September 2023 I was a postdoctoral researcher at the scientific research institute SISSA (Scuola Internazionale Superiore di Studi Avanzati) and IGAP (Institute for Geometry and Physics) Trieste, Italy, working with Antonio Lerario, in the groups Geometry and Mathematical Physics and Mathematical Analysis, Modelling and Applications.

Between February 2019 and September 2020 I was a postdoctoral researcher in the Nonlinear Algebra Group of Bernd Sturmfels, at Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig, Germany.

In October 2018 I defended my PhD thesis in France at Université de Lille, Laboratoire Paul Painlevé, where I was financially supported by Laboratoire d’Excellence Centre Européen pour les Mathématiques, la Physique et leurs interaction (CEMPI) and by Région Hauts-de-France. My PhD advisors were Arnaud Bodin and Patrick Popescu-Pampu.

My main research interests:

Real Algebraic Geometry and Applied Algebra:

- topology and geometry of real and complex singularities;

- algebraic statistics;

- polynomial dynamical systems inspired by interaction networks.

Picture credit: Özde Bayer as part of the 2019 compilation: Nonlinear Algebra People

From October 2020 to September 2023 I was a co-organizer of the Geometric Structures Research Seminar at SISSA, Trieste, Italy - see also here.

Some recent activities and news:

April 16, 2024: colloquium talk on "Combinatorial study of morsifications of real univariate singularities", Augsburger Mathematisches Kolloquium (Sommersemester), Universität Augsburg, Institut für Mathematik, Augsburg, Germany.

March 8, 2024: talk on "How to measure non-convexity?" for the First Annual FORTHEM Conference: FORTHEM - For the Future (Johannes-Gutenberg Universität Mainz, Jyväskylän yliopisto, Latvijas Universitate, Università degli Studi di Palermo, Universitat de València, Universitetet i Agder, Université de Bourgogne, Uniwersytet Opolski, Lucian Blaga University of Sibiu)

February 26 - March 8, 2024: I taught 6 lectures (in total 6 hours) on "Disguised toric dynamical systems" (4 courses and 2 tutorials) for the

CIMPA Research School on Algebra and Algebraic Geometry for Applications, LUMS, Lahore, Pakistan.

One of the main goals of the School was to provide a comprehensive understanding of modern algebraic and geometric methods, as well as their practical applications. Click here to see videos for:

Course 1, Course 2, Tutorial 1, Course 3, Course 4, Tutorial 2.

CIMPA - Centre International de Mathématiques Pures et Appliquées: "founded in France in 1978, CIMPA is a nonprofit organization that promotes research in Mathematics in developing countries. Located in Nice, it is a UNESCO Category 2 centre and is part of the Laboratoire d'Excellence CARMIN (Centres d'Accueil et de Rencontres Mathématiques Internationales). It benefits from the financial support of Germany, France, Norway, Spain and Switzerland. CIMPA co-organizes and sponsors numerous activities in developing countries, on all continents."

January 22-28, 2024: talk on "Combinatorial study of morsifications of real univariate singularities", Congreso Bienal de la Real Sociedad Matemática Española 2024, Universidad Pública de Navarra, Pamplona, Spain, for the Special Session "Geometría Algebraica entre Aplicaciones y Computación".

October 30-November 2, 2023: talk on "Combinatorial study of morsifications of real univariate singularities", at the Research School on Real Algebraic Geometry organized by SISSA (Scuola Internazionale Superiore di Studi Avanzati) and IGAP (Institute for Geometry and Physics), Trieste, Italy.

September 28, 2023: new preprint on "The toric locus of a reaction network is a smooth manifold" (Gheorghe Craciun, Jiaxin Jin, Miruna-Stefana Sorea) is on arxiv: https://arxiv.org/abs/2309.15241

September, 2023: attending the Fall Semester on "Algebraic Statistics and Our Changing World - New Methods for New Challenges" at the Institute for Mathematical and Statistical Innovation, hosted by University of Chicago, U.S.A.

September 2023: talk on "A quadratic identity in the shuffle algebra and an alternative proof for de Bruijn’s formula" at Trends in Representation Theory and Related Topics, Babes-Bolyai University of Cluj-Napoca, Romania.

July 2023: poster presentation on "The Structure of the Moduli Spaces of Toric Dynamical Systems" (joint work with Gheorghe Craciun and Jiaxin Jin) at SIAM AG23, TU Eindhoven, the Netherlands.

July 2023: talk on "(Disguised) toric dynamical systems and their (disguised) toric locus" at SIAM AG23, TU Eindhoven, the Netherlands.

July 2023: together with Pratik Misra and Angélica Torres I co-organized the mini-symposium "Algebraic Methods in Biological Systems", at SIAM AG23, TU Eindhoven, the Netherlands.

July 2023: talk on "(Disguised) toric dynamical systems and their (disguised) toric locus" at The Tenth Congress of Romanian Mathematicians 2023, University of Pitesti, Romania.

June 2023: our article "The Disguised Toric Locus and Affine Equivalence of Reaction Networks" (Sabina J. Haque, Matthew Satriano, Miruna–Ştefana Sorea, and Polly Y. Yu) is published online in SIADS (SIAM Journal on Applied Dynamical Systems), DOI: 10.1137/22M149853X

June 2023: talk on "(Disguised) toric dynamical systems and their (disguised) toric locus" at the National School on Algebra - Interactions between Algebra and Geometry in Bucharest 2023, University of Bucharest & IMAR, Romania.

June 2023: our new preprint "Combinatorial study of morsifications of real univariate singularities" ( Arnaud Bodin, Evelia Rosa García Barroso, Patrick Popescu-Pampu, Miruna-Stefana Sorea) is on the arXiv.

May 2023: talk on "Poincaré-Reeb graphs of real algebraic domains", Algebraic and Geometric Methods of Analysis, Institute of Mathematics of National Academy of Sciences of Ukraine.

May 2023: our article "Poincaré-Reeb graphs of real algebraic domains" (Arnaud Bodin, Patrick Popescu-Pampu, Miruna-Stefana Sorea) is published online in Revista Matematica Complutense, DOI: 10.1007/s13163-023-00469-y

April 2023: talk on "Exact Solutions in Log-Concave Maximum Likelihood Estimation", Applied CATS (Combinatorics, Algebra, Topology and Statistics) seminar, Mathematics of Data and AI, KTH Stockholm, Sweden.

April 2023: our updated preprint "The structure of the moduli spaces of toric dynamical systems" (Gheorghe Craciun, Jiaxin Jin, Miruna-Stefana Sorea) is on the arXiv.

March 2023: our paper "Symmetrically colored Gaussian graphical models with toric vanishing ideal" (Jane Ivy Coons, Aida Maraj, Pratik Misra and Miruna-Stefana Sorea) has been published in SIAGA (SIAM Journal on Applied Algebra and Geometry): you can read it here.

March 2023: talk on "Disguised toric dynamical systems", Mathematics of Reaction Networks Seminar (Harvard University / Politecnico di Torino / Texas A&M University / University of Vienna): video

February 2023: talk on "Disguised toric dynamical systems", Segundo Congreso Internacional de Álgebra y Sistemas Dinámicos, Universidad Nacional Mayor De San Marcos, Lima, Perú.

January 2023, our paper "The disguised toric locus and affine equivalence of reaction networks" (Sabina J. Haque, Matthew Satriano, Miruna-Stefana Sorea, Polly Y. Yu) has been accepted for publication in SIADS (SIAM Journal on Applied Dynamical Systems).

January 2023, talk on "Poincaré-Reeb graphs of real algebraic domains", at the Copenhagen-Jerusalem Combinatorics Seminar.

December 2022, our paper "Symmetrically colored Gaussian graphical models with toric vanishing ideal" (Jane Ivy Coons, Aida Maraj, Pratik Misra and Miruna-Stefana Sorea) has been accepted for publication in SIAGA (SIAM Journal on Applied Algebra and Geometry).

November-December 2022: I taught the PhD course "Singular points of complex algebraic plane curves" (10 lectures, a total of 20 hours) at SISSA, Trieste, Italy.

Abstract: The aim of this course is to provide a local study of the singular points of plane curves. The theory of singularities of complex algebraic plane curves is situated at the crossroads of many interesting areas of mathematics, making the study of curve singularities particularly fruitful up to this day. We start with a short introduction to the subject, where we briefly review results about manifolds and plane algebraic curves. Moreover, we focus on polar curves, Puiseux's theorem and resolution of singularities. Next, we show how combinatorial tools such as the Eggers tree can be used in the study of the contact of two branches of a curve. One of the core concepts in the first part of the course is equisingularity of curves. In the second part of the course we study the geometry of the link of a singularity, Milnor's fibration theorem and the Milnor number. In addition, we also see a proof of Klein's equation (using Euler characteristics of constructible functions), which relates invariants of a projective curve with invariants of its dual curve. Time permitting, we will also tackle the decomposition of the link complement and the computation of the monodromy of the Milnor fibration.

December 6, 2022: talk on "Disguised toric dynamical systems", SISSA Junior Math Days 2022, Trieste, Italy.

November 16, 2022: talk on "Realization of Poincaré-Reeb graphs by real algebraic domains", Seminario Geometría Algebraica: singularidades e invariantes GASIULL, Universidad de La Laguna, Tenerife, Spain.

November 9, 2022: talk on "Poincaré-Reeb graphs of real algebraic domains", Bringing Young Mathematicians Together (BYMAT) 2022, Universidad de Valencia, Spain.

November 8, 2022: talk on "Poincaré-Reeb graphs of real algebraic domains", Seminario Geometría Algebraica: singularidades e invariantes GASIULL, Universidad de La Laguna, Tenerife, Spain.

October 25, 2022: video: talk on "Poincaré-Reeb graphs of real algebraic domains", Conference on Real Algebraic Geometry, CIRM, Marseille, France.

October 21, 2022: our paper "Exact solutions in log-concave maximum likelihood estimation" (Alexandros Grosdos, Alexander Heaton, Kaie Kubjas, Olga Kuznetsova, Georgy Scholten, Miruna-Stefana Sorea) has been published online in Advances in Applied Mathematics. You can read it at this link.

October 4, 2022: talk on "Poincaré-Reeb graphs of real algebraic domains", Singularity theory and its applications, Research Institute for Mathematical Sciences, Kyoto University, Japan.

September 19-23, 2022: I attended "From Statistical Physics to Random Geometry" Summer School, at SISSA, Trieste, Italy.

September 13, 2022: talk on "Poincaré-Reeb graphs of real algebraic domains", ICATA2022, Lucian Blaga University, Sibiu, Romania.

September 1, 2022: talk on "Disguised toric dynamical systems" at XVème Colloque Franco-Roumain de Mathématiques Appliquées, Toulouse, France.

August 8, 2022: our paper "Families of Polytopes with Rational Linear Precision in Higher Dimensions" (Isobel Davies, Eliana Duarte, Irem Portakal, Miruna-Stefana Sorea) has been published online in Foundations of Computational Mathematics - you can read it here.

July 29, 2022: plenary talk on "Poincaré-Reeb graphs of real algebraic domains", 17th International Workshop on Real and Complex Singularities, Sao Carlos, Brazil - online. video

July 14, 2022: new preprint "Poincaré-Reeb graphs of real algebraic domains" (Arnaud Bodin, Patrick Popescu-Pampu, Miruna-Stefana Sorea) is on arXiv: https://arxiv.org/abs/2207.06871

July 7, 2022: my research paper "Permutations encoding the local shape of level curves of real polynomials via generic projections" was published online in Annales de l'Institut Fourier - see at this link.

July 7, 2022: talk on "Poincaré-Reeb graphs of real algebraic domains", Meeting of GDR Singularités 2022, Centre Paul Langevin, Aussois, France.

May 19, 2022: talk on "Multinomial staged tree models and polytopes with rational linear precision", Workshop for Young Researchers in Mathematics (WYRM), Institute of Mathematics of the Romanian Academy (IMAR), Bucharest, Romania - online.

April 26, 2022: talk on "Disguised Toric Dynamical Systems", at the Formal Reaction Kinetics Seminar, Budapest, Hungary - online.

February 9, 2022: poster presentation on "Disguised Toric Dynamical Systems" at The Virtual 13th Conference on Dynamical Systems Applied to Biology and Natural Sciences, DSABNS 2022, Basque Center for Applied Mathematics in Bilbao, Basque Country, Spain - online.

February 7, 2022: plenary talk on "The shapes of level curves of real polynomials near strict local minima" at The 2nd International Meeting of Young Researchers in Singularity Theory and Related Fields, Sao Carlos, Brazil - online.

December 20, 2021: talk on "Poincaré-Reeb trees of real Milnor fibres" at SISSA Junior Math Days, Trieste, Italy.

A long version of my CV is available upon request.

Review activity for: SIADS (SIAM Journal on Applied Mathematics), SIAGA (SIAM Journal on Applied Algebra and Geometry), AMS Mathematical Reviews (MathSciNet), The Graduate Journal of Mathematics