Melkana Brakalova-Trevithick

Education

• Master of Education - MEd Harvard University Graduate School of Education (1992 — 1993)
• Doctor of Philosophy - PhD Sofia Unibversity (1983.09 — 1988.06)
• Doctor of Philosophy - PhD Sofia University St. Kliment Ohridski (1982 — 1988)

RESEARCH INTERESTS

My work falls mostly under the umbrella of geometric function theory, in particular, quasiconformal mappings and Teichmüller theory. I am also interested in the theory of minimal surfaces, harmonic mappings, as well as dynamical systems. I am currently working on smoothness and geometric properties of the p–integrable subspaces of the universal Teichmüller space.

POSITIONS

Academic Positions

• Professor, Fordham University, Bronx, NY, September 2020 –
• Associate Professor, Fordham University, Bronx, NY, September 2011 – August 2020.
• Visiting Scientist, Max Planck Institute for Mathematics, Bonn, Germany, September 1– September 30 and December 7 – December 22, 2017.
• Senior Fellow, Institute for Pure and Applied Mathematics, UCLA, program on Interactions between Analysis and Geometry, March 11, 2013 – June 14, 2013.
• Assistant Professor, Fordham University, Bronx, NY, September 2004 – June 2011.
• Teacher of Mathematics, Hotchkiss School, Lakeville, CT, September 1993 – 2004, on leave (Sabbatical) 2002 – 2003.
• Visiting Professor, Institute for Mathematical Sciences and Department of Mathematics, SUNY, Stony Brook, NY, September 2002 – June 2003.
• Analytics Instructor, KSG Summer Program, Harvard University, Cambridge, MA, August 1995.
• Visiting Lecturer, Tufts University, Medford, MA, Spring 1993.
• Assistant Professor, American University in Bulgaria, Blagoevgrad, BG, September 1991 – June 1992.
• Researcher, Bulgarian Academy of Sciences, Institute of Mathematics, Sofia, Bulgaria, 1986 – 1991.
• Visiting Assistant Professor, Washington University, St. Louis, MO, September 1990 – June 1991.
• Visiting Lecturer, University of Minnesota, Minneapolis, MN, September 1989 – June 1990.
• Wissenschaftliche Hilfskraft, University of Regensburg, Regensburg, West Germany, Fall 1988 – Spring 1989.
• Teaching Assistant, Sofia University, Sofia, Bulgaria, Fall 1986.
• Teaching Assistant, High Institute of Engineering and Architecture, Sofia, Bulgaria, Fall 1984.

Administrative Positions (Fordham University, NY)

• Department Chair, June 2020 – July 2021.
• Associate Chair, Rose Hill campus, Bronx, July 2019 – July 2020;
• Associate Chair, Lincoln Center campus, Manhattan, July 2018 – July 2020.
• Department Chair, July 2011 – July 2014 (on Faculty fellowship leave, Spring 2013).

PUBLICATIONS

• V. Alberge and M. Brakalova, On Smoothness of the elements of some integrable Teichmüller spaces. Math. Rep. 23(73), 95–105, 2021.
• V. Alberge, M. Brakalova and A. Papadopoulos, Teichmüller’s work on the type problem. in Handbook of Teichmüller Theory (A. Papadopoulos, ed.), Volume VII, EMS Publishing House, Zürich, 2020, arXiv:1912.11291.
• V. Alberge, M. Brakalova and A. Papadopoulos, A commentary on Teichmüller’s paper ”Untersuchungen über konforme and quasikonforme Abbildung”, (Investigations on conformal and quasiconformal mappings) in Handbook of Teichmüller Theory (A. Papadopoulos, ed.), Volume VII, EMS Publishing House, Zürich, 2020, arXiv:1912.11290.
• M. Brakalova and M. Weiss, translation from the German of a paper by O. Teichmüller, Investigation on conformal and quasiconformal mappings. (Untersuchungen über konforme und quasikonforme Abbildung, Deutsche Math. 3 (1938), 621–678) in Handbook of Teichmüller Theory (A. Papadopoulos, ed.), Volume VII, EMS Publishing House, Zürich, 2020.
• M. Brakalova, translation from the German of a paper by H. Grötzsch On the distortion of univalent non-conformal mappings and a related extension of the Picard theorem. (Über die Verzërrung bei schlichten nichtkonformen Abbildungen and über eine damit zusammenhängende Erweiterung des Picardschen Satzes. Berichte über die Verhandlungen der Sachsischen Akad. der Wissenschaften zu Leipzig Math.-Physische Klasse. Bd. 80 (1928), 503–507 von Herbert Grötzsch in Leipzig Vorgelegt von Herrn Koebe) in Handbook of Teichmüller Theory (A. Papadopoulos, ed.), Volume VII, EMS Publishing House, Zürich, 2020.
• M. Brakalova, translation from the German of a paper by H. Grötzsch On closest-to-conformal mappings of schlicht domains II. (Über möglist konformen Abbildungen von schlichten Bereichen. Berichte bër die Verhandlungen der Sachsischen Akad. der Wissenschaften zu Leipzig Math.-Physische Klasse. Bd. 84 (1932), 114–120. von Herbert Grötzsch in Leipzig Vorgelegt von Herrn Koebe) in Handbook of Teichmüller Theory (A. Papadopoulos, ed.), Volume VII, EMS Publishing House, Zürich, 2020.
• M. Brakalova, Translation of a paper by H. Grötzsch On Some Extremal problems of the conformal mapping II. (from German: Über einige Extremalprobleme der konformen Abbildung II Berichte über die Verhandlungen der Sachsischen Akad. der Wissenschaften zu Leipzig Math.-Physische Klasse. Bd. 80 (1928), 497–502 von Herbert Grötzsch in Leipzig, Vorgelegt von Herrn Koebe) in Handbook of Teichmüller Theory, (A. Papadopoulos, ed.), Volume VII, EMS Publishing House, Zürich, 2020.
• M. Brakalova, Translation from the German of a paper by O. Teichmüller, An application of quasiconformal mappings to the type problem. (Eine Anwendung quasikonformer Abbildungen auf das Typenproblem Deutsche Math. 2, 321–327 (1937)) in Handbook of Teichmüller Theory (A. Papadopoulos, ed.), Volume VII, EMS Publishing House, Zürich, 2020.
• M. Brakalova, Symmetric properties of p-integrable Teichmüller spaces. Analysis and Mathematical Physics, 8 (2018) 541–549, Springer Verlag.
• M. Brakalova, I. Markina and A. Vasil’ev, Extremal functions for modules of systems of measures. J. d’Analyse Math. 133, 1 (2017) 335–359. (arXiv:1409.1626)
• M. Brakalova, I. Markina and A. Vasil’ev, Modules of systems of measures on polarizable Carnot groups. Arkiv för Mat. 54 (2016) 2, 371–401. (originally submitted to arXiv:1409.1626)
• M. Brakalova, On local stability of solutions to the Beltrami equation with degeneration. Proceedings of International Conference in Complex Analysis and Applications’13, Sofia (2013) 67–77.