Largo Bruno Pontecorvo 5, Pisa, Italy

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1 Aleks Jevnikar Curriculum Vitae Name Personal Information Aleks Jevnikar Date of birth December 30, 1987 Place of birth Nationality Work address Web page Trieste, Italy Italian University of Pisa Largo Bruno Pontecorvo 5, Pisa, Italy Current Position Since 02/2018 From 02/2019 Post-doc, University of Pisa, Italy. Advisor: Prof. Matteo Novaga Post-doc, Scuola Normale Superiore, Pisa, Italy. Junior visiting position - Centro de Giorgi 11/ / / /2017 Previous Positions Post-doc,, Italy. Research project: Analytical problems in Mathematical Physics Scientific referent: Prof. Alessandra Celletti Advisor: Prof. Gabriella Tarantello Post-doc,, Italy. Research project: Variational and perturbative aspects in nonlinear differential problems Advisor: Prof. Gabriella Tarantello Education Ph.D. in Mathematics, SISSA, Trieste, Italy. Advisor: Prof. Andrea Malchiodi (Scuola Normale Superiore - Pisa) Mark: cum laude 1/8

2 Master Degree in Mathematics, University of Trieste, Italy (Joint curriculum between SISSA and the University of Trieste). Advisor: Prof. Andrea Malchiodi Mark: 110/110 cum laude Bachelor Degree in Mathematics, University of Trieste, Italy. Advisor: Dr. Martino Prizzi Mark: 110/110 Research Interests My research interests lie in the field of Geometric Analysis, namely in nonlinear elliptic partial differential equations that arise in mathematical physics and geometry. In particular, I mainly deal with Liouville-type equations, Toda systems, Sinh-Gordon equations and Moser-Trudinger inequalities. We investigate existence of solutions, blow-up analysis, Leray-Schauder degree, symmetry and uniqueness issues. Publications [1] A. Jevnikar, An existence result for the mean-field equation on compact surfaces in a doubly supercritical regime, Proc. Royal Soc. Edinburgh A 143 (2013), no. 5, pp ( [2] L. Battaglia, A. Jevnikar, A. Malchiodi, D. Ruiz, A general existence result for the Toda system on compact surfaces, Adv. Math. 285 (2015), ( [3] S. Kallel, A. Jevnikar, A. Malchiodi, A topological join construction and the Toda system on compact surfaces of arbitrary genus, Anal. PDE 8 (2015), no. 8, ( [4] A. Jevnikar, New existence results for the mean field equation on compact surfaces via degree theory, Rend. Semin. Mat. Univ. Padova 136 (2016), ( [5] A. Jevnikar, A note on an multiplicity result for the mean field equation on compact surfaces, Adv. Nonlinear Stud. 16 (2016), no. 2, ( [6] A. Jevnikar, J. Wei, W. Yang, Classification of blow-up limits for Sinh-Gordon equation, Differential and Integral Equations, to appear ( [7] A. Jevnikar, J. Wei, W. Yang, On the topological degree of the mean field equation with two parameters, Indiana Univ. Math. J. 67 (2018), no. 1, ( [8] A. Jevnikar, W. Yang, Analytic aspects of the Tzitzéica equation: blow-up analysis and existence results, Calc. Var. and PDEs 56 (2017), no. 2, 56:43, doi: /s ( 2/8

3 [9] A. Jevnikar, W. Yang, A mean field equation involving positive supported probability measures: blow-up phenomena and variational aspects, Proc. Royal Soc. Edinburgh A, to appear ( [10] A. Jevnikar, Blow-up analysis and existence results in the supercritical case for an asymmetric mean field equation with variable intensities, J. Diff. Eq. 263 (2017), , doi: /j.jde ( [11] C. Gui, A. Jevnikar, A. Moradifam, Symmetry and uniqueness of solutions to some Liouville-type equations and systems, Comm. PDEs., to appear ( [12] D. Bartolucci, A. Jevnikar, Y. Lee, W. Yang, Uniqueness of bubbling solutions of the mean field equations, J. Math. Pures Appl., to appear ( [13] W. Ao, A. Jevnikar, W. Yang, On the boundary behavior for the blow up solutions of the sinh-gordon equation and rank N Toda systems in bounded domains, Preprint (2017) ( [14] D. Bartolucci, A. Jevnikar, Y. Lee, W. Yang, Non degeneracy, Mean Field Equations and the Onsager theory of 2D turbulence, Preprint (2017) ( [15] W. Ao, A. Jevnikar, W. Yang, Wave equations associated to Liouville-type problems: global existence in time and blow up criteria, Preprint (2018) ( [16] D. Bartolucci, C. Gui, A. Jevnikar, A. Moradifam, A singular Sphere Covering Inequality: uniqueness and symmetry of solutions to singular Liouville-type equations, Preprint (2018) ( Seminar Presentations 02/2018 Young in PDE Roma, Sapienza - University of Rome, Italy 02/2018 Variational Methods in Analysis, Geometry and Physics, Scuola Normale Superiore, Pisa, Italy 10/2017 Analysis Seminars, University of Padua, Italy 10/2017 Analysis Seminars, University of Pisa, Italy 06/2017 From students to mathematicians: an excellence master program in Trieste, SISSA, Trieste, Italy 05/2017 Analysis Seminars, Justus-Liebig University, Gießen, Germany 03/2017 University of Texas at San Antonio, Texas, USA 12/2016 University of Basel, Switzerland 06/2016 EWM-EMS Summer School: Geometric and Physical aspects of Trudinger-Moser type inequalities, Institut Mittag-Leffler, Djursholm, Sweden 3/8

4 04/2016 Nonlinear differential problems seminars, Sapienza - University of Rome, Italy 12/2015 Workshop Giornata di Dipartimento 2015,, Italy 12/2015 Differential Equations Seminars,, Italy 02/2015 Analysis Junior Seminars, SISSA, Trieste, Italy 06/2014 Thematic Program on Nonlinear PDEs in Geometry and Physics Conference, University of Notre Dame, Indiana, USA 05/2014 Poster session, SISSA, Trieste, Italy 04/2014 Analysis Junior Seminars, SISSA, Trieste, Italy 01/2014 6th South West Regional PDE Winter School, University of Oxford, UK 01/2014 Conference on variational methods in elliptic equations and systems, University of Lisbon, Portugal 02/2013 University of Warwick, Coventry, UK 07/2012 University of Granada, Spain Forthcoming seminars 04/2018 BIRS Workshop Physical, Geometrical and Analytical Aspects of Mean Field Systems of Liouville Type, Banff, Canada 2018 Justus-Liebig University, Gießen, Germany 2018 Wuhan University, Hubei, China Visits 05/2017 Justus-Liebig University, Gießen, Germany (1 week) 03/2017 University of Texas at San Antonio, Texas, USA (2 weeks) 03/2016 Scuola Normale Superiore, Pisa, Italy (1 week) 07/2015 Scuola Normale Superiore, Pisa, Italy (1 week) 03/2015 University of British Columbia, Vancouver, Canada (1 month) 02/2015 Scuola Normale Superiore, Pisa, Italy (1 week) 09 11/ / / / /2012 University of Warwick, Coventry, UK (4 months) University of Granada, Spain (3 weeks) 09 11/2012 Institut Henri Poincaré, Paris, France (2 months) Forthcoming visits 2018 Justus-Liebig University, Gießen, Germany 4/8

5 2018 Wuhan University, Hubei, China Conferences and Schools Attended 02/2018 Young in PDE Roma, Sapienza - University of Rome, Italy 02/2018 Variational Methods in Analysis, Geometry and Physics, Scuola Normale Superiore, Pisa, Italy 01/2018 2nd Italian-Chilean Workshop in PDE s, Indam, Rome, Italy 06/2017 Nonlinear Analysis Conference, University of Notre Dame s Rome Global Gataway, Rome, Italy 06/2017 From students to mathematicians: an excellence master program in Trieste, SISSA, Trieste, Italy 01/2016 Roma Caput PDE, Sapienza - University of Rome, Italy 06/ EWM-EMS Summer School: Geometric and Physical aspects of Trudinger- Moser type inequalities, Institut Mittag-Leffler, Djursholm, Stockholm 05/2016 New Trends in Calculus of Variations, Accademia Nazionale dei Lincei, Rome, Italy 01/2016 Winter School Ascona 2016: Nonlinear Partial Differential Equations and Geometric Analysis, Ascona, Switzerland 06/2015 Geometric non-linear analysis: Conference on the occasion of Michael Struwe s 60th birthday, ETH, Zurich, Switzerland 01/2015 Complex Patterns in Nonlinear Phenomena, University of Torino, Italy 01/2015 Sixth Itinerant Meeting in PDEs, SISSA, Trieste, Italy 12/2014 Two-day meeting in honor of Antonio Ambrosetti, Venice, Italy 12/2014 Advances and Perspectives in the Calculus of Variations, SISSA, Trieste, Italy 11/2014 Asymptotics for Nonlinear Geometric PDEs, Centro De Giorgi - Scuola Normale Superiore, Pisa, Italy 06/2014 Thematic Program on Nonlinear PDEs in Geometry and Physics Conference, University of Notre Dame, Indiana, USA 06/2014 Thematic Program on Nonlinear PDEs in Geometry and Physics Graduate and Postdoc Summer School, University of Notre Dame, Indiana, USA 05/2014 Recent Trends in Nonlinear Partial Differential Equations and Applications, University of Trieste, Italy 03/2014 Spring school on nonlinear PDEs, Sapienza - University of Rome, Italy 01/2014 6th South West Regional PDE Winter School, University of Oxford, UK 01/2014 Variational methods in elliptic equations and systems, University of Lisbon, Portugal 09/2013 A day in Analysis and Geometry, University of Warwick, Coventry, UK 09/2012 Conformal and Kahler Geometry, Institut Henri Poincaré, Paris, France 10/2012 Geometry and Physics, Institut Henri Poincaré, Paris, France 11/2012 Geometric PDEs, Institut Henri Poincaré, Paris, France 07/2012 A day in honor of Antonio Ambrosetti, Venice, Italy 06/2012 ICTP-ESF School and Conference on Geometric Analysis, ICTP, Trieste, Italy 5/8

6 Forthcoming Conferences and Schools 04/2018 BIRS Workshop Physical, Geometrical and Analytical Aspects of Mean Field Systems of Liouville Type, Banff, Canada Honors and Awards Fellowship for Ph.D. studies, based on international exams, SISSA, Trieste, Italy 2014 Prize Irene Galante for the best M.Sc. thesis in the period , University of Trieste, Italy 2011 Diploma supplement for the Master of Science in Mathematics, SISSA, Trieste, Italy (Diploma for students of the joint curriculum between SISSA and the University of Trieste) Teaching experience 2017/18 Teaching assistant for the course Mathematical Analysis I, Faculty of Engineering, 2017/18 Teaching assistant for the course Mathematical Analysis I - taught in English, Faculty of Engineering, 2017/18 Teaching assistant for the course Calculus - taught in English, Global Governance, Faculty of Economics, 2017/18 Math pre-courses - taught in English, Global Governance, Faculty of Economics, 2016/17 Teaching assistant for the course Mathematical Analysis I, Faculty of Engineering, 2016/17 Teaching assistant for the course Mathematical Analysis I - taught in English, Faculty of Engineering, 2015/16 Teaching assistant for the course Mathematical Analysis I, Faculty of Engineering, 2015/16 Teaching assistant for the course Mathematical Analysis I - taught in English, Faculty of Engineering, Referee activity Referee for the journals: Calculus of Variations and Partial Differential Equations, Proceedings of the Royal Society of Edinburgh: Section A. Research groups PRIN Nonlinear elliptic problems in the study of vortices and related topics PI: Prof. A. Malchiodi PRIN Variational and perturbative aspects of nonlinear differential problems PI: Prof. A. Malchiodi 6/8

7 PRIN Variational Methods and Nonlinear PDEs PI: Prof. A. Malchiodi FIRB Analysis and Beyond PI: Prof. A. Malchiodi Languages Italian Slovene English Mother tongue Mother tongue Professional proficiency Referees Prof. Andrea Malchiodi Prof. Gabriella Tarantello Prof. Jun-cheng Wei Scuola Normale Superiore Piazza dei Cavalieri 7, Pisa, Italy Via della Ricerca Scientifica 1, Roma, Italy University of British Columbia V6T 1Z2 Vancouver, Canada Research topics On one side we consider the Toda system, a Liouville-type system arising in Mathematical Physics in the non-abelian Chern-Simons theory and in Geometry in the description of holomorphic curves in CP n. The approach is based on its variational structure and associated energy functional. We derive new improved Moser-Trudinger inequalities which allow us to carry on min-max methods (and Morse theory) yielding existence of solutions. The existence issue in a general setting is still open. On the other hand we consider the Sinh-Gordon equation, a Liouville-type equation arising in fluid dynamics. The existence issue is addressed by exploiting its variational structure and new improved Moser-Trudinger inequalities. As for the Toda system, the existence of solutions in a general setting is still open. Moreover, the blow-up analysis is performed yielding quantization/non-quantization of blow-up masses and exclusion of boundary blow-up points. However, the general blow-up picture has to be completed. Finally, some partial results concerning the Leray-Schauder degree are obtained. More recently, we investigate on symmetry and uniqueness issues concerning Liouvilletype problems, both on bounded domains and on spheres. The argument is based on the Alexandrov-Bol inequality and on the Sphere Covering Inequality which estimates the total mass of two different solutions to a Liouville equation. 7/8

8 In a recent project we are concerned with the bifurcation diagram of the standard Liouville equation, namely the mean field equation related to the Onsager description of two-dimensional turbulence, showing the uniqueness and non degeneracy of its bubbling solutions. Exploiting the latter analysis we study negative specific heat states in the Onsager theory proving that the related entropy is convex. 8/8