PhD Student in Harmonic Analysis

I am a PhD students in harmonic analysis since 2017. My advisor is prof. Jacek Dziubański. My research concerns some aspect of harmonic analysis (i.e. characterizations of Hardy spaces, multipliers, singular integral operators, semigroups of operators) and generalizations of them (i.e. in the rational Dunkl setting).

Curriculum Vitae

Education

  • University of Wrocław
    PhD Studies, Mathematics, 2017-...
  • University of Wrocław
    Master's degree, Mathematics, 2015-2017.
    Specialty: theoretical mathematics.
    Advisor: Jacek Dziubański, Full Professor.
    Thesis topic: "On localized sharp functions".
  • University of Wrocław
    Bachelor's degree, Mathematics, 2012-2015.
    Specialty: theoretical mathematics.
  • University of Wrocław
    Bachelor's degree, Computer Science, 2012-2015.

Seminar talks

  • Fefferman-Phong inequality and its applications in the rational Dunkl setting, Analiza harmoniczna i rozwinięcia ortogonalne, Wrocław, Poland, 26.02.2020 and 4.03.2020 (www)
  • Singular integrals in the rational Dunkl setting, Analiza harmoniczna i rozwinięcia ortogonalne, Wrocław, Poland, 16.10.2019 (www)
  • Dunkl theory and Hörmander's multiplier theorem in the rational Dunkl setting, , Seminario di Matematica, Pisa, Italy, 9.04.2019 (www)
  • Hörmander's multiplier theorem for the Dunkl transform, , Functional Analysis seminar, Wrocław, Poland, 29.11.2018 (www)
  • Hörmander's multiplier theorem for the Dunkl transform, Analiza harmoniczna i rozwinięcia ortogonalne, Wrocław, Poland, 10.10.2018 and 17.10.2018 (www)
  • Hardy spaces in the rational Dunkl setting, Analiza harmoniczna i rozwinięcia ortogonalne, Wrocław, Poland, 29.05.2018 (www)
  • Dunkl operators: heat kernel estimates and applications, Theory of Markov Semigroups and Schrödinger Operators, Wrocław, Poland, 18.05.2018 (www)
  • Hardy spaces in the rational Dunkl setting, Functional Analysis seminar, Wrocław, Poland, 26.04.2018 (www)
  • Remarks on localizated sharp functions on certain sets in Rn, Oberseminar Harmonic Analysis, Kiel, Germany, 19.04.2018 (www)
  • Remarks on localizated sharp functions on certain sets in Rn, Analiza harmoniczna i rozwinięcia ortogonalne, Wrocław, Poland, 22.03.2017 (www)
  • Remarks on localizated sharp functions on certain sets in Rn, Functional Analysis seminar, Wrocław, Poland, 23.02.2017 (www)

Conference talks

  • On semigroups associated with Dunkl operators, Jubileuszowy Zjazd Matematyków Polskich w stulecie PTM, (www), Kraków, Poland, 2019.
  • On semigroups associated with Dunkl operators, Probability and Analysis 2019, (www),Będlewo, Poland 2019 (slides).
  • Harmonic analysis in the rational Dunkl setting, Joint meeting of the Italian Mathematical Union, the Italian Society of Industrial and Applied Mathematics and the Polish Mathematical Society (www), Wrocław, Poland 2018.
  • Remarks on localizated sharp functions on certain sets in Rn,Probabilistic Aspects of Harmonic Analysis in honor of Professor Ewa Damek (www), Będlewo, Poland 2018.

Organizing activities

  • Organizing Committee Member, Probabilistic Aspects of Harmonic Analysis in honor of Professor Ewa Damek (www), Będlewo, Poland 2018.
  • Organizing Committee Member, Analysis and Applications in honor of Professor Elias M. Stein (www), Wrocław, Poland 2017.

Grants

  • Grant NCN 2017/25/B/ST1/00599, Harmonic analysis related to differential, difference and differential-difference operators (principal investigator M. Preisner).

Awards

  • Award of the Polish Mathematical Society for Young Mathematicians (www)
  • First prize in the student competition "Krok w przyszłość" organized by mBank (www)
  • Second prize in the J. Marcinkiewicz Competition for the best Master’s thesis in Mathematics (www)
  • Best Master’s Thesis of the year, Marshal’s of Lower Silesia Award (www)
  • Finalist of Polish Mathematical Olympiad (www)

Conferences

  • Jubileuszowy Zjazd Matematyków Polskich w stulecie PTM (www), Kraków, Poland, 2019.
  • 4th BCAM-UPV/EHU summer school on harmonic analysis and PDEs: Restriction theory (www), Bilbao, Spain, 2019 (certificate of attendance).
  • Probability and Analysis 2019 (www), Będlewo, Poland 2019.
  • Joint meeting of the Italian Mathematical Union, the Italian Society of Industrial and Applied Mathematics and the Polish Mathematical Society (www), Wrocław, Poland, 2018.
  • INdAM meeting Geometric Aspects of Harmonic Analysis a conference on the occasion of Fulvio Ricci’s 70th birthday (www), Cortona, Italy, Cortona, Italy, 2018.
  • Probabilistic Aspects of Harmonic Analysis in honor of Professor Ewa Damek (www), Będlewo, Poland 2018.
  • Analysis and Applications in honor of Professor Elias M. Stein (www), Wrocław, Poland 2017.
  • Workshop Harmonic analysis and its interactions: in honour of Tony Carbery (www), Edinburgh, Great Britain 2017.
  • Probability and Analysis (www), Będlewo, Poland 2017.
  • Probabilistic Aspects of Harmonic Analysis (www), Będlewo, Poland 2016.

Minor conferences, workshops, schools and other

  • "Algebra vincit omnia" - obóz letni KNMT, Pisary, Poland, 2019. I have given a mini course on Fourier analysis during this summer school (certificate).
  • Per algebra ad astra - letnia szkoła KNMT, Pisary, Poland, 2018.
  • V School of Analysis in memory of A. Pełczyński (www), Będlewo, Poland 2017.
  • XI Zimowa Szkoła Matematyki KNMT, Będlewo, Poland 2016.
  • Toruńska Letnia Szkoła Matematyki (www), Toruń, Poland 2016.
  • Ogólnopolska Matematyczna Konferencja Studentów "OMatko!" (www), Wrocław, Poland 2016.
  • X Zimowa Szkoła Matematyki KNMT(www), Będlewo, Poland 2015.
  • Horizons in Mathematics - WCMCS conference for students (www), Będlewo, Poland 2016.
  • 18th International Workshop for Young Mathematicians Algebraic and Differential Topology,(www), Kraków, Poland 2015.
  • Małe Ciche Niskowymiarowe Tatra conference in Low-dimensional topology(www), Małe Ciche, Poland 2015.
  • Letnia Szkoła Matematyki(www), Lądek Zdrój, Poland 2015.
  • Horizons in Mathematics - WCMCS conference for students (www), Będlewo, Poland 2015.
  • Ogólnopolska Matematyczna Konferencja Studentów "OMatko!" (www), Wrocław, Poland 2015.
  • IX Zimowa Szkoła Matematyki KNMT(www), Będlewo, Poland 2014.

Research Interests

  • Harmonic Analysis
  • Maximal Operators
  • Operators in harmonic analysis
  • Hardy Spaces
  • Dunkl Theory
  • Multipliers
  • Connections of harmonic analysis and PDE
  • Schrödinger operators

Publications

  • Dziubański, J., Hejna, A. Remarks on localized sharp functions on certain sets in Rn, Monatsh Math (2018)
  • Anker, J.-Ph., Dziubański, J., Hejna, A. Harmonic functions, conjugate harmonic functions and the Hardy space H1 in the rational Dunkl setting, JFAA (2019)
  • Hejna, A. Hardy spaces for the Dunkl harmonic oscillator, to appear in Math. Nach.
  • Dziubański, J., Hejna, A. Remark on atomic decompositions for Hardy space H1 in the rational Dunkl setting, Studia Math. (2020)
  • Dziubański, J., Hejna, A. Hörmander's multiplier theorem for the Dunkl transform, JFA (2019)
  • Dziubański, J., Hejna, A. On semigroups generated by sums of even powers of Dunkl operators
  • Dziubański, J., Hejna, A. Singular integrals in the rational Dunkl setting
  • Hejna, A. Schrödinger operators with reverse Hölder class potentials in the Dunkl setting and their Hardy spaces
  • Hejna, A. Behavior of eigenvalues of certain Schrödinger operators in the rational Dunkl setting
  • Dziubański, J., Hejna, A. Upper and lower bounds for Littlewood-Paley square functions in the Dunkl setting

Master's thesis (in Polish)

  • Hejna, A. O zlokalizowanych sharp funkcjach (link)