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

  • 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

  • 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.

Research stays

  • Christian-Albrechts-Universität zu Kiel, Kiel, Germany (upon invitation of professor Detlef Müller, one week), April 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

  • 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

  • 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

  • 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
  • Hardy Spaces
  • Dunkl Theory
  • Multipliers

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
  • Hejna, A. Hardy spaces for the Dunkl harmonic oscillator
  • Dziubański, J., Hejna, A. Remark on atomic decompositions for Hardy space H1 in the rational Dunkl setting
  • Dziubański, J., Hejna, A. Hörmander's multiplier theorem for the Dunkl transform

Master's thesis (in Polish)

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

Konsultacje w semestrze letnim 2018/2019

Poniedziałki 14:00-15:00, pokój 10.3 (na samej górze). W razie braku możliwości przyjścia na konsultacje w podanym terminie możliwe jest mailowe umówienie się na konsultacje w innym terminie.

Funkcje analityczne 1, 2018/2019

Czwartki, 12:15-14:00, sala 604. Listy zadań dostępne są na stronie internetowej wykładowcy.