Marco Fraccaroli

RG Analysis and Partial Differential Equations


Archives of the Mathematisches Forschungsinstitut Oberwolfach


Contact

Postal address:
Mathematisches Institut
Universität Bonn
Endenicher Allee 60
D - 53115 Bonn
         Office:
Endenicher Allee 60, N2.008
Phone: +49 (0) 228 73-6888
E-mail: mfraccar (at) math.uni-bonn.de

ORCiD: ORCID iD iconhttps://orcid.org/0000-0003-1120-8707

Google scholar: Marco Fraccaroli

arXiv: Marco Fraccaroli

I am currently a PhD student. My advisor is Prof. Dr. Christoph Thiele.
My CV.

Research interests

My main areas of interest are real and harmonic analysis.

My first main research interest lies in Lp theory for outer measure spaces. In particular, I am studying the duality properties of the single and double iterated outer Lp spaces.

My second main research interest lies in time-frequency analysis. In particular, I am studying boundedness properties of multilinear forms with symmetries given by modulations and matrix dilations.

Finally, I have studied the uniform restriction problem for convex planar curves, without any additional assumption on their smoothness.

Publications and preprints

Duality for outer Lpμ(ℓr) spaces and relation to tent spaces.
in J. Fourier Anal. Appl. 27, 67 (2021). https://doi.org/10.1007/s00041-021-09869-4
arXiv preprint: https://arxiv.org/abs/2001.05903

Duality for double iterated outer Lp spaces.
arXiv preprint: https://arxiv.org/abs/2104.09472
Submitted, April 2021.

Uniform Fourier restriction for convex curves in ℝ2.
arXiv preprint: https://arxiv.org/abs/2111.06874
Submitted, November 2021.

A uniform phase-plane projection. (with Olli Saari, Christoph Thiele)
In preparation.

Boundedness of multilinear forms associated with determinantal multipliers. (with Gennady Uraltsev)
In preparation.

Theses

My Master’s Degree was obtained from Universität Bonn, Germany, by March 1st, 2017, with a thesis on the topic of:
On distributions with GL2(ℝ) dilation symmetry.
Advisor: Prof. Dr. Christoph Thiele.
In this thesis we give a complete classification of the tempered distributions homogeneous of a certain degree under the GLn(ℝ) dilations for n=1 and n=2.

My Bachelor’s Degree was obtained from Università degli Studi di Padova, Italy, by September 26th, 2014, with a thesis on the topic of:
The Yamabe equation: analysis and solutions via the moving sphere method and the maximum principle (in Italian).
Advisor: Prof. Dr. Roberto Monti.

Teaching

Tutoring exercise class for V4B5: Real and Harmonic Analysis (summer term 2018).

Course notes of V4B5: Real and Harmonic Analysis (winter term 2016/2017).

Seminars coorganized

Graduate seminar on Advanced topics in PDE (summer term 2021).