Bozhidar Velichkov

PREVIOUS POSITIONS AND CURSUS:

- 04/2019 - 05/2020. Associate Professor (Professore Associato) at Universita' degli Studi di Napoli Federico II (Italy);

- 09/2014 - 03/2019. Assistant Professor (Maître de Conférences) at Universite' Grenoble Alpes (France);

- 02/2014 - 08/2014. Post-doc at Universita' di Pisa;

- 10/2010 - 11/2013. PhD at Scuola Normale Superiore and (since 2012) Universite' de Savoie;

- 10/2005 - 10/2010. Student in Mathematics at Scuola Normale Superiore and Universita' di Pisa.


HONORS AND AWARDS:

- 2020. Book Prize UMI

- 2019. I am P.I. of the project ERC Starting Grant VAREG

- 2015. I won PEDR - Prime d’Encadrement Doctoral et de Recherche

- 2015. I was P.I. of the project VariForm financed by Universite' Grenoble Alpes.

- 2013. My PhD Thesis was selected for publication in Edizioni della Normale.


PhD THESIS (discussed in November 2013 at SNS, Pisa):

- Title: "Existence and Regularity Result for Some Shape Optimization Problems"

- Published in: Edizioni della Normale, Tesi 19, Springer 2015, ISBN 978-88-7642-526-4


LINKS:

- My personal web page: www.velichkov.it

- My page on the preprint server CVGMT: http://cvgmt.sns.it/person/336/

- My ArXiv page: https://arxiv.org/a/velichkov_b_1.html


PhD STUDENTS:

- Baptiste Trey (09/2016 - 06/2020) at Universite' Grenoble Alpes.

- Francois Generau (09/2017 - 06/2020) at Universite' Grenoble Alpes.



SELECTED PUBLICATIONS (a complete list can be found on my page www.velichkov.it):

- G. De Philippis, L. Spolaor, B. Velichkov. "Regularity of the free boundary for the two-phase Bernoulli problem."
Invent. Math. (2021).

- M. Engelstein, L. Spolaor, B. Velichkov. "Uniqueness of the blow-up at isolated singularities for the Alt-Caffarelli functional."
Duke Math J., Volume 169, Number 8 (2020), 1541--1601.

- D. Mazzoleni, S. Terracini, B. Velichkov. "Regularity of the optimal sets for some spectral functionals."
Geom. Funct. Anal., Volume 27 (2017), 373–426.

- L. Spolaor, B. Velichkov. "An epiperimetric inequality for the regularity of some free boundary problems: the 2-dimensional case."
Comm. Pure. Appl. Math., Volume 72, Number 2 (2018), 375--421.

- M. Colombo, L. Spolaor, B. Velichkov. "A logarithmic epiperimetric inequality for the obstacle problem."
Geom. Funct. Anal. Volume 28, Number 4 (2018), 1777–1831.

- D. Bucur, D. Mazzoleni, A. Pratelli, B. Velichkov. "Lipschitz Regularity of the Eigenfunctions on Optimal Domains."
Arch. Rat. Mech. Anal. Volume 216 (2015), 117–151.



SELECTED TALKS (a complete list can be found on my page www.velichkov.it):

- "Regularity of the two-phase free boundaries."
Workshop Calculus of Variations (Oberwolfach, 2020).

- "Regularity of the two-phase free boundaries."
XXX Convegno Nazionale di Calcolo delle Variazioni (Levico Terme, 2020).

- "On the logarithmic epiperimetric inequality."
Partial Differentials Equations (Oberwolfach, 2019).

- "Regularity of the one-phase free boundaries." (6 hours mini-cours)
Indam Intensive Period: Shape optimization, control and inverse problems for PDEs (Napoli, 2019).

- "On the logarithmic epiperimetric inequality."
XXIX Convegno Nazionale di Calcolo delle Variazioni (Levico Terme, 2019).

- "Variational approach to the regularity of the singular free boundaries."ETH Zurich, 13/03/2018.

- "Regularity of the free boundaries around isolated singularities." Universite' Paris Sud - Orsay, 26/01/2018.

- "Regularity of the optimal sets for spectral functionals." Max Planck Institut Leipzig, 13/05/2016.

- "Regularity of the optimal sets for spectral functionals." Unuversitat Zürich, 13/04/2016.