My research is currently supported by NSF Analysis grant DMS-2050113.

Previous funding:

- Email : malik.younsi@gmail.com

- Office : Physical Science Building (PSB) 321

- M. Younsi, Continuous analytic capacity, rectifiability and holomorphic motions, submitted.
- T. Ransford, M. Younsi and W.-H. Ai, Continuity of capacity of a holomorphic motion,
*Adv. Math.*374 (2020), 107376. - D. Ntalampekos, M. Younsi, Rigidity theorems for circle domains,
*Invent. Math.*220 (2020), 129-183. - S. Pouliasis, T. Ransford and M. Younsi, Analytic Capacity and Holomorphic Motions,
*Conform. Geom. Dyn.*23 (2019), 130-134. - M. Younsi, Peano curves in Complex Analysis,
*Amer. Math. Monthly*126 (2019), no. 7, 635-640. - T. Richards, M. Younsi, Computing polynomial conformal models for low-degree Blaschke products,
*Comput. Methods. Funct. Theory*19 (2019), no. 1, 173-182. - M. Younsi, Analytic Capacity : computation and related problems,
*The First NEAM: Conference Proceedings*, Theta Ser. Adv. Math. 22 (2018), 121-152. - M. Younsi, On the analytic and Cauchy capacities,
*J. Anal. Math.*135 (2018), no. 1, 185–202. - M. Younsi, Removability and non-injectivity of conformal welding,
*Ann. Acad. Sci. Fenn. Math.*43 (2018), 463-473. - K. Lindsey, M. Younsi, Fekete polynomials and shapes of Julia sets,
*Trans. Amer. Math. Soc.*371 (2019), 8489-8511. - M. Younsi, Removability, rigidity of circle domains and Koebe's Conjecture,
*Adv. Math.*303 (2016), 1300-1318. - T. Richards, M. Younsi, Conformal models and fingerprints of pseudo-lemniscates,
*Constr. Approx.*45 (2017), no. 1, 129-141. - M. Younsi, Shapes, fingerprints and rational lemniscates,
*Proc. Amer. Math. Soc.*144 (2016), 1087-1093. - M. Younsi, On removable sets for holomorphic functions,
*EMS Surv. Math. Sci.*2 (2015), no. 2, 219-254. - M. Fortier Bourque, M. Younsi, Rational Ahlfors functions,
*Constr. Approx.*41 (2015), no. 1, 157-183. - M. Younsi, T. Ransford, Computation of analytic capacity and applications to the subadditivity problem,
*Comput. Methods. Funct. Theory*13 (2013), no. 3, 337-382.

- M. Younsi, A. Lacasse, A combinatorial conjecture from PAC-Bayesian machine learning, submitted.

- Calcul de la capacité analytique et fonctions d'Ahlfors rationnelles, Ph.D. Thesis, Université Laval (2014).
- La méthode de renormalisation de Zalcman et ses applications, Masters Thesis, Université Laval (2010).

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Below is the filled Julia set of a polynomial of degree 351 approximating the shapes of a heart, a fish and a diamond. Here, a zoomed portion of the boundary of the fish where one can see small distorted copies of the heart and the diamond. Below is the filled Julia set of a polynomial of degree 701 approximating the shape of a rabbit. Below is the filled Julia set of a polynomial of degree 701 approximating the shape of Batman. Finally, below is the filled Julia set of a polynomial of degree 2001 approximating the initials K,L,M,Y.