I am currently an Associate Professor in the Department of Mathematics at the University of Hawaii. Previously, I was an Acting Assistant Professor in the Department of Mathematics at the University of Washington, working with Don Marshall. Before that, I spent two years as a NSERC Postdoctoral Fellow at the Department of Mathematics of Stony Brook University, working with Chris Bishop. I did my Ph.D. at Université Laval and my thesis advisor was Thomas Ransford.
My main interests are in complex analysis, more precisely geometric function theory. This includes subjects such as removability, extremal problems in spaces of analytic functions (mainly analytic capacity), conformal and quasiconformal mappings, conformal welding, etc. I am also interested in holomorphic dynamics, numerical methods in complex analysis, Schramm-Loewner Evolution and potential theory.
My research is currently supported by NSF Analysis grant DMS-2050113. During Fall 2023, I will be visiting the CRM (Centre de Recherches Mathématiques), funded by the Simons-CRM Scholar-in-Residence Program.
Simons Foundation Collaboration Grants for Mathematicians 712236.
NSF Analysis Grant DMS-1758295 (formerly DMS-1664807).
Faculty Mentoring Grant for Summer Undegraduate Research and Creative Works sponsored by the Undergraduate Research Opportunities Program.
Email : firstname.lastname@example.org
Office : Physical Science Building (PSB) 321
University of Hawaii :
MATH 331 (Introduction to Real Analysis) in Spring 2023.
MATH 649D (Topics: Brownian Motion and Harmonic Measure) in Fall 2022.
MATH 633 (Functional Analysis) in Spring 2022.
MATH 244 (Calculus IV) in Fall 2021.
MATH 241 (Calculus I) in Fall 2021.
MATH 644 (Analytic Function Theory) in Spring 2021.
MATH 252A(Accelerated Calculus II) in Spring 2021.
MATH 251A (Accelerated Calculus I) in Fall 2020.
MATH 331 (Introduction to Real Analysis) in Spring 2020.
MATH 311(Introduction to Linear Algebra) in Spring 2020.
MATH 649D (Topics: Complex Analysis and Riemann Surfaces) in Fall 2019.
MATH 444 (Complex Analysis) in Spring 2019.
MATH 241 (Calculus I) in Fall 2018.
MATH 631 (Theory of Functions of a Real Variable) in Fall 2018.
MATH 444 (Complex Analysis) in Spring 2018.
University of Washington :
MATH 307 K (Introduction to Differential Equations) in Spring 2017.
MATH 307 J,K (Introduction to Differential Equations) in Winter 2017.
MATH 307 P (Introduction to Differential Equations) in Autumn 2016.
MAT 627 (Topics in Complex Analysis: Loewner Theory, with an introduction to SLE) in Spring 2016.
MAT 200 (Logic, Language and Proof) in Fall 2015.
MAT 550 (Real Analysis II) in Spring 2015.
A. Fuhrer, T. Ransford and M. Younsi,
Holomorphic motions, dimension, area and quasiconformal mappings, J. Math. Pures Appl. 177 (2023), 455-483.
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.
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.
Analytic Capacity : computation and related problems, The First NEAM: Conference Proceedings, Theta Ser. Adv. Math. 22 (2018), 121-152.
On the analytic and Cauchy capacities, J. Anal. Math. 135 (2018), no. 1, 185–202.
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.
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.
Shapes, fingerprints and rational lemniscates, Proc. Amer. Math. Soc. 144 (2016), 1087-1093.
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.
As a Summer research project part of the Undergraduate Research Opportunities Program, Irvin Chang and I developed an executable program for the numerical computation of Analytic Capacity:
here for more information and to download the program.
Here are some pictures from the paper Fekete polynomials and shapes of Julia sets.
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.