Aleksandra Maalaoui (Niepla)

Contact

Department of Mathematics

102 Malott Hall

Cornell University

Ithaca, NY 14853

email (work): an489@cornell.edu

(personal): aleksandra.niepla@gmail.com

About Me

I am a sixth year PhD candidate in mathematics at Cornell University expecting to graduate in August 2021. My research advisor is Camil Muscalu and my research area is in Harmonic Analysis. During my first three years at Cornell I focused my studies on time-frequency analysis tecniques which play a fundamental role in the proofs of L^p estimates for operators such as the Bilinear Hilbert transform and the Biest operator. The topic of my thesis work was proving estimates for iterated fractional integral operators and oscillatory integrals. In particular, we applied our results to prove estimates for Fourier integral operators with rational symbol, which have proven to be relevant in applications to dispersive PDEs.

Here is my CV. Here is my research statement.

Teaching

Current

Spring 2021 - Complex Analysis

Previous

Fall 2020 - Math 1920 Multivariable Calculus for Engineers (Head TA and coordinator)

Spring 2020 - MATH 4280 Introduction to Partial Differential Equations (TA/Grader)

Fall 2019 - This semester I will be on the Hutchinson Fellowship, I will resume teaching in the Spring.

Spring 2019- Math 4180 Complex Analysis (TA/Grader)

Fall 2018 - Math 2930 Differential Equations for Engineers (Head TA)

Spring 2018 - I did not teach this semester.

Fall 2017 - MATH 1920 Multivariable Calculus for Engineers (Head TA)

Spring 2017 - MATH 1920 Multivariable Calculus for Engineers (TA)

Fall 2016 - MATH 1910 Calculus for Engineers (TA)

Mathematics

Publications

Decay Rate of n-linear Oscillatory Integral Operators in R². (with Kevin O'Neill and Zhen Zeng), to published in Proceedings of the American Mathematical Society.
Estimating Oscillatory Integrals of Convolution Type in R^d. (with Kevin O'Neill and Zhen Zeng), in preparation.

Other

Here is a draft of my A-exam presentation: An Overview of the Bilinear Hilbert Transform

Here is a handout I gave out during a final presentation for Math 6150 (PDE): Singular Integral Handout

Here is the final essay I wrote for math 6120 (Real Analysis): Generalization of the Calderon-Zygmund Decomposition

I participated in an REU at Indiana University, Bloomington during the summer of 2014, here is a compilation of our final papers: Indiana REU Summer 2014 Reports

While I was an undergraduate at Rutgers University, I gave a talk about the opportunities offered to math undergrads at Rutgers. While many things may have changed since then, some of the content in these notes may be useful: Math at Rutgers