CV

Education:

• PhD:  University of California, Irvine

  • March 2023

  • Doctoral advisors: Svetlana Jitomirskaya (Georgia Tech) and Wencai Liu (Texas A&M University)

• Master’s Degree:  University of California, Irvine

  • December 2020

• Bachelor’s Degree:  University of California, Irvine (2014-2018)

  • Magna Cum Laude in 2018 with University Honors and Campuswide Honors

  • Graduated with Mathematics Department Honors

Publications (see Research tab for links):

• M. Powell. Continuity of the Lyapunov exponent for analytic multi-frequency quasiperiodic cocycles. 2022. Preprint. arXiv:2210.09285 (Available here)

• M. Powell. Positivity of the Lyapunov exponent for analytic quasiperiodic operators with arbitrary finite-valued background. June 2022. arxiv:2206.04159 (Available here)

• M. Landrigan and M. Powell. Fine dimensional properties of spectral measures. J. Spectr. Theory, to appear. 2022 arxiv:2107.10883 (Available here)

• S. Jitomirskaya and M. Powell. Logarithmic quantum dynamical bounds for arithmetically defined ergodic Schrodinger operators with smooth potentials. To appear in Analysis at Large: Dedicated to the Life and Work of Jean Bourgain, Springer ( A. Avila, M. Rassias, Y. G. Sinai, eds.) November 2021. arxiv:2110.11883 (Available here)

• M. Powell. Fractal dimensions of spectral measures of rank one perturbations of a positive self-adjoint operator. J. Math. Anal. App., 475(2):1803–1817, July 2019. (Available here)

Conferences/Invited Speaker/Seminars:

• GaTech Mathematical Physics seminar (Jan 2023)

  • Title: Regularity results for the Lyapunov exponent for analytic multifrequency quasi-periodic cocycles

• UC Berkeley joint Mathematics and Physics seminar (Dec 2022)

• University of Houston Annual SIAM Chapter Meeting (Nov 2022)

• Rice University Spectral Theory Seminar (Oct 2022)

  • Title: Continuity of the Lyapuov exponent for analytic multifrequency quasi-periodic cocycles

• GLAMP at MSU (June 2022)

  • Title: Positivity of Lyapunov exponents for analytic quasiperiodic operators with arbitrary finite-valued background

• New directions in quantum systems (June 2022)

  • Title: Positivity of Lyapunov exponents for analytic quasiperiodic operators with arbitrary finite-valued background

• BIRS meeting for almost periodic operators (April 2022)

  • Title: Positivity of Lyapunov exponents for analytic quasiperiodic operators with arbitrary finite-valued background

• GLAMP at Oberlin College (June 2019)

Conference Organization

• AMS Special Session at Georgia Tech (March 2023)

• 37th Western States Mathematical Physics meeting (March 2020)

Recent journal referees

• Journal of Spectral Theory (2022)

Pedagogical Lecture Series:

• 2022: 

  • 15-week mini course: Continuity of the Lyapunov exponent for multifrequency quasiperiodic Schrödinger operators

• 2018 - present:  Ergodic Schrödinger operators seminar.

  • 2021:  Dynamical bounds for quasiperiodic operators.

  • 2020:  Spectral dimension of 1D operators.

  • 2019:  Kotani theory.

  • 2018:  Hausdorff measures and quantum dynamics.

• Winter 2021 Texas A&M University Seminar: Critical almost Mathieu operators in the rational case.

  • The Aubry-Andre conjecture.

• Fall 2020 Texas A&M University Seminar: Periodic Schrödinger operators.

  • Gilbert-Pearson subordinacy theory.

Awards and Honors:

• 2022:  UCI math department von Neumann Award

• 2021:  UCI math department Connelly Award for outstanding research and teaching

• 2018:  Accepted into Phi Beta Kappa honor society

• 2018:  UCI Chancellor’s Award for Outstanding Undergraduate Research

• 2016:  Accepted into Pi Mu Epsilon math honors society

Outreach:

• Undergraduate mentor 2022: Olufemi Aruleba

• 2021: Putnam exam

  • Putnam exam preparation course (UCI MATH 194)

  • Local sign-up, logistics

• 2020 - present:  Irvine Formula of Unity local competition manager and organizer

• 2019 - present:  Irvine Tournament of the Towns organizer

• 2018 - 2020:  UCI AMS Chapter secretary/webmaster 

• 2017 - present:  Irvine Tournament of the Towns grader and proctor

• 2017:  Guest speaker as leader of UCI Math Circle Level 1

• 2016 - present:  Pi mu epsilon math honors society

  • 2016 talk: The Baire Category Theorem

  • 2017 talk: The Open Mapping Theorem

Teaching Experience:

• 2023 - present: Instructor at GaTech

  • Spring 2023: Math 4320 (Complex Analysis)

• 2020 - 2022: Instructor at UCI

  • Winter 2022:  3D (differential equations)

  • Summer 2021:  5B (mathematics for the life sciences)

• 2018 - present:  TA in the UCI math department:

  • Fall 2022:  140A (introduction to analysis)

  • Fall 2022:  194 (problem solving seminar and the Putnam exam)

  • Winter 2021:  210B (graduate real analysis)

  • Fall 2020:  210A (graduate real analysis)

  • Summer 2020:  140B (introduction to analysis)

  • Spring 2020:  210C (graduate real analysis)

  • Winter 2020:  140B (introduction to analysis)

  • Winter 2020:  3A (linear algebra)

  • Summer 2019:  2E (calculus III) 

  • Spring 2019:  2D (calculus II)

  • Winter 2019:  3D (differential equations)

  • Fall 2018:  3A (linear algebra)

• Spring 2016:  Math 141 (topology) grader