I am interested in the well-posedness theory and dynamics of partial differential equations.

Papers

Journal publications

  1. A note on global existence for the Zakharov system on the torus, submitted.

  2. (with N. Tzirakis). Low-regularity global well-posedness for the Klein-Gordon-Schrödinger system on the half line, submitted.

  3. (with N. Tzirakis). Low-regularity well-posedness for the “good” Boussinesq equation on the half-line. J. Differential Equations 262(12), 5824–5859.

  4. Smoothing for the Klein-Gordon-Schrodinger and Zakharov systems on Euclidean spaces. SIAM J. Math. Anal. 49 (5), 4206–4231.

  5. Smoothing and global attractors for the Majda-Biello system on the torus. Differential Integral Equations 29 no. 3/4 (2016), 269–308.

Conference proceedings and other publications

  1. (with collaborators). Network behavioral analytics. Department of Defense internal publication, August 2014.

  2. (with M. Bayeh, T. Lindsey, S. Melczer, N. Orlow, and Z. Voller). Ink constrained halftoning with application to QR codes. Color Imaging XIX, IS&T/SPIE Electronic Imaging Symposium, San Francisco, CA. February 2014.

  3. A smoothing estimate for the nonlinear Schrodinger equation, UIUC Research Experiences for Graduate Students report, August 2013.

Selected presentations

  • Global existence for the periodic Zakharov system. SIAM Annual Meeting, Portland, OR, July 2018.
  • Well-posedness for dispersive PDEs on the half-line. MIT Analysis Seminar, MIT, Cambridge, MA, November 2017.
  • Dynamics of a periodic coupled KdV system. Boston University Dynamics Seminar, BU, Boston, MA, November 2017.
  • Dynamics of the “good” Boussinesq on the half-line. FRG Conference, Princeton University, Princeton, NJ, October 2017,
  • Well-posedness and smoothing for the “good” Boussinesq on a half-line. INDAM-MSRI-SMI-GSSI Summer Graduate School, Cortona, Italy, July 2017.
  • Well-posedness and smoothing for the “good Boussinesq” equation on the half-line. Ohio River Analysis Meeting, UC, Cincinnati, OH, March 2017.
  • Smoothing for the Zakharov system on higher-dimensional Euclidean spaces. FRG conference, MIT, Cambridge, MA, September 2016.
  • Smoothing estimates for dispersive partial differential equations. Harmonic Analysis and Differential Equations Seminar, UIUC, Urbana, IL, March 2016.
  • Dynamics of the periodic Majda-Biello system. New Mexico Analysis Seminar, UNM, Albuquerque, NM, February 2016.
  • Smoothing and Global Attractors for the Periodic Majda-Biello System. AMS Central Sectional Meeting, MSU, East Lansing, MI, March 2015.
  • Network Behavioral Analytics. Department of Defense briefing, July, 2014.
  • Sequences and Conserved Quantities via Cluster Algebras. UIUC REGS Day, UIUC, Urbana, IL, October 2012.
  • Differential Forms and the Generalized Stokes’ Theorem. MAA Mathfest, Lexington, KY, August 2011.

Travel

  • FRG Conference, University of Chicago, Chicago, IL, October 19-21, 2018.
  • IAS/PCMI Harmonic Analysis Program, Park City, UT, July 14–20, 2018.
  • SIAM Annual Meeting, Portland, OR, July 9–13, 2018.
  • Conference on Nonlinear Waves, Brown University, Providence, RI. May 14–17, 2018.
  • Nonlinear Waves: Stability vs. Turbulence, Georgia Institute of Technology, Atlanta, GA. May 7–10, 2018.
  • AMS Sectional Meeting, Northeastern University, Boston, MA, April 21-22, 2018.
  • FRG Conference for Women in Mathematics, University of Massachusetts, Amherst, MA, March 2–4, 2018.
  • FRG Conference, Princeton University, Princeton, NJ. October 20–22, 2017.
  • INDAM-MSRI-SMI-GSSI Summer Graduate School, Cortona, Italy. July 17–28, 2017.
  • Ohio River Analysis Meeting, UC, Cincinnati, OH. March 25–26, 2017.
  • FRG Conference. MIT, Cambridge, MA. September 9–11, 2016.
  • Nonlinear Waves Summer School, IHES, Bures-sure-Yvette, France. July 16–28, 2016.
  • Mathematical modeling internship, CERT, Software Engineering Institute, Carnegie Mellon University. Pittsburgh, PA. Summer 2016
  • New Mexico Analysis Seminar. University of New Mexico, Albuquerque, NM. February 19–21, 2016.
  • New challenges in PDE: Deterministic dynamics and randomness in high and infinite dimensional systems. MSRI, Berkeley, CA. October 19–30, 2015.
  • Introductory Workshop: Randomness and long time dynamics in nonlinear evolution differential equations. MSRI, Berkeley, CA. August 24–28, 2015.
  • Communications Consulting internship. San Diego, CA. June 18–August 22, 2015.
  • Workshop for Women in Analysis and PDE. IMA, Minneapolis, MN. May 28–31, 2015.
  • AMS Central Sectional Meeting. Michigan State University, East Lansing, MI. March 14–15, 2015.
  • Midwest PDE Meeting. University of Illinois, Urbana, IL. October 18–19, 2014.
  • C.E. Kenig Conference. University of Chicago, Chicago, IL. September 19–21, 2014.
  • Summer School on Dispersive PDEs. MSRI, Berkeley, CA. June 16–27, 2014.
  • Defense Department mathematics internship. May 19–August 22, 2014.
  • Careers and Opportunities in Industry for Mathematical Scientists. IMA, Minneapolis, MN. April 7–9, 2014.
  • Joint Mathematics Meetings. Baltimore, MD. January 15–18, 2014.
  • Mathematical Modeling in Industry XVII. IMA, Minneapolis, MN. August 7–16, 2013.
  • Joint Mathematics Meetings. Boston, MA. January 4–7, 2012.
  • MAA MathFest. Lexington, KY. August 4–6, 2011.
  • Summer Program for Women in Mathematics. George Washington University, Washington D.C. June 25–July 30, 2011.