About Me

I am an Assistant Professor in the Department of Mathematical Sciences at the University of Cincinnati. Previously, I was a postdoc at the University of Michigan, where my research mentor was Peter D. Miller. My PhD thesis advisor was Irina Nenciu. My research has so far focused on problems arising in nonlinear wave formation and propagation.

Interests

  • Nonlinear waves
  • Integrable systems and their perturbations
  • Riemann-Hilbert problems
  • Dispersive PDEs

Education

  • PhD in Mathematics, 2015

    University of Illinois at Chicago

  • BSci & MSci in Mathematics, 2009

    Bogazici University

Projects

Rogue Wave Formation and Asymptotics for Large-Order Coherent Structures

Asymptotic properties of large-order coherent structures in nonlinear integrable wave models and dynamical stability properties of rogue waves.

A Robust Inverse Scattering Transform for Arbitrary Spectral Singularities

Development of a robust inverse scattering transform to treat arbitrary spectral singularities, in particular including rogue wave solutions of nonlinear integrable dispersive PDEs.

Numerical Inverse Scattering Transforms

Making solutions of integrable nonlinear dispersive wave equations computationally available to the nonlinear waves community using their Riemann-Hilbert problem representations via developing numerical inverse scattering transform tools. Riemann-Hilbert problems play the role of Fourier-type integral representations we have for solutions of linear problems.

Solitary Wave Resolution: Long-Time Asymptotics for Near-Integrable Systems

Long-time asymptotics for perturbations of integrable wave models that admit solitary wave solutions.

Recent Posts

Upcoming Talks

I will be giving talks at the following upcoming events: 10th Ohio River Analysis Meeting (March 20-21, 2021), Departmental Colloquium at the University of Wisconsin-Milwaukee (April 2, 2021), SIAM Annual Meeting 2021 (July 2021). Click on the post title for the links.

Taft Lecture: Percy Deift

Percy Deift, Silver Professor of Mathematics from the Courant Institute of Mathematical Sciences, New York University, will be giving the Taft Lecture in Spring 2020 at the University of Cincinnati. See the announcement. Mark your calendars for March 4, 2020, 4:00 PM! Location: Room 500 Swift Hall.

AMS Special Session: Modern Trends in Integrable Systems

To be held on October 20-21, 2018 in Ann Arbor, MI. Organizers: Deniz Bilman, Peter D. Miller, Amber Music, Guilherme Silva.

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