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Dorian Goldman 

Department of Pure Mathematics and Mathematical Statistics
University of Cambridge

Email

dg443 at dpmms dot cam dot ac dot uk

Office

E014 Pavillion E

Postal Address

Department of Pure Mathematics and Mathematical Statistics,
Centre for Mathematical Sciences,
University of Cambridge,
Wilberforce Road,
Cambridge, CB3 0WB



I am currently Herchel Smith Postdoctoral Fellow at the DPMMS at the University of Cambridge. I successfully defended my Ph.D in May 2013, under the supervision of Sylvia Serfaty at the Courant Institute of Mathematical Sciences and in September 2013 at the Universite Pierre et Marie Curie (UPMC). I work in the area of nonlinear partial differential equations, focusing primarily on variational methods for problems arising in mathematical physics. I also am interested in fluid equations and optimal transportation.

Teaching

Fall 2012 - Calculus 1 Teaching Evaluation
Fall 2011 - Calculus 1 Teaching Evaluation

Publications

Asymptotics of non-minimizing critical points of the Ohta-Kawasaki energy. (Preprint)
An optimal a priori bound for Burgers' equation, with Felix Otto. (In preparation)
On the regularity of stationary points of a non-local isoperimetric problem, with Alexander Volkmann. (Submitted to Interfaces and Free Boundaries)
The Gamma-limit of the two dimensional Ohta-Kawasaki energy. II. Derivation of the Renormalized energy, with Sylvia Serfaty and Cyrill Muratov. Arch. Ration. Mech. Anal., 212:445–501, 2014
Uniqueness results for critical points of a non-local isoperimetric problem via curve shortening. (Submitted to Calc. Vars. & PDE)
The Gamma-limit of the two-dimensional Ohta-Kawasaki energy. I. Droplet density, with Sylvia Serfaty and Cyrill Muratov. Arch. Ration. Mech. Anal., 210:581–613, 2013.
Chaotic response of the 2D semi-geostrophic and 3D quasi-geostrophic equations to gentle periodic forcing, with Robert McCann. Nonlinearity 21 (2008) 1455-1470 doi 10.1088/0951-7715/21/7/005.
Weak lagrangian solutions to a one dimensional model of the moist semi-geostrophic equations. Masters Thesis (2008), University of Toronto.

Curriculum Vitae

Teaching Statement

Research Statement

Or click here for a 2 page thesis summary with future directions.

Conference Talks

The Gamma limit of the Ohta-Kawasaki energy. Droplet density and the Renormalized energy (Slides)
Online video recorded version of my presentation at CMU November 6th, 2012
Fall Speaking Schedule
2013 SIAM Conference on Mathematical Aspects of Materials Science (June 12, Philadelphia) (Minisimposium: Geoemtric Variational Problems with Long-range Interactions)

Cambridge University (November 23, 2012)
Max Planck Institute Golm (Berlin) (November 19, 2012)
Oxford (November 16, 2012)
ETH Zurich (November 13, 2012)
Carnegie Mellon (November 6, 2012)
MIT (October 16, 2012)
Columbia (October 4, 2012)
Courant Institute (NYU) (October 4, 2012)
Meeting on applied mathematics and the Calc. of Var. Rome, Italy (September 5, 2012)
Max Planck Institute Golm (April 16, 2012)
University of Toronto (January 5,2012)
International conference on optimal transportation with applications to geophysics and geometry (Edinburgh, Scotland)