Trinh @ Bath

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collaborators [2016/05/09 11:43]
trinh
collaborators [2017/06/17 10:50]
trinh [Rafael (Raffi) Grinberg]
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 {{ :collaborators:prof_chapman.jpg?nolink|}} {{ :collaborators:prof_chapman.jpg?nolink|}}
 OCIAM, Mathematical Institute \\ OCIAM, Mathematical Institute \\
-University of Oxford <html><img src="_media/collaborators/uk.png"/></html> \\+University of Oxford {{:collaborators:uk.png?nolink|}} \\
 [[http://www.maths.ox.ac.uk/people/profiles/jon.chapman|Homepage]] [[http://www.maths.ox.ac.uk/people/profiles/jon.chapman|Homepage]]
  
-**Worked together:** 2007-Present  +**Worked together:** 2007-Present  \\
 **What we worked on:** Exponential asymptotics, free-surface flows, gravity-capillary waves **What we worked on:** Exponential asymptotics, free-surface flows, gravity-capillary waves
  
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 {{ :collaborators:prof_howell.jpg?nolink|}} {{ :collaborators:prof_howell.jpg?nolink|}}
 OCIAM, Mathematical Institute \\ OCIAM, Mathematical Institute \\
-University of Oxford <html><img src="http://www.ptrinh.com/_media/collaborators/uk.png"/></html> \\+University of Oxford {{:collaborators:uk.png?nolink|}} \\
 [[https://www.maths.ox.ac.uk/people/peter.howell|Homepage]] [[https://www.maths.ox.ac.uk/people/peter.howell|Homepage]]
  
-**Worked together:** 2012-Present +**Worked together:** 2012-Present \\
 **What we worked on:** Thin film flows on curved surfaces **What we worked on:** Thin film flows on curved surfaces
  
 <html><div style="clear:both;"><!-- --></div></html>   <html><div style="clear:both;"><!-- --></div></html>  
  
-==== Dr. Colin B. Macdonald ==== 
-{{ :collaborators:prof_macdonald.jpg?nolink|}} 
-OCIAM, Mathematical Institute \\ 
-University of Oxford <html><img src="http://www.ptrinh.com/_media/collaborators/uk.png"/></html> \\ 
-[[https://people.maths.ox.ac.uk/macdonald|Homepage]] 
- 
-**Worked together:** 2012-Present 
- 
-**What we worked on:** Thin film flows on curved surfaces; the Closest Point Method 
- 
-<html><div style="clear:both;"><!-- --></div></html>  
 ==== Prof. Colin P. Please ==== ==== Prof. Colin P. Please ====
 {{ :collaborators:prof_please.jpg?nolink|}} {{ :collaborators:prof_please.jpg?nolink|}}
 OCIAM, Mathematical Institute \\ OCIAM, Mathematical Institute \\
-University of Oxford <html><img src="http://www.ptrinh.com/_media/collaborators/uk.png"/></html> \\+University of Oxford {{:collaborators:uk.png?nolink|}} \\
 [[https://www.maths.ox.ac.uk/people/colin.please|Homepage]] [[https://www.maths.ox.ac.uk/people/colin.please|Homepage]]
  
-**Worked together:** 2013-Present +**Worked together:** 2013-Present \\
 **What we worked on:** Morphoelasticity and tissue growth on curved substrates **What we worked on:** Morphoelasticity and tissue growth on curved substrates
  
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 {{ :collaborators:prof_vandenbroeck.jpg?nolink|}} {{ :collaborators:prof_vandenbroeck.jpg?nolink|}}
 Department of Mathematics \\ Department of Mathematics \\
-University College London <html><img src="http://www.ptrinh.com/_media/collaborators/uk.png"/></html> \\+University College London {{:collaborators:uk.png?nolink|}} \\
 [[http://iris.ucl.ac.uk/iris/browse/profile?upi=JVAND65|Homepage]] [[http://iris.ucl.ac.uk/iris/browse/profile?upi=JVAND65|Homepage]]
  
-**Worked together:** 2008-2012 +**Worked together:** 2008-2012 \\
 **What we worked on:** Free-surface flows, boundary integral methods, ship waves **What we worked on:** Free-surface flows, boundary integral methods, ship waves
  
 <html><div style="clear:both;"><!-- --></div></html>   <html><div style="clear:both;"><!-- --></div></html>  
  
-==== Dr. Dominic Vella ====+==== Prof. Dominic Vella ====
 {{ :collaborators:prof_vella.jpg?nolink|}} {{ :collaborators:prof_vella.jpg?nolink|}}
 OCIAM, Mathematical Institute \\ OCIAM, Mathematical Institute \\
-University of Oxford <html><img src="http://www.ptrinh.com/_media/collaborators/uk.png"/></html> \\+University of Oxford {{:collaborators:uk.png?nolink|}} \\
 [[http://people.maths.ox.ac.uk/vella/|Homepage]] [[http://people.maths.ox.ac.uk/vella/|Homepage]]
  
-**Worked together:** 2013-Present  +**Worked together:** 2013-Present \\
 **What we worked on:** Elastocapillary dynamics and wrinkling of thin membranes **What we worked on:** Elastocapillary dynamics and wrinkling of thin membranes
  
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 {{ :collaborators:prof_wilson.jpg?nolink|}} {{ :collaborators:prof_wilson.jpg?nolink|}}
 Department of Mathematics \\ Department of Mathematics \\
-University of Strathclyde <html><img src="http://www.ptrinh.com/_media/collaborators/uk.png"/></html> \\+University of Strathclyde {{:collaborators:uk.png?nolink|}} \\
 [[https://www.strath.ac.uk/mathstat/staff/professorstephenwilson/|Homepage]] [[https://www.strath.ac.uk/mathstat/staff/professorstephenwilson/|Homepage]]
  
-**Worked together:** 2011-Present +**Worked together:** 2011-Present \\
 **What we worked on:** Interactions between thin free-surface flows and elastic structures **What we worked on:** Interactions between thin free-surface flows and elastic structures
  
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 {{ :collaborators:prof_e.jpg?nolink|}}  {{ :collaborators:prof_e.jpg?nolink|}} 
 PACM and Department of Mathematics \\ PACM and Department of Mathematics \\
-Princeton University <html><img src="http://www.ptrinh.com/_media/collaborators/usa.png"/></html> \\+Princeton University {{:collaborators:usa.png?nolink|}} \\
 [[https://web.math.princeton.edu/~weinan/|Homepage]] [[https://web.math.princeton.edu/~weinan/|Homepage]]
  
-**Worked together:** 2010-2012 +**Worked together:** 2010-2012 \\
 **What we worked on:** Singularities in fluid mechanics, the moving contact line problem **What we worked on:** Singularities in fluid mechanics, the moving contact line problem
  
 <html><div style="clear:both;"><!-- --></div></html>   <html><div style="clear:both;"><!-- --></div></html>  
 +
 ==== Prof. Howard A. Stone ==== ==== Prof. Howard A. Stone ====
 {{ :collaborators:prof_stone.jpg?nolink|}} {{ :collaborators:prof_stone.jpg?nolink|}}
 Mechanical and Aerospace Engineering \\ Mechanical and Aerospace Engineering \\
-Princeton University <html><img src="http://www.ptrinh.com/_media/collaborators/usa.png"/></html> \\+Princeton University {{:collaborators:usa.png?nolink|}} \\
 [[https://www.princeton.edu/mae/people/faculty/stone/|Homepage]] [[https://www.princeton.edu/mae/people/faculty/stone/|Homepage]]
  
-**Worked together:** 2010-Present +**Worked together:** 2010-Present \\
 **What we worked on:** Viscous flows, free-surfaces interacting with elastic structures, thin film flows on curved surfaces **What we worked on:** Viscous flows, free-surfaces interacting with elastic structures, thin film flows on curved surfaces
  
 <html><div style="clear:both;"><!-- --></div></html>   <html><div style="clear:both;"><!-- --></div></html>  
 +
 ==== Prof. Thomas P. Witelski ==== ==== Prof. Thomas P. Witelski ====
 {{ :collaborators:prof_witelski.jpg?nolink|}} {{ :collaborators:prof_witelski.jpg?nolink|}}
 Department of Mathematics \\ Department of Mathematics \\
-Duke University <html><img src="http://www.ptrinh.com/_media/collaborators/usa.png"/></html> \\+Duke University {{:collaborators:usa.png?nolink|}} \\
 [[http://fds.duke.edu/db/aas/math/faculty/witelski|Homepage]] [[http://fds.duke.edu/db/aas/math/faculty/witelski|Homepage]]
  
-**Worked together:** 2010-2011, 2013-Present +**Worked together:** 2010-2011, 2013-Present \\
 **What we worked on:** Rupturing processes in thin films and solids, singular perturbation theory **What we worked on:** Rupturing processes in thin films and solids, singular perturbation theory
  
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 [[http://people.math.carleton.ca/~dave/|Homepage]] [[http://people.math.carleton.ca/~dave/|Homepage]]
  
-**Worked together:** 2005-2007  +**Worked together:** 2005-2007 \\
 **What we worked on:** Nonlinear waves, Korteweg-de Vries equations, sloshing, perturbation theory **What we worked on:** Nonlinear waves, Korteweg-de Vries equations, sloshing, perturbation theory
  
 <html><div style="clear:both;"><!-- --></div></html>   <html><div style="clear:both;"><!-- --></div></html>  
 +
 +==== Prof. Colin B. Macdonald ====
 +{{ :collaborators:prof_macdonald.jpg?nolink|}}
 +Department of Mathematics \\
 +University of British Columbia {{:collaborators:canada.png?nolink|}} \\
 +[[https://www.math.ubc.ca/~cbm/|Homepage]]
 +
 +**Worked together:** 2012-Present \\
 +**What we worked on:** Thin film flows on curved surfaces; the Closest Point Method
 +
 +<html><div style="clear:both;"><!-- --></div></html> 
  
 ==== Prof. David Sankoff ==== ==== Prof. David Sankoff ====
 {{ :collaborators:prof_sankoff.jpg?nolink|}} {{ :collaborators:prof_sankoff.jpg?nolink|}}
 Department of Mathematics and Statistics \\ Department of Mathematics and Statistics \\
-University of Ottawa <html><img src="http://www.ptrinh.com/_media/collaborators/canada.png"/></html> \\+University of Ottawa {{:collaborators:canada.png?nolink|}} \\
 [[http://albuquerque.bioinformatics.uottawa.ca/|Homepage]] [[http://albuquerque.bioinformatics.uottawa.ca/|Homepage]]
  
-**Worked together:** 2002-2004  +**Worked together:** 2002-2004 \\
 **What we worked on:** Mathematical genomics  **What we worked on:** Mathematical genomics 
  
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 {{ :collaborators:prof_ward.jpg?nolink|}} {{ :collaborators:prof_ward.jpg?nolink|}}
 Department of Mathematics \\ Department of Mathematics \\
-University of British Columbia <html><img src="http://www.ptrinh.com/_media/collaborators/canada.png"/></html> \\+University of British Columbia {{:collaborators:canada.png?nolink|}} \\
 [[https://www.math.ubc.ca/~ward/|Homepage]] [[https://www.math.ubc.ca/~ward/|Homepage]]
  
-**Worked together:** 2013-2014  +**Worked together:** 2013-2014 \\
 **What we worked on:** Localized spot patterns on the surface of the sphere **What we worked on:** Localized spot patterns on the surface of the sphere
  
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 ==== Prof. Weiqing Ren ==== ==== Prof. Weiqing Ren ====
 Department of Mathematics \\ Department of Mathematics \\
-National University of Singapore <html><img src="http://www.ptrinh.com/_media/collaborators/singapore.png"/></html> \\+National University of Singapore {{:collaborators:singapore.png?nolink|}} \\
 [[http://www.math.nus.edu.sg/~matrw/|Homepage]] [[http://www.math.nus.edu.sg/~matrw/|Homepage]]
  
-**Worked together:** 2010-2012 +**Worked together:** 2010-2012 \\
 **What we worked on:** Singularities in fluid mechanics, the moving contact line problem **What we worked on:** Singularities in fluid mechanics, the moving contact line problem
  
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 {{ :collaborators:prof_auton.jpg?nolink|}} {{ :collaborators:prof_auton.jpg?nolink|}}
 Mathematical Institute \\ Mathematical Institute \\
-University of Oxford <html><img src="http://www.ptrinh.com/_media/collaborators/uk.png"/></html> +University of Oxford {{:collaborators:uk.png?nolink|}} 
  
-**Worked together:** 2013-2014+**Worked together:** 2013-2014 \\ 
 +**What we worked on:** (MMath) Multiple scales and discrete difference equations \\ 
 +**Now working at:** D.Phil. Engineering at the University of Oxford 
  
-**What we worked on:** (MMath) Multiple scales and discrete difference equations+<html><div style="clear:both;"><!-- --></div></html>
  
-**Now working at:** D.Phil. Engineering at the University of Oxford +==== Thomas Chandler ==== 
 +{{ :collaborators:prof_chandler.jpg?nolink|}} 
 +Mathematical Institute \\ 
 +University of Oxford {{:collaborators:uk.png?nolink|}}  
 + 
 +**Worked together:** 2015-2017 \\ 
 +**What we worked on:** (BA) Jets, waterfalls, and splashes from angled slots, (MMath) Complex singularities near the intersection of a free-surface and a rigid wall \\ 
 +**Now working at:** D.Phil. student in Mathematics at the University of Oxford (to begin 2017-2018)
  
 <html><div style="clear:both;"><!-- --></div></html>   <html><div style="clear:both;"><!-- --></div></html>  
 +  
 +
 ==== Samuel Crew ==== ==== Samuel Crew ====
 {{ :collaborators:prof_crew.jpg?nolink|}} {{ :collaborators:prof_crew.jpg?nolink|}}
 Mathematical Institute \\ Mathematical Institute \\
-University of Oxford <html><img src="http://www.ptrinh.com/_media/collaborators/uk.png"/></html> +University of Oxford {{:collaborators:uk.png?nolink|}} 
  
-**Worked together:** 2015--2016+**Worked together:** 2015--2016 \\ 
 +**What we worked on:** Complex singularities in Stokes waves \\ 
 +**Now working at:** Ph.D. student in Physics at the University of Cambridge
  
-**What we worked on:** Complex singularities in Stokes waves+<html><div style="clear:both;"><!-- --></div></html>  
  
-**Now working at:** MMathPhys, University of Oxford 
  
-<html><div style="clear:both;"><!-- --></div></html>   
 ==== Jamie Cruickshank ==== ==== Jamie Cruickshank ====
 {{ :collaborators:prof_cruickshank.jpg?nolink|}} {{ :collaborators:prof_cruickshank.jpg?nolink|}}
 Mathematical Institute \\ Mathematical Institute \\
-University of Oxford <html><img src="http://www.ptrinh.com/_media/collaborators/uk.png"/></html>  +University of Oxford {{:collaborators:uk.png?nolink|}} 
- +
-**Worked together:** 2014-2015 +
  
 +**Worked together:** 2014-2015 \\
 **What we worked on:** (MMath) Tissue growth in a mono-layered epithelium **What we worked on:** (MMath) Tissue growth in a mono-layered epithelium
  
 <html><div style="clear:both;"><!-- --></div></html>   <html><div style="clear:both;"><!-- --></div></html>  
 +
 +====John Fitzgerald ====
 +{{ :collaborators:prof_fitzgerald.jpg?nolink|}}
 +Mathematical Institute \\
 +University of Oxford {{:collaborators:uk.png?nolink|}} 
 +
 +**Worked together:** 2016-2017 \\
 +**What we worked on:** (BA) Exponential asymptotics, complex ray theory and applications to free-surface flows
 +
 ==== Alexander Gower ==== ==== Alexander Gower ====
 {{ :collaborators:prof_gower.jpg?nolink|}} {{ :collaborators:prof_gower.jpg?nolink|}}
 Mathematical Institute \\ Mathematical Institute \\
-University of Oxford <html><img src="http://www.ptrinh.com/_media/collaborators/uk.png"/></html>  +University of Oxford {{:collaborators:uk.png?nolink|}} 
- +
-**Worked together:** 2014-2015 +
  
 +**Worked together:** 2014-2015 \\
 **What we worked on:** (MMath) Phase field models and the thin film limit **What we worked on:** (MMath) Phase field models and the thin film limit
  
 <html><div style="clear:both;"><!-- --></div></html>   <html><div style="clear:both;"><!-- --></div></html>  
 +
 ==== Rafael (Raffi) Grinberg ==== ==== Rafael (Raffi) Grinberg ====
 {{ :collaborators:prof_raffi.jpg?nolink|}} {{ :collaborators:prof_raffi.jpg?nolink|}}
 Department of Mathematics \\ Department of Mathematics \\
-Princeton University <html><img src="http://www.ptrinh.com/_media/collaborators/usa.png"/></html> +Princeton University {{:collaborators:usa.png?nolink|}} 
- +
-**Worked together:** 2011-2012 +
  
 +**Worked together:** 2011-2012 \\
 **What we worked on:** Raffi wrote and published his thesis, "Real Analysis for the Non-Genius", which was later incorporated into the Real Analysis course at Princeton. **What we worked on:** Raffi wrote and published his thesis, "Real Analysis for the Non-Genius", which was later incorporated into the Real Analysis course at Princeton.
  
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 {{ :collaborators:prof_guyomard.jpg?nolink|}} {{ :collaborators:prof_guyomard.jpg?nolink|}}
 Mathematical Institute \\ Mathematical Institute \\
-University of Oxford <html><img src="http://www.ptrinh.com/_media/collaborators/uk.png"/></html> +University of Oxford {{:collaborators:uk.png?nolink|}} 
  
-**Worked together:** 2014--2015+**Worked together:** 2014--2015 \\ 
 +**What we worked on:** (M.Sc.) The multi-dimensional method of steepest descents \\ 
 +**Now working at:** Frontier Developments, UK
  
-**What we worked on:** (M.Sc.) The multi-dimensional method of steepest descents+<html><div style="clear:both;"><!-- --></div></html>  
  
-**Now working at:** Frontier Developments, UK+==== Sean Jamshidi ==== 
 +{{ :collaborators:prof_jamshidi.jpg?nolink|}} 
 +Mathematical Institute \\ 
 +University of Oxford {{:collaborators:uk.png?nolink|}}  
 + 
 +**Worked together:** 2015-2016 \\ 
 +**What we worked on:** (MMath) Searching for new gravity-capillary waves 
 +**Now working at:** Ph.D. student in Mathematics at University College London
  
 <html><div style="clear:both;"><!-- --></div></html>   <html><div style="clear:both;"><!-- --></div></html>  
-==== Thomas Pettifor ==== + 
-{{ :collaborators:prof_pettifor.jpg?nolink|}}+==== Yyanis Johnson-Llambias ==== 
 +{{ :collaborators:prof_johnson.jpg?nolink|}}
 Mathematical Institute \\ Mathematical Institute \\
-University of Oxford <html><img src="http://www.ptrinh.com/_media/collaborators/uk.png"/></html> +University of Oxford {{:collaborators:uk.png?nolink|}} 
  
-**Worked together:** 2013-2014 +**Worked together:** 2016-2017 \\ 
- +**What we worked on:** (MMath) Complex Singularities of the finite-depth Stokes wave
-**What we worked on:** (MMath) Discrete and continuum models for in vitro tissue growth+
  
 <html><div style="clear:both;"><!-- --></div></html>   <html><div style="clear:both;"><!-- --></div></html>  
 +
 ==== Naima Hammoud ==== ==== Naima Hammoud ====
 {{ :collaborators:prof_hammoud.jpg?nolink|}} {{ :collaborators:prof_hammoud.jpg?nolink|}}
 Mechanical and Aerospace Engineering \\ Mechanical and Aerospace Engineering \\
-Princeton University <html><img src="http://www.ptrinh.com/_media/collaborators/usa.png"/></html> \\+Princeton University {{:collaborators:usa.png?nolink|}} \\
 [[https://www.princeton.edu/~stonelab/|Homepage]] [[https://www.princeton.edu/~stonelab/|Homepage]]
  
-**Worked together:** 2012-Present +**Worked together:** 2012-Present \\
 **What we worked on:** (Ph.D.) Thin films on curved surfaces, fluid instabilities **What we worked on:** (Ph.D.) Thin films on curved surfaces, fluid instabilities
  
 <html><div style="clear:both;"><!-- --></div></html>   <html><div style="clear:both;"><!-- --></div></html>  
 +
 +==== Thomas Pettifor ====
 +{{ :collaborators:prof_pettifor.jpg?nolink|}}
 +Mathematical Institute \\
 +University of Oxford {{:collaborators:uk.png?nolink|}} 
 +
 +**Worked together:** 2013-2014 \\
 +**What we worked on:** (MMath) Discrete and continuum models for in vitro tissue growth
 +
 +<html><div style="clear:both;"><!-- --></div></html>  
 +
 ==== Stephanie Yayoi Teramoto ==== ==== Stephanie Yayoi Teramoto ====
 {{ :collaborators:prof_teramoto.jpg?nolink|}} {{ :collaborators:prof_teramoto.jpg?nolink|}}
 Department of Mathematics \\ Department of Mathematics \\
-Princeton University <html><img src="http://www.ptrinh.com/_media/collaborators/usa.png"/></html>  +Princeton University {{:collaborators:usa.png?nolink|}} 
- +
-**Worked together:** 2011-2014 +
- +
-**What we worked on:** Mathematics of patterns and reaction-diffusion equations+
  
 +**Worked together:** 2011-2014 \\
 +**What we worked on:** Mathematics of patterns and reaction-diffusion equations \\
 **Now working at:** D.Phil. Neuroscience at the University of Oxford  **Now working at:** D.Phil. Neuroscience at the University of Oxford 
  
 <html><div style="clear:both;"><!-- --></div></html>   <html><div style="clear:both;"><!-- --></div></html>  
 +
 ==== Melissa Varney ==== ==== Melissa Varney ====
 {{ :collaborators:prof_varney.jpg?nolink|}} {{ :collaborators:prof_varney.jpg?nolink|}}
 Mathematical Institute \\ Mathematical Institute \\
-University of Oxford <html><img src="http://www.ptrinh.com/_media/collaborators/uk.png"/></html>  +University of Oxford {{:collaborators:uk.png?nolink|}} 
- +
-**Worked together:** 2013-2014 +
- +
-**What we worked on:** (MMath) Mathematical models for the wrinkling of thin sheets+
  
 +**Worked together:** 2013-2014 \\
 +**What we worked on:** (MMath) Mathematical models for the wrinkling of thin sheets \\
 **Now at:** Teaching PGCE at University of Cambridge **Now at:** Teaching PGCE at University of Cambridge
  
 <html><div style="clear:both;"><!-- --></div></html>   <html><div style="clear:both;"><!-- --></div></html>  
 +
 ==== Jason Wexler ==== ==== Jason Wexler ====
 {{ :collaborators:prof_wexler.jpg?nolink|}} {{ :collaborators:prof_wexler.jpg?nolink|}}
 Mechanical and Aerospace Engineering \\ Mechanical and Aerospace Engineering \\
-Princeton University <html><img src="http://www.ptrinh.com/_media/collaborators/usa.png"/></html> \\+Princeton University {{:collaborators:usa.png?nolink|}} \\
 [[https://www.princeton.edu/~stonelab/|Homepage]] [[https://www.princeton.edu/~stonelab/|Homepage]]
  
-**Worked together:** 2011-2012 +**Worked together:** 2011-2012 \\
 **What we worked on:** Deformation of fibres due to viscous flows in Hele-Shaw cells **What we worked on:** Deformation of fibres due to viscous flows in Hele-Shaw cells
  
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 {{ :collaborators:prof_whitlock.jpg?nolink|}} {{ :collaborators:prof_whitlock.jpg?nolink|}}
 Mathematical Institute \\ Mathematical Institute \\
-University of Oxford <html><img src="http://www.ptrinh.com/_media/collaborators/uk.png"/></html>  +University of Oxford {{:collaborators:uk.png?nolink|}} 
- +
-**Worked together:** 2014--2015+
  
 +**Worked together:** 2014--2015 \\
 **What we worked on:** (MMath) Models for thin film flow on curved surfaces **What we worked on:** (MMath) Models for thin film flow on curved surfaces
  
 <html><div style="clear:both;"><!-- --></div></html>   <html><div style="clear:both;"><!-- --></div></html>  
 +
 ==== Daniel Wu ==== ==== Daniel Wu ====
 {{ :collaborators:prof_wu.jpg?nolink|}} {{ :collaborators:prof_wu.jpg?nolink|}}
 Department of Mathematics \\ Department of Mathematics \\
-Princeton University <html><img src="http://www.ptrinh.com/_media/collaborators/usa.png"/></html> +Princeton University {{:collaborators:usa.png?nolink|}} 
- +
-**Worked together:** 2011-2012+
  
 +**Worked together:** 2011-2012 \\
 **What we worked on:** Applications of functional analysis to applied mathematics, Hahn-Banach Theorem  **What we worked on:** Applications of functional analysis to applied mathematics, Hahn-Banach Theorem