Frontiers in Mathematics Lecture Series
Frontiers in Mathematics is the premier lecture series in the
Texas A&M University Department of Mathematics. Each year up to ten
distinguished mathematicians are invited to visit the campus for a
week, and to deliver series of lectures on current research. This also
provides opportunities for interactions with our faculty and graduate
students. We invite you to view our current list of speakers, and to
browse through our archives below.
Speakers for the academic year 20152016
Alicia Dickenstein  University of Buenos Aires 
JeanClaude Saut  University of Paris Sud, Orsay 

Date Time 
Location  Speaker 
Title – click for abstract 

09/11 4:00pm 
Blocker 117 
Diego Cordoba Consejo Superior de Investigaciones Científicas, Madrid, Spain 
Graduate Lecture: Splash and splat singularities for incompressible fluid interfaces
The evolution of an interface between two immiscible incompressible fluids can develop singularities in finite time. In particular those contour dynamics that are given by basic fluid mechanics systems: Euler´s equations, Darcy´s law and the Quasigeostrophic equation. These give rise to problems such as water wave, Muskat, and the evolution of sharp fronts of temperature. In this lecture we will present the main ideas and arguments of the formation in finite time of splash and splat singularities. A splash singularity is when the interfaceremains smooth but selfintersects at a point and a splat singularity is when it selfintersects along an arc. 

09/12 4:00pm 
Blocker 117 
Diego Cordoba Consejo Superior de Investigaciones Científicas, Madrid, Spain 
Colloquium: Global existence results for the Surface Quasigeostrophic equations (SQG)
There has been high scientific interest to understand the behavior of the SQG equation because it is a possible model to explain the formation of fronts of hot and cold air. In a different direction P. Constantin, A. Majda and E. Tabak (1994) proposed this system as a 2D model for the 3D vorticity intensification and showed that there is a geometric and analytic analogy with 3D incompressible Euler equations. It is not known at this moment if this equation can produce singularities. In this lecture I will discuss some recent work, joint with Angel Castro, Javier GomezSerrano and Alex Ionescu, on the existence of non trivial families of global solutions of the inviscid surface quasigeostrophic equation. 

09/14 4:00pm 
Blocker 117 
Diego Cordoba Consejo Superior de Investigaciones Científicas, Madrid, Spain 
Colloquium: Shift of stability and mixing solutions for the Muskat problem
The Muskat equation governs the motion of an interface separation of two
incompressible fluids in a porous media. In this talk I will present the following recent results: (1) The existence of solutions which shift stability regimes in the following sense: they start stable, then become unstable, and finally return back to the stable regime before it breaks down (joint work with J. GomezSerrano and A. Zlatos). (2) The existence of mixing solutions of the incompressible porous media equation for all Muskat type H^5 initial data in the fully unstable regime (joint work with A. Castro and D. Faraco). 
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