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Math Calendar

Upcoming Events

November 30, 2018 (Friday), 3:10 pm

Talk Title TBA

Frank Thorne, University of South Carolina
Location: Stevenson 1310

November 30, 2018 (Friday), 4:10 pm

Stability with Modified Scattering of Almost Plane-wave Solutions to the Membrane Equations

Willie Wongu, Michigan State University
Location: Stevenson Center 1307

I will present a recent result with my student L. Abbrescia, where we prove the global nonlinear stability of planar travelling wave solutions to the membrane equations in three and higher spatial dimensions. The membrane equations exhibit good null structure, and hence this result is complementary to the earlier result of Speck, Holzegel, Luk, and the speaker showing nonlinear stability of plane-symmetric blow-up for genuinely nonlinear quasilinear wave equations. An interesting facet of our proof is that the structure of the perturbed equations forces us to close the estimates with modified rates of scattering. This can be interpreted as a leakage of energy from the infinite-energy background travelling wave to the perturbation.

December 5, 2018 (Wednesday), 4:00 pm

Qualifying Examination:

Jun Yang, Vanderbilt University
Location: Stevenson Center 1432

December 5, 2018 (Wednesday), 4:10 pm

Talk Title TBA

Matthew Haulmark, Vanderbilt University
Location: SC 1308

December 7, 2018 (Friday), 3:10 pm

Talk Title TBA

Gueo Grancharov, Florida International University
Location: Stevenson 1310

December 7, 2018 (Friday), 4:10 pm

Recent Progress on Boundary Layer Problems in Periodic Homogenization

Jinping Zhuge, University of Kentucky
Location: Stevenson Center 1307

This talk is concerned with periodic homogenization of linear elliptic equations in divergence form with oscillating Dirichlet data or Neumann data of rst order. For example, the Dirichlet problem with oscillating data reads as follows:

-div(A(x/ε) ∇ uε) in Ω ,
uε(x)=f(x,x/ε) on ∂Ω

where A(y) and f(x, y) are 1-periodic in y, and ε > 0 is tiny. Recently, it has been known that, if Ω is uniformly convex (and smooth), the above equation homogenizes (convergence in some sense) to

-div(Â ∇ u0) in Ω ,
u0(x)=f̄(x) on ∂Ω

where  is the homogenized coecient matrix (constant) and f̄ is the homogenized boundary data. In this talk, I will present the recent progress on this problem, including the sharp convergence rates and the regularity of the homogenized boundary data.

February 7, 2019 (Thursday), 4:10 pm

Talk Title TBA

Dennis Sullivan, Suny at Stony Brook
Location: Stevenson 5211

Tea at 3:33 pm in Stevenson 1425. (Contact Person: Marcelo Disconzi)

April 18, 2019 (Thursday), 4:10 pm

Talk Title TBA

Vladimir Sverak, University of Minnesota
Location: Stevenson 5211

Tea at 3:33 pm in Stevenson 1425. (Contact Person: Gieri SImonett)

May 19, 2019 (Sunday), 8:00 am

Approximation Theory 16, May 19-22, 2019

Location: Vanderbilt University

This meeting will be the sixteenth in a series of international conferences on Approximation Theory held every three years at various locations in the U.S. For more information, please visit the conference website.