Department of Mathematics
Applied Mathematics Seminar, Spring 2019

Mondays 4:00 PM - 5:00 PM, LCB 215

January 11, Friday (Special Seminar), Room LCB 219. Time 3pm - 4pm
Speaker: William Feldman, Department of Mathematics, University of Chicago
Title: Recent developments in stochastic homogenization of Hamilton-Jacobi equations
Abstract: I will describe some background and some new developments in the theory homogenization of Hamilton-Jacobi equations in random environments. The primary difficulties in this field have been around understanding the roles of convexity and coercivity (controllability). Many interesting problems, especially involving interface motions, lack one or both of these properties. I will discuss some positive results and some counter-examples where homogenization does not hold.

January 18, Friday (Special Seminar), Room LCB 215. Time 4pm - 5pm.
Speaker: Ian Tobasco, Department of Mathematics, University of Michigan, Ann Arbor
Title: Optimal design of wall-bounded heat transport
Abstract: Flowing a fluid is a familiar and efficient way to cool: fans cool electronics, water cools nuclear reactors, and the atmosphere cools the surface of the Earth. In this talk, we discuss a class of problems from fluid dynamics which ask for the design of incompressible wall-bounded flows achieving optimal rates of heat transport for a given flow intensity budget. Guided by a perhaps unexpected connection between this optimal design problem and various "energy-driven pattern formation" problems from materials science, we construct flows achieving nearly optimal rates of heat transport in their scaling with respect to a prescribed intensity budget. The resulting flows share striking similarities with self-similar elastic wrinkling patterns, such as can be seen in the shape of a hanging drape or nearby the edge of a torn plastic sheet. They also remind of (carefully designed versions) of the complex multi-scale patterns seen in turbulent fluids. Nevertheless, we prove that in certain cases natural buoyancy-driven convection is not capable of achieving optimal rates of cooling. This is joint work with Charlie Doering.

March 4
Speaker: Piotr Kokoszka, Department of Statistics, Colorado State University
Title: Fundamental concepts of functional data analysis and an application to global cooling
Abstract: The talk will consist of two parts. In the first part I will review the basic concepts of functional data analysis (FDA), mostly by showing relevant graphical displays. In FDA, a single observation is a curve rather than a number. The curves exist as mathematical objects, but are never fully observed. For example, a child has a height at any time point, but it is generally recorded about once a year. In the second part of the talk, I will focus on the problem of testing if there is a global cooling trend in the ionosphere. It has been conjectured almost 30 years ago that green house gases should radiate heat into space once they enter the ionosphere. This should result in its thermal contraction. The height of the ionosphere can be approximately measured only directly over a terrestrial observatory. These observatories are unevenly spaced and have operated over different time periods. I will explain how the data collected by them can be used to test the conjecture of the thermal contraction of the ionosphere. The talk will be accessible to anyone with an undergraduate background in statistics.

April 1
Speaker: Lars Ruthotto, Department of Mathematics and Computer Science, Emory University
Title: TBA
Abstract: TBA

April 8 (reserved)
Speaker: TBA
Title: TBA
Abstract: TBA

Seminar organizer: Yekaterina Epshteyn (epshteyn (at)

Past lectures: Fall 2018, Spring 2018, Fall 2017, Spring 2017, Spring 2016, Fall 2015, Spring 2015, Fall 2014, Spring 2014, Fall 2013, Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009, Spring 2009, Fall 2008, Spring 2008, Fall 2007, Spring 2007, Fall 2006, Spring 2006, Fall 2005, Spring 2005, Fall 2004, Spring 2004, Fall 2003, Spring 2003, Fall 2002, Spring 2002, Fall 2001, Spring 2001, Fall 2000, Spring 2000, Fall 1999, Spring 1999, Fall 1998, Spring 1998, Winter 1998, Fall 1997, Spring 1997, Winter 1997, Fall 1996, Spring 1996, Winter 1996, Fall 1995.

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