The Department of Applied Mathematics at IIT will host Thomas Yizhao Hou, Charles Lee Powell Professor of Applied and Computational Mathematics, California Institute of Technology, as the 2016 Karl Menger Lecturer. He will speak on "Recent Progress in the Clay Millennium Problem on Navier-Stokes Equations and Related Models" on March 28 at 3:15 p.m. The event is part of the ninth annual Karl Menger Lecture and Awards, March 28-29, Illinois Institute of Technology Mies (Main) Campus.
Made possible with the generous support of the Menger family; Department of Applied Mathematics, Illinois Institute of Technology; and the Menger Fund.
Monday, March 28, 2016
Pre-lecture events will begin at 12:45 p.m. and will take place in the McCloska Ballroom, located in the McCormick Tribune Campus Center (MTCC).
12:45-1:40 p.m. - Math Club Meeting
Professor Thomas Yizhao Hou will give the talk "How Mathematics Improves the Quality of Our Life." All alumni are welcome. Light lunch provided.
2:00 p.m. - Memories of IIT
Join in as alumni and friends tell their stories of IIT and Professor Karl Menger.
2:50pm p.m. - Poster Session
Viewing of student research posters. Light refreshments available.
3:15-4:15 pm p.m. - Lecture, McCloska Auditorium, MTCC
"Recent Progress in the Clay Millennium Problem on Navier-Stokes Equations and Related Models" delivered by Professor Thomas Yizhao Hou, Charles Lee Powell Professor of Applied and Computational Mathematics, California Institute of Technology.
Fluid flows are ubiquitous in scientific and engineering applications as well as in our daily life. It is well known that the motion of fluid flows is governed by the Navier-Stokes equations. Despite the widespread applications of these equations, the global existence and regularity of the three-dimensional incompressible Navier-Stokes equations remains one of the most challenging open questions in fluid dynamics and mathematics. This challenging question has been posted as one of seven Millennium Prize Problems by the Clay Mathematics Institute. In this lecture, Hou will review some of the classical results for the Navier-Stokes equations and explain why this problem is so challenging. The earliest work due to Leray led to the notion of weak solutions for partial differential equations. In recent years, there has been a growing interest in the study of the Navier-Stokes equations. This includes the celebrated partial regularity result due to Caffarelli-Kohn-Nirenberg, the work of Sverak and Tsai on the non-existence of self-similar solutions under certain conditions, the role of geometric regularity of vorticity vectors in depleting potential singularity due to Constantin-Fefferman-Majda, and the very recent work due to Terence Tao on the finite time blowup of a model of the Navier-Stokes equations. Hou also will review some of his recent work in Navier-Stokes equations and related models, which demonstrates the stabilizing effect of convection. Very recently, he obtained strong numerical evidence on the finite time blowup of the incompressible 3-D Euler equations.
4:15-4:25 p.m. - Presentation of Awards
Presentation of the IIT Karl Menger Student Award for exceptional scholarship by a student and the Applied Mathematics poster competition winners.
4:25 p.m. - Reception, McCloska Ballroom, MTCC
Tuesday, March 29, 2016
Professor Hou will meet with students and faculty.
11:25 a.m. - Research Seminar, Life Sciences Building, Room 240
"Blowup or no blowup? The interplay between theory and computation in the study of 3-D Euler equations" delivered by Professor Hou
Whether the 3-D incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This question is closely related to the Clay Millennium Problem on 3-D Navier-Stokes Equations. Hou will first review some recent theoretical and computational studies of the 3-D Euler equations. His study suggests that the convection term could have a nonlinear stabilizing effect for certain flow geometry. He will then present strong numerical evidence that the 3-D Euler equations develop finite time singularities. To resolve the nearly singular solution, he developed specially designed adaptive (moving) meshes with a maximum effective resolution of order 1012 in each direction. A careful local analysis also suggests that the blowing-up solution is highly anisotropic and is not of Leray type. A 1-D model is proposed to study the mechanism of the finite time singularity. Very recently, he proved rigorously that the 1-D model develops finite time singularity. This is a joint work with Professor Guo Luo.
4:40-5:30 p.m. - Discussion, Life Sciences Building, Room 152
"How to Be a Successful Applied Mathematician" with Professor Hou
Complimentary parking is available in the A4 Visitor’s Lot (entrance at 32nd and State streets). Contact Gladys Collins at 312.567.8980 or collinsg(at)iit(dot)edu for details.
Out-of-state travelers: for questions or hotel suggestions, please call 312.567.3132
About the Menger Lecturer
Thomas Yizhao Hou is the Charles Lee Powell Professor of Applied and Computational Mathematics at Caltech. Hou's research interests are centered around developing mathematical analysis and effective computational l methods for vortex dynamics, interfacial flows, multiscale problems and data analysis. He received his Ph.D. from UCLA in 1987, and joined the Courant Institute as a junior faculty member in 1989. He moved to Caltech in 1993 as a tenured associate professor and was named the Charles Lee Powell Professor in 2004. Hou has received a number of honors and awards, including becoming a member of American Academy of Arts and Sciences in 2011, a member of the inaugural class of SIAM Fellows in 2009 and AMS Fellows in 2012, the Computational and Applied Sciences Award from USACM in 2005, the Morningside Gold Medal in Applied Mathematics in 2004, the SIAM Wilkinson Prize in Numerical Analysis and Scientific Computing in 2001, the Frenkiel Award from the Division of Fluid Mechanics of APS in 1998, the Feng Kang Prize in Scientific Computing in 1997, and a Sloan fellow from 1990 to 1992. He also was the founding Editor-in-Chief of the SIAM Journal on Multiscale Modeling and Simulation from 2002 to 2007.
Karl Menger was a faculty member in the Department of Mathematics at IIT from 1946 to 1971, and influenced many students, fellow faculty members, and friends during his lifetime. Regarded as one of the finest mathematicians of the 20th century, he made significant contributions to the fields of dimension theory, probability, economics, ethics, geometry, and calculus.
Each year we invite an outside speaker to be the Karl Menger Lecturer. It is the centerpiece of two days of events for students, faculty, and alumni.
- Biography of Karl Menger, compiled by Professor Greg Fasshauer at IIT.
- Calculus: A Modern Approach, Menger's Calculus textbook.
- Selecta Mathematica, Vol 1 & 2, a compilation of Menger's major mathematical papers.
- Unexplored Dimensions: Karl Menger on Economics and Philosophy, a collection of Menger's papers while at the University of Vienna.
Previous Menger Lecturers
- Remembering Menger 2015: Andrea Bertozzi
- Remembering Menger 2014
- Remembering Menger 2013: Philip Protter
- Remembering Menger 2012: Philip Holmes
- Remembering Menger 2011: Peter Winkler
- Remembering Menger 2010: Donald Saari
- Remembering Menger 2009: Richard Durrett [slideshow]
- Remembering Menger 2008: Lloyd N. Trefethen FRS [slideshow]
- Remembering Menger 2007: Karl Sigmund