An internationally recognized mathematician, Terence Tao visits KAIST June 13-25, 2017 to give Distinguished Lecture Series, sponsored by the Center for Mathematical Challenges (CMC) at the Korea Institute for Advanced Study (KAIS).
Terence Tao, a professor of the University of California, Los Angeles, has been known as a math prodigy from childhood. He received many prestigious awards and honors, including the 2006 Fields Medal, the 2014 Breakthrough Prize in Mathematics, and the MacArthur Fellowship in 2006.
Today, Tao is regarded as the world’s finest mathematician working on a number of areas in the field. He published many outstanding results, including solutions and crucial progresses on long-standing open problems. Among others, he solved a well-known conjecture in number theory in 2015, the Erdős discrepancy problem, which had long been considered impossible to prove.
Paul Erdős, a renowned Hungarian mathematician, proposed the discrepancy problem in the 1930s, wondering a random, infinite sequence of numbers purely consisting of +1s and -1s would always contain internal patterns of numbers or values. Erdős supposed that if the infinite sequence is cut off at a certain point to create finite sub-sequences within that part of the sequence, for example, taking only every third number or every fourth in the sequence, adding up the numbers in a sub-sequence results in a discrepancy. This acts as a measure of the pattern of the sub-sequence and in turn, the structure of the infinite sequence. He thought that for any infinite sequence, it would always be possible to find a finite sub-sequence summing to a number larger than any you choose, but could not prove it.
On June 15th, Tao presented a talk entitled “The Erdős Discrepancy Problem” and discussed how he was able to prove Erdős’s hypothesis that discrepancies become higher when an infinite subsequence becomes longer.
The next day, June 16th, Tao spoke on finite time blowup problems of super-critical partial differential equations. In the super-critical regime, almost no methods are available to establish the global regularity of solutions. He presented a way to construct supercritical equations and solutions, which exhibit finite time blow up in the class of nonlinear wave equations or nonlinear Schrodinger equations, as well as Navier-Stokes equations. Most importantly, for the Navier-Stokes equations, this argument shows that if one allows some modifications, there are finite time blow up solutions while still obeying important features of the equations such as conservation laws. Although this work does not directly impact the conjecture of true Navier-Stokes equations, it rules out some potential approaches to establish global regularity. The talk was titled “Finite Time Blowup Constructions for Supercritical Equations.”
Tao will stay KAIST until June 25th, researching and discussing mathematics with faculty and students of the Department of Mathematical Sciences (DMS). The DMS will hold a special tea time with Terence Tao on 23th, Friday, 4 pm, at Rm 1401 of the E6-1 building, which will be open to all DMS members.