Sloan Fellowship Recipient Li-Cheng Tsai Joins Math Department in July In July, the Department of Mathematics will welcome Assistant Professor pus and Utah.
Li-Cheng Tsai to the U cam-
Tsai, who recently received a Sloan Research Fellowship, is currently teaching and doing research at Rutgers University, New Brunswick. The Sloan Fellowship is awarded to outstanding early-career researchers in scientific and technical fields. Tsai is one of 118 in the U.S. and Canada to receive the two-year fellowship from the Alfred P. Sloan Foundation. “I’m deeply honored to receive this prestigious award,” said Tsai. “The fellowship will provide me with the resources to further my research, which I plan to continue in Utah.” Tsai is looking forward to joining the U. “The Math Department has a really rich research portfolio, and the research directions of the probability group are well aligned with my own,” he said. “I look forward to fruitful interactions with my future colleagues in the department’s vibrant research environment.”
Probability and stochastic analysis Tsai’s research is about understanding unexpected universal patterns in stochastic systems. It turns out that systems that are random and governed by very different underlying rules can exhibit similar patterns. For example, consider two lists of numbers: the first list is the populations of U.S. counties. The second list is the height of the 1,000 tallest structures in the world in meters. These two lists of numbers should have nothing in common, but, surprisingly, the leading digit of each number follows the same distribution on both lists. “One might think that maybe the distribution of the leading digit just follows a uniform distribution (where 1, 2, 3, … 9 all have the same frequency of
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Li-Cheng Tsai occurrence), but that’s not the case,” said Tsai. In fact, the probability of the leading digit being 1 is about 30%, and the probability of being 9 is under 5%. This is known as Benford’s Law, or the first-digit law, and it occurs in a wide range of data sets: bills, taxes, and stock prices to name a few. In fact, the pattern is so universal that it is used as a standard test to see if a data set has been manipulated. Tsai looks for these kinds of universal patterns, but in systems that are related to rough interfaces, such as the edge of a coffee stain, the front of a burning paper, or a randomly played tetris game. Despite having very different underlying physical mechanisms, the interfaces in these systems all share the same statistical pattern, and the pattern defies the standard law (or Gaussian) in probability textbooks. This universal phenomenon was discovered in the 1980s by physicists and has since grown into an active area of research in math and physics. Tsai’s work focuses on developing and applying a strand of mathematical tools called stochastic analysis to understand the universal pattern in these systems.