Anyons are quasiparticles in two dimensions. They do not belong to the two classes of elementary particles, bosons and fermions. Instead, they obey Abelian or non-Abelian fractional statistics. Their quantum mechanical states are determined by fusion or braiding, to which braid groups and conformal field theories are naturally applied. Some of non-Abelian anyons are central in realization of topological qubits and topological quantum computing. I will introduce the basic properties of anyons and their recent experimental signatures observed in systems of topological order such as fractional quantum Hall systems and topological superconductors.

The temporal credit assignment, the problem of determining which actions in the past are responsible for the current outcome (long-term cause and effect), is difficult to solve because one needs to backpropagate the error signal through space and time. Despite its computational challenges, humans are very good at solving this problem. Our lab uses reinforcement learning theory and algorithms to explore the nature of computations underlying the brain’s ability to solve the temporal credit assignment. I will outline two-fold approaches to this issue: (1) training a computational model from human behavioral data without underfitting and overfitting (Brain → AI) and (2) using the trained model to manipulate the way the human brain solves the temporal credit assignment problem (AI → brain).

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Education/employments PhD, KAIST (2009)Postdoc, MIT (2010-2011), Caltech (2011-2015)Faculty, KAIST (2015-now) Honors/awards IBM Academic Research Award (2021)Google Faculty Research Award (2017)Della-Martin Fellowship (2014) KAIST Breakthroughs (2020)KAIST Songam Distinguished Research Award (2019)KAIST Top 10 Technologies (2019)KAIST Institute Faculty Award (2019) KIIS Young Investigator Award (2016)ICROS Young Investigator Award (2016)

In his famous 1900 presentation, Hilbert proposed so-called the Hilbert’s 6thproblem, namely “Mathematical Treatment of the Axioms of Physics”. He mentioned that “Boltzmann's work on the principles of mechanics suggests the problem of developing mathematically the limiting processes, there merely indicated, which lead from the atomistic view to the laws of motion of continua.” In this lecture, we present some recent development of the Hilbert’s 6th problem in the Boltzmann theory when the various fluid models have natural “singularities” such as unbounded vorticity and formation of boundary layers.

The objective of the study is to evaluate neural circuitry supporting a cognitive control task, and associated practice-related changes via acquisition of blood oxygenation level dependent (BOLD) signal collected using functional magnetic resonance imaging (fMRI). FMR images are acquired from participants engaged in antisaccade (generating a glance away from a cue) performance at two scanning sessions: 1) pre-practice before any exposure to the task, and 2) post-practice, after one week of daily practice on antisaccades, prosaccades (glancing towards a target) or fixation (maintaining gaze on a target). The three practice groups are compared across the two sessions, and analyses are conducted via the application of a model-free clustering technique based on wavelet analysis. This series of procedures is developed to address analysis problems inherent in fMRI data and is composed of several steps: data aggregation, no trend test, decorrelation, principal component analysis and K-means clustering. Also, we develop a semiparametric approach under shape invariance to quantify and test the differences in sessions and groups using the property that brain signals from a task-related experiment may exhibit a similar pattern in regions of interest across participants. We estimate the common function with local polynomial regression and estimate the shape invariance model parameters using evolutionary optimization methods. Using the proposed approach, we compare BOLD signals in multiple regions of interest for the three practice groups at the two sessions and quantify the effects of task practice in these groups.