"ai is like nuclear energy–both promising and dangerous."
bill gates, 2019

data science is central to ai and has driven most of recent advances in biomedicine and beyond. human judgment calls are ubiquitous at every step of a data science life cycle (dslc): problem formulation, data cleaning, eda, modeling, and reporting. such judgment calls are often responsible for the "dangers" of ai by creating a universe of hidden uncertainties well beyond sample-to-sample uncertainty.

to mitigate these dangers, veridical (truthful) data science is introduced based on three principles: predictability, computability and stability (pcs). the pcs framework and documentation unify, streamline, and expand on the ideas and best practices of statistics and machine learning. in every step of a dslc, pcs emphasizes reality check through predictability, considers computability up front, and takes into account expanded uncertainty sources including those from data curation/cleaning and algorithm choice to build more trust in data results. pcs will be showcased through collaborative research in finding genetic drivers of a heart disease, stress-testing a clinical decision rule, and identifying microbiome-related metabolite signatures for possible early cancer detection. 

i will explain how the fourier transform takes us from functions on g to functions on g dual and switches convolution with pointwise operator multiplication. i’ll motivate from the case of abelian groups, where g dual has a group structure.

partitions arise in linear algebra as smith normal forms of finite dvr-modules. this viewpoint has given rise to several important objects in symmetric function theory; they are indexed by partitions. what if we replace the dvr by other rings? the analogous objects can no longer be indexed by partitions, but certain general properties can still be proved. they show up in discrete random matrix theory (joint with gilyoung cheong) and algebraic geometry (joint with ruofan jiang). in some special cases, these objects can still be expressed in partitions (though more convoluted), and the proven general properties give rise to new identities involving hall polynomials that do not seem to have a direct combinatorial proof.

this presentation focuses on applying the discrete approximation method to establish necessary optimality conditions in an optimization problem for fully controlled constrained sweeping processes. additionally, we explore its applications in various practical dynamical models. the first model deals with the dynamics of mobile robots navigating obstacles, while the second pertains to model predictive control utilizing neural networks.

we give a new short proof of the theorem due to marquis and sabok, which states that the orbit equivalence relation induced by the action of a finitely generated hyperbolic group on its gromov boundary is hyperfinite. our methods permit moreover to show that every such action has finite borel asymptotic dimension. this is a joint work with andrea vaccaro.

in the presence of a large group action, even non-noetherian rings sometimes behave like noetherian rings. for example, cohen proved that every symmetric ideal in the infinite variable polynomial ring is generated by finitely many polynomials (and their orbits under the infinite symmetric group). in this talk, i will give a brief introduction to equivariant commutative algebra where we systematically study such noetherian phenomena in infinite variable polynomial rings, and explain my work over fields of positive characteristic.