Algebra ⟶ non-linear statistics and applications in social sciences

I build statistical models for discrete relational data that capture more complex behavior than traditional models, study them through the algebrogeometric lens, prove their interpretability in practice, and develop scalable model/data fit testing methodologies using a blend of combinatorial, algebraic, probabilistic, and Bayesian algorithms.

Randomness ⟶ non-linear algebra and applications in optimization

I study randomized algorithm approaches to computational algebra problems whose expected runtimes are much lower then the well-known worst-case complexity bounds, develop probabilistic models to study average and extreme behavior of algebraic objects, and use machine learning to predict and improve behavior of algebraic computations.

Randomized algorithms for solving massive discrete optimization  problems


DOE Office of Science, Randomized Algorithms for Scientific Computing, Award number 1010629. Joint with Argonne National Laboratory (2022-2025). Full list of awards can be found here

Algebraic statistics for network models


DARPA FA9550-12-1-0392 (2012-2013), AFOSR FA9550-14-1-0141 (2014-2017).

Simons Foundation, through a Travel Support for Mathematicians Gift 854770 (2022-2026).

Randomness and learning for non-linear algebra


NSF DMS-1522662 (2015-2019) joint with UCDavis.

Simons Foundation, through a Collaboration Grant for Mathematicians 854770 (2021-2022) and a Travel Support for Mathematicians Gift (2022-2026).

Statistical models in human sciences


2018 CISC seed grant with Mahima Saxena, formerly with IIT Psychology, and Lulu Kang, IIT Applied Math.

Curious? Check out research summary slides from April 2017.