Research

I have broad mathematical interests. You can find the arxiv versions of my published papers here. Here is an old Research Statement from 2019 when I was on the postdoc job market.  

Explainable AI

• Stability of game-theoretic feature explanations for machine learning models, with Alexey Miroshnikov and  Konstandinos Kotsiopoulos and Arjun Ravi Kannan. Submitted (2024). (The manuscript is based on the first half of this preprint.) 

• On marginal feature attributions of tree-based models, with Alexey Miroshnikov and  Konstandinos Kotsiopoulos and Arjun Ravi Kannan. Foundations of Data Science (2024). 

• Approximation of group explainers with coalition structure using Monte Carlo sampling on the product space of coalitions and features, with Alexey Miroshnikov and  Konstandinos Kotsiopoulos and Arjun Ravi Kannan. Preprint (2023). 

Mathematics of Deep Neural Networks (expressive power)

• • On PDE characterization of smooth hierarchical functions computed by neural networks, with Roozbeh Farhoodi and Konrad Kording. Neural Computation 33 (2021), no. 12, 3204–3263.  (The paper has a considerable overlap with this preprint.)

  • On functions computed on trees, with Roozbeh Farhoodi and Ilenna Jones and Konrad Kording. Neural Computation 31 (2019), no. 11, 2075–2137.

Dynamical Systems

• • On the rank of the Thurston pullback map. International Mathematics Research Notices 24 (2023),  21838–21873.

  • Monotonicity of entropy for real quadratic rational maps.  Nonlinearity 34 (2021), 6587–6626.  (A related recent talk by John Milnor)

  • Real entropy rigidity under quasi-conformal deformations. Conformal Geometry and Dynamics 25 (2021), 1–33.

  • Entropy Behavior of Real Rational Maps. PhD Thesis, September 2020. 

  • On the non-monotonicity of entropy for a class of real quadratic rational maps, with Kevin Pilgrim. Journal of Modern Dynamics 16 (2020), 225–254. 

Algebraic Topology

• • Topological aspects of the dynamical moduli space of rational maps, with Maxime Bergeron and Sam Nariman. Advances in Mathematics  397 (2022).  

Algebraic Curves (mostly computational aspects)

• • The Belyi Characterization of a Class of Modular Curves. Journal de Théorie des Nombres de Bordeaux 30 (2018), no. 2, 409–429.

  • A descent method for explicit computations on curves. Bulletin of the Iranian Mathematical Society 43 (2017), no. 6, 1989–2016.

  • Dessins on Modular Curves, with Ali Kamalinejad. Preprint (2016). 

Miscellaneous

• • Results and questions on matchings in abelian groups and vector subspaces of fields, with Mohsen Aliabadi. Journal of Algebra  598 (2022),  85–104. 

  • Integral of groups, with Babak Miraftab. Communications in Algebra 45 (2017), no. 3, 1105–1113.

From another life!

• • My theses at Sharif University (in Persian) could be found here and here.