Publication list
Arithmetic-Geometric Correspondence of Character Stacks via Topological Quantum Field Theory (with Ángel González-Prieto and Jesse Vogel), submitted (2023)
Logarithmic Hochschild co/homology via formality of derived intersections (with Leo Herr and Francesca Leonardi), submitted, (2023), dedicated to LCI
Finitely Presentable Higher-Dimensional Automata and the Irrationality of Process Replication (with Henning Basold andThomas Baronner), Relational and Algebraic Methods in Computer Science (RAMICS 2024)
Virtual Classes of Character Stacks (with Ángel González-Prieto and Jesse Vogel), submitted, (2022)
Virtual Classes of Representation Varieties of Upper Triangular Matrices via Topological Quantum Field Theories (with Jesse Vogel), SIGMA 18 (2022), 095, 38 pages
Non-Noetherian representation categories of generalized fields (with Maël Denys and Giacomo Negrisolo), submitted, (2020)
Weak E2-Morita equivalences via quantization of the 1-shifted cotangent bundle submitted, (2018)
Algebraic Geometry over the residue field of the infinite place (with Mate L. Juhász), Communications in Algebra, Volume 46, Issue 10, 4149-4173 (2018)
Derived intersections over the Hochschild cochain complex submitted, (2016)
Explicit computations of Hida families via overconvergent modular symbols (with Evan Dummit, Robert Harron, Lalit Jain, Robert Pollack, Daniel Ross), Research in Number Theory, 2:25, (2016)
Hodge theorem for the logarithmic de Rham complex via derived intersections, Research in the Mathematical Sciences, 7, 24, (2020)
On the number of rich lines in high dimensional real vector spaces (with Zachary Scherr), Discrete and Computational Geometry, 55(4), 955-962, (2016)
Formality of derived intersections and the orbifold HKR isomorphism (with Dima Arinkin and Andrei Caldararu), Journal of Algebra, Volume 540, 100-120, (2019)
On the joints problem with multiplicities submitted, (2014)
Derived intersections and the Hodge theorem (with Dima Arinkin and Andrei Caldararu), Algebraic Geometry 4 (2017), 394-423
An incidence conjecture of Bourgain over fields of positive characteristic (with Jordan S. Ellenberg), Forum of Mathematics, Sigma, 4, E23 (2016)
Kakeya sets over non-archimedean local rings (with Evan Dummit) Mathematika, 59, 257-266, (2013)
Power map permutations and symmetric differences in finite groups (with Guillermo Mantilla-Soler), Journal of Algebra and Applications (10) (2011), 947-959
Publications with Polyhedral Structures Laboratory
Polyframe2, Graphic Statics plugin, with Yao Lu, Andrei Nejur, Mathias Bernhard, Mostafa Akbari, and Masoud Akbarzadeh
Algebraic 3D Graphic Statics with Edge and Vertex Constraints: A comprehensive approach to extend solution space for polyhedral form-finding (with Yao Lu and Masoud Akbarzadeh), Computer-Aided Design, Volume 166, Jan (2024),
3D auxetic materials designed with algebraic polyhedral graphic statics, with Yao Lu, Abdolhamid Akbarzadeh, Masoud Akbarzadeh, Proceedings of the IASS Annual Symposium 2023: Integration of Design and Fabrication, (2023)
Generation of a compression-tension combined funicular polyhedral beam structure, with Hua Chai, Yao Lu, and Masoud Akbarzadeh, Proceedings of the IASS Annual Symposium 2023: Integration of Design and Fabrication, (2023)
Dragonfly-Inspired Wing Design Enabled by Machine Learning and Maxwell's Reciprocal Diagrams (with Hao Zheng, Hossein Mfatteh, Masoud Akbarzadeh, and Abdolhamid Akbarzadeh), Advanced Science, Volume10, Issue18 (2023)
Designing the Geometry of Auxetic Materials using Graphic Statics (with Masoud Akbarzadeh), Proceedings of the IASS Symposium 2021, University of Surrey, UK (2021). A short survey video can be seen here.
Developing a polyhedral graphic statics formulation for tetrahedral truss analysis (with Salma Mozaffari, Masoud Akbarzadeh, and Thomas Vogel), Proceedings of the IASS Symposium 2021, University of Surrey, UK (2021)
Lightweight Structures and the Geometric Equilibrium in Dragonfly Wings (with Hao Zheng and Masoud Akbarzadeh), Proceedings of the IASS Symposium 2021, University of Surrey, UK (2021)
Algebraic 3D Graphic Statics: Constrained Areas (with Masoud Akbarzadeh), Computer-Aided Design, Volume 141, (2021)
Geometric Degrees of Freedom and Non-Conventional Spatial Structural Forms (with Masoud Akbarzadeh), Impact: Design With All Senses, Springer Nature (2019), 1-17
Algebraic 3D Graphic Statics: reciprocal constructions (with Masoud Akbarzadeh, Yi Guo), Computer-Aided Design, Volume 108, (2019), 30-41
Developing Algebraic Constraints for Reciprocal Polyhedral Diagrams of 3D Graphic Statics (with Masoud Akbarzadeh, Yi Guo), Proceedings of the IASS Symposium 2018, Creativity in Structural Design, MIT, Boston, USA, July 16-20, (2018).
Software
PolyFrame 2 | Food4Rhino (with Yao Lu, Dr. Andrei Nejur, Dr. Mathias Bernhard, Dr. Mostafa Akbari, Dr. Masoud Akbarzadeh)