*Please contact me for updated versions.
Obstructions to Overconvergent Lifts of Formal Solutions to PDEs (Updated Version: PDF )
The D-Geometric Hilbert Scheme -- Part II: Hilbert and Quot DG-Schemes (with A. Sheshmani) arXiv:2411.02387
The D-Geometric Hilbert Scheme -- Part I: Involutivity and Stability (with A. Sheshmani) arXiv:2507.07937
Spencer Hypercohomologies in the Geometric Theory of Partial Differential Equations (with V. Rubtsov): (Accepted (2025): PDF)
Conservation Laws and Cohomological Intersections: Accepted: Journal of Geometry and Physics, 2026 https://doi.org/10.1016/j.geomphys.2026.105763.
Derived Moduli Spaces of Nonlinear PDEs II: Variational Tricomplex and BV Formalism (with A. Sheshmani, S-T Yau) arXiv:2406.16825 (Submitted Version: PDF )
Derived Moduli Spaces of Nonlinear PDEs I: Singular Propagations (with A. Sheshmani, S-T Yau) arXiv:2312.05226 (Submitted Version: PDF)
Tyurin Degenerations, Derived Lagrangians and Categorification of DT Invariants (with A. Sheshmani) arXiv:2510.20325
Functors of Differential Calculus in Diolic Algebras, arxiv:2009.04024
Differential Calculus in Triole Algebras, arxiv:2303.17868
Differential Calculus over Graded Commutative Algebras and Vector Bundles with Inner Structures (AMS, Contemporary Mathematics, Vol. 789, 2023) arxiv:2312.04842
Gauge Manifolds their cohomologies and Chern-Weil Theory with Inner Structures (Draft, In progress)
Derived geometry and PDEs, Seminar of mathematical physics and algebraic topology, LAREMA, University of Angers (January 2019)
Introduction to Derived Geometries: Mini course at University of Salerno. (February 2019)
Derived geometry, higher structures and physics: Mini course at LAMA, University of Chambery. (November 2019)
Non-linear PDE geometry from a higher and derived point of view: Doctoral student seminar, LAREMA, Department of Mathematics. (March 2020)
Differential Calculus in Diole Algebras: participant talk at the Wisla 2021 winter school and workshop (January 2021) (slides)
Local gauge field theory from the perspective of non-linear PDE geometry: Junior Global Poisson Workshop (May 2021) (plenary talk, parallel talk)
What are non-linear PDEs? A homotopical point of view: 'Gong show' talk and poster contribution for Higher Structures in QFT and String Theory, virtual conference for junior researchers (poster)
Understanding Non-linear PDEs: a derived geometric perspective: BIMSA-YMSC Post-Doc Workshop B Fall Semester (November 2022)
Differential Calculus in Vector Bundles from a (graded) Algebraic Approach: BIMSA-BIT Differential Geometry Seminar (November 2022)
Modern Homotopy Theory and the Geometry of Non-linear PDEs: Advances in Modern Homotopy IV Conference (June 2023)
Moduli Spaces of Solutions to Non-linear PDEs in Derived (Differential) Geometry: BIMSA-BIT Differential Geometry Seminar (September 2023)
Propagation of Solution Singularities for Non-linear PDEs: BIMSA-YMSC Post-Doc Workshop Fall Semester (November 2023)
Derived Geometry and Non-linear PDEs (Physics LATAM Seminar) (Invited Lecture Series), August 07,09 ,2024 (Online)
Moduli Stacks of Solutions to Non-linear PDEs and their related Singularities: SIMIS Seminar on Derived and Non-commutative geometry, September 16, Shanghai, China
D-ideal sheaves, D-Hilbert Schemes and enumerative geometry of Non-linear PDE: HSE-BIMSA Conference in Algebraic Geometry and Mathematical Physics, November 06, 2024, Moscow, Russia (*online)
Non-linear PDEs and Secondary Calculus via Derived Algebraic Geometry: BIMSA Algebraic Geometry Seminar, December 12, 2024
Singularities and Bi-complexes for PDEs: Geometry of Differential Equation Seminar, February 19, 2025 (*online)
Yiyou Scholar Qiuzhen College, Tsinghua University (Spring 2023, Fall 2023, Spring 2024): at Qiuzhen College. I mentored four pre-college students, met with them frequently and advised them on their academic journey.
Riemannian Geometry (Teaching Assistant, Spring Semester 2023): TA for Professor. Sebastian Heller.
Counting Sheaves and Objects in Derived Categories in Dimensions 2,3,4,5 Part I (Teaching Assistant,Fall Semester 2023): TA for Professor. Artan Sheshmani.
Counting Sheaves and Objects in Derived Categories in Dimensions 2,3,4,5 Part II (Teaching Assistant, Spring Semester 2024): TA for Professor. Artan Sheshmani.
Theory of schemes and stacks, Derived Categories and Intersection theory I (Teaching Assistant, Fall Semester 2024): TA for Professor Artan Sheshmani.
Theory of schemes and stacks, Derived Categories and Intersection theory II (Teaching Assistant, Spring Semester 2025): TA for Professor Artan Sheshmani.
Theory of schemes and stacks, Derived Categories and Intersection theory I (Teaching Assistant, Fall Semester 2025): TA for Professor Artan Sheshmani.
Introduction to the Donaldson-Uhlenbeck-Yau Theorem (Teaching Assistant, Fall Semester 2025): TA for Professor Yuuji Tanaka.
Misc.
PhD Thesis: I defended my PhD thesis titled: "Cohomological aspects of the Hamiltonian formalism: steps towards quantum observability" on July 19, 2021. This thesis was prepared at LAREMA, University of Angers and was advised by Volodya Rubtsov (LAREMA) and the late Alexandre Vinogradov. The slides from my thesis defence are available here.