185 papers
This thesis extends the relative -contractibility of Koras-Russell threefolds and their higher-dimensional prototypes to arbitrary Noetherian base schemes, thereby establishing the existence of the first known family of smooth "exotic" motivic spheres in dimensions that are -homotopic to, but not isomorphic to, the punctured affine space .
This paper demonstrates the existence of planar rational curves over the finite field with arbitrarily large degrees that possess a unique singularity of multiplicity 2, a phenomenon that is restricted to degrees of at most 6 in characteristic 0.
This paper introduces an algebraic method, based on Eisenbud et al. (1977), for computing the index of completely mixed equilibria in finite games to demonstrate that any integer can be such an index, while showing that for monogenic equilibria the index is restricted to with non-zero values equivalent to payoff-robustness, and further extends these findings to extensive-form and boundary equilibria.
These lecture notes from the 2024 Les Houches school provide an introduction to the moduli space of Riemann surfaces, covering their recursive boundary structure, Witten's conjecture via topological recursion, and their connections to JT gravity and topological strings.
This paper presents a complete classification of dimer integrable systems associated with the 16 reflexive polygons, detailing their Hamiltonian structures and spectral curves while identifying 16 birational equivalences that group them into five distinct classes and demonstrate how brane tiling deformations preserve key moduli space invariants.