@article{10772, abstract = {We introduce tropical corals, balanced trees in a half-space, and show that they correspond to holomorphic polygons capturing the product rule in Lagrangian Floer theory for the elliptic curve. We then prove a correspondence theorem equating counts of tropical corals to punctured log Gromov–Witten invariants of the Tate curve. This implies that the homogeneous coordinate ring of the mirror to the Tate curve is isomorphic to the degree-zero part of symplectic cohomology, confirming a prediction of homological mirror symmetry.}, author = {Arguez, Nuroemuer Huelya}, issn = {1469-7750}, journal = {Journal of the London Mathematical Society}, number = {1}, pages = {343--411}, publisher = {London Mathematical Society}, title = {{Mirror symmetry for the Tate curve via tropical and log corals}}, doi = {10.1112/jlms.12515}, volume = {105}, year = {2022}, } @article{12793, abstract = {Let F be a global function field with constant field Fq. Let G be a reductive group over Fq. We establish a variant of Arthur's truncated kernel for G and for its Lie algebra which generalizes Arthur's original construction. We establish a coarse geometric expansion for our variant truncation. As applications, we consider some existence and uniqueness problems of some cuspidal automorphic representations for the functions field of the projective line P1Fq with two points of ramifications.}, author = {Yu, Hongjie}, issn = {1945-5844}, journal = {Pacific Journal of Mathematics}, keywords = {Arthur–Selberg trace formula, cuspidal automorphic representations, global function fields}, number = {1}, pages = {193--237}, publisher = {Mathematical Sciences Publishers}, title = {{ A coarse geometric expansion of a variant of Arthur's truncated traces and some applications}}, doi = {10.2140/pjm.2022.321.193}, volume = {321}, year = {2022}, } @article{6965, abstract = {The central object of investigation of this paper is the Hirzebruch class, a deformation of the Todd class, given by Hirzebruch (for smooth varieties). The generalization for singular varieties is due to Brasselet–Schürmann–Yokura. Following the work of Weber, we investigate its equivariant version for (possibly singular) toric varieties. The local decomposition of the Hirzebruch class to the fixed points of the torus action and a formula for the local class in terms of the defining fan are recalled. After this review part, we prove the positivity of local Hirzebruch classes for all toric varieties, thus proving false the alleged counterexample given by Weber.}, author = {Rychlewicz, Kamil P}, issn = {1469-2120}, journal = {Bulletin of the London Mathematical Society}, number = {2}, pages = {560--574}, publisher = {Wiley}, title = {{The positivity of local equivariant Hirzebruch class for toric varieties}}, doi = {10.1112/blms.12442}, volume = {53}, year = {2021}, } @article{9099, abstract = {We show that on an Abelian variety over an algebraically closed field of positive characteristic, the obstruction to lifting an automorphism to a field of characteristic zero as a morphism vanishes if and only if it vanishes for lifting it as a derived autoequivalence. We also compare the deformation space of these two types of deformations.}, author = {Srivastava, Tanya K}, issn = {14208938}, journal = {Archiv der Mathematik}, number = {5}, pages = {515--527}, publisher = {Springer Nature}, title = {{Lifting automorphisms on Abelian varieties as derived autoequivalences}}, doi = {10.1007/s00013-020-01564-y}, volume = {116}, year = {2021}, } @article{9173, abstract = {We show that Hilbert schemes of points on supersingular Enriques surface in characteristic 2, Hilbn(X), for n ≥ 2 are simply connected, symplectic varieties but are not irreducible symplectic as the hodge number h2,0 > 1, even though a supersingular Enriques surface is an irreducible symplectic variety. These are the classes of varieties which appear only in characteristic 2 and they show that the hodge number formula for G¨ottsche-Soergel does not hold over haracteristic 2. It also gives examples of varieties with trivial canonical class which are neither irreducible symplectic nor Calabi-Yau, thereby showing that there are strictly more classes of simply connected varieties with trivial canonical class in characteristic 2 than over C as given by Beauville-Bogolomov decomposition theorem.}, author = {Srivastava, Tanya K}, issn = {0007-4497}, journal = {Bulletin des Sciences Mathematiques}, number = {03}, publisher = {Elsevier}, title = {{Pathologies of the Hilbert scheme of points of a supersingular Enriques surface}}, doi = {10.1016/j.bulsci.2021.102957}, volume = {167}, year = {2021}, }