Ivan Smith
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View article: Orbifold Hamiltonian Floer theory for global quotients
Orbifold Hamiltonian Floer theory for global quotients Open
We construct bulk-deformed orbifold Hamiltonian Floer theory for a global quotient orbifold, that is the quotient of a smooth closed symplectic manifold by a finite group acting faithfully via symplectomorphisms. The moduli spaces define a…
View article: Demonstration of T-Cell Monotypia Using Anti-TCRbeta1/2 (TRBC1/2) Immunostaining as a Rapid and Cost-Effective Alternative to PCR-Based Clonality Studies for the Diagnosis of T-Cell Lymphoma
Demonstration of T-Cell Monotypia Using Anti-TCRbeta1/2 (TRBC1/2) Immunostaining as a Rapid and Cost-Effective Alternative to PCR-Based Clonality Studies for the Diagnosis of T-Cell Lymphoma Open
Background/Objectives: T-cell lymphomas are often histologically indistinguishable from benign T-cell infiltrates, and diagnosis typically relies on slow, complex, and expensive multiplexed PCR reactions, requiring significant training and…
View article: Spectral Floer theory and tangential structures
Spectral Floer theory and tangential structures Open
In \cite{PS}, for a stably framed Liouville manifold $X$ we defined a Donaldson-Fukaya category $\mathcal{F}(X;\mathbb{S})$ over the sphere spectrum, and developed an obstruction theory for lifting quasi-isomorphisms from $\mathcal{F}(X;\m…
View article: Symplectomorphisms and spherical objects in the conifold smoothing
Symplectomorphisms and spherical objects in the conifold smoothing Open
Let $X$ denote the ‘conifold smoothing’, the symplectic Weinstein manifold which is the complement of a smooth conic in $T^*S^3$ or, equivalently, the plumbing of two copies of $T^*S^3$ along a Hopf link. Let $Y$ denote the ‘conifold resol…
View article: Gromov-Witten Invariants in Complex and Morava-Local K-Theories
Gromov-Witten Invariants in Complex and Morava-Local K-Theories Open
Given a closed symplectic manifold X , we construct Gromov-Witten-type invariants valued both in (complex) K -theory and in any complex-oriented cohomology theory $\mathbb{K}$ which is K p ( n )-local for some Morava K -theory K p ( n ). W…
View article: Bordism of flow modules and exact Lagrangians
Bordism of flow modules and exact Lagrangians Open
For a stably framed Liouville manifold X , we construct a "Donaldson-Fukaya category over the sphere spectrum" F(X; S). The objects are closed exact Lagrangians whose Gauss maps are nullhomotopic compatibly with the ambient stable framing,…
View article: Gromov-Witten invariants in complex and Morava-local $K$-theories
Gromov-Witten invariants in complex and Morava-local $K$-theories Open
Given a closed symplectic manifold $X$, we construct Gromov-Witten-type invariants valued both in (complex) $K$-theory and in any complex-oriented cohomology theory $\mathbb{K}$ which is $K_p(n)$-local for some Morava $K$-theory $K_p(n)$. …
View article: Symplectomorphisms and spherical objects in the conifold smoothing
Symplectomorphisms and spherical objects in the conifold smoothing Open
Let $X$ denote the `conifold smoothing', the symplectic Weinstein manifold which is the complement of a smooth conic in $T^*S^3$, or equivalently the plumbing of two copies of $T^*S^3$ along a Hopf link. Let $Y$ denote the `conifold resolu…
View article: Subleading asymptotics of link spectral invariants and homeomorphism groups of surfaces
Subleading asymptotics of link spectral invariants and homeomorphism groups of surfaces Open
This paper continues the study of link spectral invariants on compact surfaces, introduced in our previous work and shown to satisfy a Weyl law in which they asymptotically recover the Calabi invariant. Here we study their subleading asymp…
View article: Quantitative Heegaard Floer cohomology and the Calabi invariant
Quantitative Heegaard Floer cohomology and the Calabi invariant Open
We define a new family of spectral invariants associated to certain Lagrangian links in compact and connected surfaces of any genus. We show that our invariants recover the Calabi invariant of Hamiltonians in their limit. As applications, …
View article: Complex cobordism, Hamiltonian loops and global Kuranishi charts
Complex cobordism, Hamiltonian loops and global Kuranishi charts Open
Let $(X,ω)$ be a closed symplectic manifold. A loop $ϕ: S^1 \to \mathrm{Diff}(X)$ of diffeomorphisms of $X$ defines a fibration $π: P_ϕ \to S^2$. By applying Gromov-Witten theory to moduli spaces of holomorphic sections of $π$, Lalonde, Mc…
View article: Fukaya–Seidel categories of Hilbert schemes and parabolic category $\mathcal{O}$
Fukaya–Seidel categories of Hilbert schemes and parabolic category $\mathcal{O}$ Open
We realise Stroppel’s extended arc algebra [13, 51] in the Fukaya–Seidel category of a natural Lefschetz fibration on the generic fibre of the adjoint quotient map on a type A nilpotent slice with two Jordan blocks, and hence obtain a symp…
View article: Quantitative Heegaard Floer cohomology and the Calabi invariant
Quantitative Heegaard Floer cohomology and the Calabi invariant Open
We define a new family of spectral invariants associated to certain Lagrangian links in compact and connected surfaces of any genus. We show that our invariants recover the Calabi invariant of Hamiltonians in their limit. As applications, …
View article: Fukaya categories of surfaces, spherical objects and mapping class groups
Fukaya categories of surfaces, spherical objects and mapping class groups Open
We prove that every spherical object in the derived Fukaya category of a closed surface of genus at least $2$ whose Chern character represents a nonzero Hochschild homology class is quasi-isomorphic to a simple closed curve equipped with a…
View article: Lagrangian cobordism and tropical curves
Lagrangian cobordism and tropical curves Open
We study a cylindrical Lagrangian cobordism group for Lagrangian torus fibres in symplectic manifolds which are the total spaces of smooth Lagrangian torus fibrations. We use ideas from family Floer theory and tropical geometry to obtain b…
View article: Double bubble plumbings and two-curve flops
Double bubble plumbings and two-curve flops Open
We discuss the symplectic topology of the Stein manifolds obtained by plumbing two 3-dimensional spheres along a circle. These spaces are related, at a derived level and working in a characteristic determined by the specific geometry, to l…
View article: Symplectic topology of K 3 K3 surfaces via mirror symmetry
Symplectic topology of K 3 K3 surfaces via mirror symmetry Open
We study the symplectic topology of certain K3K3 surfaces (including the “mirror quartic” and “mirror double plane”), equipped with certain Kähler forms. In particular, we prove that the symplectic Torelli group may be infinitely generated…
View article: Bounds on Wahl singularities from symplectic topology
Bounds on Wahl singularities from symplectic topology Open
Let X be a minimal surface of general type with p g > 0 (equivalently, b + > 1) and let K 2 be the square of its canonical class.Building on work of Khodorovskiy and Rana, we prove that if X develops a Wahl singularity of length in a Q-Gor…
View article: Rational equivalence and Lagrangian tori on K3 surfaces
Rational equivalence and Lagrangian tori on K3 surfaces Open
Fix a symplectic K3 surface X homologically mirror to an algebraic K3 surface Y by an equivalence taking a graded Lagrangian torus L\subset X to the skyscraper sheaf of a point y\in Y. We show there are Lagrangian tori with vanishing Maslo…
View article: STABILITY CONDITIONS IN SYMPLECTIC TOPOLOGY
STABILITY CONDITIONS IN SYMPLECTIC TOPOLOGY Open
We discuss potential (largely speculative) applications of Bridgeland's theory of stability conditions to symplectic mapping class groups.
View article: Bounds on Wahl singularities from symplectic topology
Bounds on Wahl singularities from symplectic topology Open
A complex surface is said to have general type if its canonical bundle is big. The moduli space of surfaces of general type with fixed characteristic numbers $K^2$ and $\chi$ admits a compactification, constructed by Kolla ́r and Shepherd-B…
View article: Khovanov homology from Floer cohomology
Khovanov homology from Floer cohomology Open
This paper realises the Khovanov homology of a link in $ S^3$ as a Lagrangian Floer cohomology group, establishing a conjecture of Seidel and the second author. The starting point is the previously established formality theorem for the sym…
View article: Khovanov homology from Floer cohomology
Khovanov homology from Floer cohomology Open
This paper realises the Khovanov homology of a link in as a Lagrangian Floer cohomology group, establishing a conjecture of Seidel and the second author. The starting point is the previously established formality theorem for the symplecti…
View article: Issue Information
Issue Information Open
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View article: Symplectomorphisms of exotic discs
Symplectomorphisms of exotic discs Open
We construct a symplectic structure on a disc that admits a compactly supported symplectomorphism which is not smoothly isotopic to the identity. The symplectic structure has an overtwisted concave end; the construction of the symplectomor…