Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

We find robust obstructions to representing a Hamiltonian diffeomorphism as a full k-th power, $$k \ge 2$$
 , and in particular, to including it into a one-parameter subgroup. The robustness is understood in the sense of Hofer’s metric. Our approach is based on the theory of persistence modules applied in the context of filtered Floer homology. We present applications to geometry and dynamics of Hamiltonian diffeomorphisms.

Autonomous Hamiltonian flows, Hofer’s geometry and persistence modules

Integrable Hamiltonian systems

We find robust obstructions to representing a Hamiltonian diffeomorphism as a full $k$-th power, $k \geq 2,$ and in particular, to including it into a one-parameter subgroup. The robustness is understood in the sense of Hofer's metric. Our approach is based on the theory of persistence modules applied in the context of filtered Floer homology. We present applications to geometry and dynamics of Hamiltonian diffeomorphisms.

Autonomous Hamiltonian flows, Hofer's geometry and persistence modules

Let $ G$ be a compact Lie group, and let $ k$ be a field of characteristic $ p \geq 0$ such that $ H^*(G)$ has no $ p$-torsion if $ p>0$. We show that a free Lagrangian orbit of a Hamiltonian $ G$-action on a compact, monotone, symplectic manifold $ X$ split-generates an idempotent summand of the monotone Fukaya category $ \mathcal {F}(X; k)$ if and only if it represents a nonzero object of that summand (slightly more general results are also provided). Our result is based on an explicit understanding of the wrapped Fukaya category $ \mathcal {W}(T^*G; k)$ through Koszul twisted complexes involving the zero-section and a cotangent fibre and on a functor $ D^b \mathcal {W}(T^*G; k) \to D^b\mathcal {F}(X^{-} \times X; k)$ canonically associated to the Hamiltonian $ G$-action on $ X$. We explore several examples which can be studied in a uniform manner, including toric Fano varieties and certain Grassmannians.

Generating the Fukaya categories of Hamiltonian G-manifolds

The wall-crossing formula and Lagrangian mutations

We prove a general form of the wall-crossing formula which relates the disk potentials of monotone Lagrangian submanifolds with their Floer-theoretic behavior away from a Donaldson divisor. We define geometric operations called mutations of Lagrangian tori in del Pezzo surfaces and in toric Fano varieties of higher dimension, and study the corresponding wall-crossing formulas that compute the disk potential of a mutated torus from that of the original one. 
In the case of del Pezzo surfaces, this justifies the connection between Vianna's tori and the theory of mutations of Landau-Ginzburg seeds. In higher dimension, this provides new Lagrangian tori in toric Fanos corresponding to different chambers of the mirror variety, including ones which are conjecturally separated by infinitely many walls from the chamber containing the standard toric fibre.

From symplectic cohomology to Lagrangian enumerative geometry

This paper introduces new operations on the string topology of a smooth manifold: gravitational descendants of its cotangent bundle, which are augmentations of the Chas-Sullivan $L_\infty$ algebra structure of the loop space. The definition extends to Liouville domains. Descendants of the $n$-torus are computed. 
To a monotone Lagrangian torus in a symplectic manifold, one associates a Laurent polynomial called the Landau-Ginzburg potential, by counting holomorphic disks. This paper proves the following mirror symmetry prediction: the constant terms of the powers of an LG potential are equal to descendant Gromov-Witten invariants of the ambient manifold.

String topology with gravitational descendants, and periods of Landau-Ginzburg potentials

Two commuting symplectomorphisms of a symplectic manifold give rise to actions on Floer cohomologies of each other. We prove the elliptic relation saying that the supertraces of these two actions are equal. In the case when a symplectomorphism f commutes with a symplectic involution, the elliptic relation provides a lower bound on the dimension of HF .f / in terms of the Lefschetz number of f restricted to the fixed locus of the involution. We apply this bound to prove that Dehn twists around vanishing Lagrangian spheres inside most hypersurfaces in Grassmannians have infinite order in the symplectic mapping class group. 53D40; 14F35, 14D05

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Dmitry Tonkonog

Papers

The wall-crossing formula and Lagrangian mutations

The wall-crossing formula and Lagrangian mutations

From symplectic cohomology to Lagrangian enumerative geometry

String topology with gravitational descendants, and periods of Landau-Ginzburg potentials

Commuting symplectomorphisms and Dehn twists in divisors