@article{105,
abstract = {Clinical Utility Gene Card. 1. Name of Disease (Synonyms): Pontocerebellar hypoplasia type 9 (PCH9) and spastic paraplegia-63 (SPG63). 2. OMIM# of the Disease: 615809 and 615686. 3. Name of the Analysed Genes or DNA/Chromosome Segments: AMPD2 at 1p13.3. 4. OMIM# of the Gene(s): 102771.},
author = {Marsh, Ashley and Novarino, Gaia and Lockhart, Paul and Leventer, Richard},
journal = {European Journal of Human Genetics},
pages = {161--166},
publisher = {Nature Publishing Group},
title = {{CUGC for pontocerebellar hypoplasia type 9 and spastic paraplegia-63}},
doi = {10.1038/s41431-018-0231-2},
volume = {27},
year = {2019},
}
@article{319,
abstract = {We study spaces of modelled distributions with singular behaviour near the boundary of a domain that, in the context of the theory of regularity structures, allow one to give robust solution theories for singular stochastic PDEs with boundary conditions. The calculus of modelled distributions established in Hairer (Invent Math 198(2):269–504, 2014. https://doi.org/10.1007/s00222-014-0505-4) is extended to this setting. We formulate and solve fixed point problems in these spaces with a class of kernels that is sufficiently large to cover in particular the Dirichlet and Neumann heat kernels. These results are then used to provide solution theories for the KPZ equation with Dirichlet and Neumann boundary conditions and for the 2D generalised parabolic Anderson model with Dirichlet boundary conditions. In the case of the KPZ equation with Neumann boundary conditions, we show that, depending on the class of mollifiers one considers, a “boundary renormalisation” takes place. In other words, there are situations in which a certain boundary condition is applied to an approximation to the KPZ equation, but the limiting process is the Hopf–Cole solution to the KPZ equation with a different boundary condition.},
author = {Gerencser, Mate and Hairer, Martin},
issn = {14322064},
journal = {Probability Theory and Related Fields},
number = {3-4},
pages = {697–758},
publisher = {Springer},
title = {{Singular SPDEs in domains with boundaries}},
doi = {10.1007/s00440-018-0841-1},
volume = {173},
year = {2019},
}
@article{439,
abstract = {We count points over a finite field on wild character varieties,of Riemann surfaces for singularities with regular semisimple leading term. The new feature in our counting formulas is the appearance of characters of Yokonuma–Hecke algebras. Our result leads to the conjecture that the mixed Hodge polynomials of these character varieties agree with previously conjectured perverse Hodge polynomials of certain twisted parabolic Higgs moduli spaces, indicating the
possibility of a P = W conjecture for a suitable wild Hitchin system.},
author = {Hausel, Tamas and Mereb, Martin and Wong, Michael},
issn = {1435-9855},
journal = {Journal of the European Mathematical Society},
number = {10},
pages = {2995--3052},
publisher = {European Mathematical Society},
title = {{Arithmetic and representation theory of wild character varieties}},
doi = {10.4171/JEMS/896},
volume = {21},
year = {2019},
}
@article{441,
author = {Kalinin, Nikita and Shkolnikov, Mikhail},
issn = {2199-6768},
journal = {European Journal of Mathematics},
number = {3},
pages = {909–928},
publisher = {Springer Nature},
title = {{Tropical formulae for summation over a part of SL(2,Z)}},
doi = {10.1007/s40879-018-0218-0},
volume = {5},
year = {2019},
}
@article{5790,
abstract = {The partial representation extension problem is a recently introduced generalization of the recognition problem. A circle graph is an intersection graph of chords of a circle. We study the partial representation extension problem for circle graphs, where the input consists of a graph G and a partial representation R′ giving some predrawn chords that represent an induced subgraph of G. The question is whether one can extend R′ to a representation R of the entire graph G, that is, whether one can draw the remaining chords into a partially predrawn representation to obtain a representation of G. Our main result is an O(n3) time algorithm for partial representation extension of circle graphs, where n is the number of vertices. To show this, we describe the structure of all representations of a circle graph using split decomposition. This can be of independent interest.},
author = {Chaplick, Steven and Fulek, Radoslav and Klavík, Pavel},
issn = {03649024},
journal = {Journal of Graph Theory},
number = {4},
pages = {365--394},
publisher = {Wiley},
title = {{Extending partial representations of circle graphs}},
doi = {10.1002/jgt.22436},
volume = {91},
year = {2019},
}