Page 253 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 253
APPLIED COMBINATORIAL AND GEOMETRIC TOPOLOGY (MS-34)
study is strictly related to the problem, posed by Kirby, of the existence of special handle-
decompositions for any simply-connected closed PL 4-manifold.
Partition extenders, skeleta of simplices, and Simon’s conjecture
Bennet Goeckner, goeckner@uw.edu
University of Washington, United States
Coauthors: Joseph Doolittle, Alexander Lazar
If a pure simplicial complex is partitionable, then its h-vector has a combinatorial interpre-
tation in terms of any partitioning of the complex. Such an interpretation does not exist for
non-partitionable complexes. Given a non-partitionable complex, we will construct a relative
complex—called a partition extender—that allows us to write the h-vector of a non-partitionable
complex as the difference of two h-vectors of partitionable complexes in a natural way. We will
show that all pure complexes have partition extenders.
A similar notion can be defined for Cohen–Macaulay and shellable complexes. We will
show precisely which complexes have Cohen–Macaulay extenders, and we will discuss a con-
nection to a conjecture of Simon on the extendable shellability of uniform matroids. This is
joint work with Joseph Doolittle and Alexander Lazar.
On the Connectivity of Branch Loci of Spaces of Curves
Milagros Izquierdo, milagros.izquierdo@liu.se
Linköping University, Sweden
Coauthor: Antonio F. Costa
Since the 19th century the theory of Riemann surfaces has a central place in mathematics putting
together complex analysis, algebraic and hyperbolic geometry, group theory and combinatorial
methods.
Since Riemann, Klein and Poincar’e among others, we know that a compact Riemann sur-
face is a complex curve, and also the quotient of the hyperbolic plane by a Fuchsian group.
In this talk we study the connectivity of the moduli spaces of Riemann surfaces (i.e in spaces
of Fuchsian groups). Spaces of Fuchsian groups are orbifolds where the singular locus is formed
by Riemann surfaces with automorphisms: the branch loci: With a few exceptions the branch
loci is disconnected and consists of several connected components.
This talk is a survey of the different methods and topics playing together in the theory of
Riemann surfaces.
Joint wotk with Antonio F. Costa.
251
study is strictly related to the problem, posed by Kirby, of the existence of special handle-
decompositions for any simply-connected closed PL 4-manifold.
Partition extenders, skeleta of simplices, and Simon’s conjecture
Bennet Goeckner, goeckner@uw.edu
University of Washington, United States
Coauthors: Joseph Doolittle, Alexander Lazar
If a pure simplicial complex is partitionable, then its h-vector has a combinatorial interpre-
tation in terms of any partitioning of the complex. Such an interpretation does not exist for
non-partitionable complexes. Given a non-partitionable complex, we will construct a relative
complex—called a partition extender—that allows us to write the h-vector of a non-partitionable
complex as the difference of two h-vectors of partitionable complexes in a natural way. We will
show that all pure complexes have partition extenders.
A similar notion can be defined for Cohen–Macaulay and shellable complexes. We will
show precisely which complexes have Cohen–Macaulay extenders, and we will discuss a con-
nection to a conjecture of Simon on the extendable shellability of uniform matroids. This is
joint work with Joseph Doolittle and Alexander Lazar.
On the Connectivity of Branch Loci of Spaces of Curves
Milagros Izquierdo, milagros.izquierdo@liu.se
Linköping University, Sweden
Coauthor: Antonio F. Costa
Since the 19th century the theory of Riemann surfaces has a central place in mathematics putting
together complex analysis, algebraic and hyperbolic geometry, group theory and combinatorial
methods.
Since Riemann, Klein and Poincar’e among others, we know that a compact Riemann sur-
face is a complex curve, and also the quotient of the hyperbolic plane by a Fuchsian group.
In this talk we study the connectivity of the moduli spaces of Riemann surfaces (i.e in spaces
of Fuchsian groups). Spaces of Fuchsian groups are orbifolds where the singular locus is formed
by Riemann surfaces with automorphisms: the branch loci: With a few exceptions the branch
loci is disconnected and consists of several connected components.
This talk is a survey of the different methods and topics playing together in the theory of
Riemann surfaces.
Joint wotk with Antonio F. Costa.
251
