BEGIN:VCALENDAR
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BEGIN:VEVENT
SUMMARY:Allison Moore (VCU)
DTSTART:20200417T180000Z
DTEND:20200417T190000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/1
DESCRIPTION:Title: Introduction to Khovanov Homology\, part 3\nby Allison Moore (VC
U) as part of VCU Geometry and Topology Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samantha Kirk (NCSU)
DTSTART:20200424T180000Z
DTEND:20200424T190000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/2
DESCRIPTION:Title: Vertex Operator Representations of Twisted Toroidal Lie algebras
\nby Samantha Kirk (NCSU) as part of VCU Geometry and Topology Seminar\n\n
\nAbstract\nA toroidal Lie algebra is the universal central extension of t
he tensor product of a simple finite-dimensional Lie algebra g and the rin
g of Laurent polynomials in 2 or more variables. Given an automorphism of
the Lie algebra g of finite order\, one can construct a "twisted" version
of a toroidal Lie algebra. In this talk\, we will discuss how to construct
vertex operator representations of twisted toroidal Lie algebras.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katherine Maxwell (University of Minnesota Twin Cities)
DTSTART:20200501T180000Z
DTEND:20200501T190000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/3
DESCRIPTION:Title: The super Mumford form and Sato grassmannian\nby Katherine Maxwe
ll (University of Minnesota Twin Cities) as part of VCU Geometry and Topol
ogy Seminar\n\n\nAbstract\nThe moduli space of curves and representations
of the Virasoro algebra each separately give rise to the number $6j^2-6j+1
$. In the 1980s\, this observation was shown not to be a mere coincidence
by involving the infinite-dimensional Sato grassmannian. In this talk\, we
will first discuss this construction of Kontsevich and Arbarello\, De Con
cini\, Kac\, and Procesi\, and then discuss a supersymmetric generalizatio
n. Our main result is the existence of a flat holomorphic connection on th
e line bundle $\\lambda_{3/2}\\otimes\\lambda^{-5}_{1/2}$ on the moduli sp
ace of triples: a super Riemann surface\, a Neveu-Schwarz puncture\, and a
formal coordinate system.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joshua Sussan (CUNY)
DTSTART:20200508T180000Z
DTEND:20200508T190000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/4
DESCRIPTION:Title: p-DG structures and categorification\nby Joshua Sussan (CUNY) as
part of VCU Geometry and Topology Seminar\n\n\nAbstract\nThe Jones polyno
mial is an invariant of links coming from the representation theory of qua
ntum groups. After reviewing its construction\, we will discuss the goals
of the categorification program and how the notion of a p-DG algebra natu
rally arises when looking to categorify the WRT 3-manifold invariant.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Taylor (Colby College)
DTSTART:20200515T180000Z
DTEND:20200515T190000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/5
DESCRIPTION:Title: Lower bounds on the tunnel number of composite spatial theta graphs<
/a>\nby Scott Taylor (Colby College) as part of VCU Geometry and Topology
Seminar\n\n\nAbstract\nThe tunnel number of a graph embedded in a 3-dimens
ional manifold is the fewest number of arcs needed so that the union of th
e graph with the arcs has handlebody exterior. The behavior of tunnel numb
er with respect to connected sum of knots can vary dramatically\, dependin
g on the knots involved. However\, a classical theorem of Scharlemann and
Schultens says that the tunnel number of a composite knot is at least the
number of factors. For theta graphs\, trivalent vertex sum is the operatio
n which most closely resembles the connected sum of knots. The analogous t
heorem of Scharlemann and Schultens no longer holds\, however. I will prov
ide a sharp lower bound for the tunnel number of composite theta graphs\,
using recent work on a new knot invariant which is additive under connecte
d sum and trivalent vertex sum. This is joint work with Maggy Tomova.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Han-Bom Moon (Fordham University)
DTSTART:20200522T180000Z
DTEND:20200522T190000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/6
DESCRIPTION:Title: Finite generation of the algebra of conformal blocks via birational
geometry.\nby Han-Bom Moon (Fordham University) as part of VCU Geometr
y and Topology Seminar\n\n\nAbstract\nA Conformal block is a representatio
n-theoretic object constructed as an example of two-dimensional conformal
field theory (WZW model). For each simple Lie algebra $\\mathfrak{g}$ and
a stable curve\, the set of conformal blocks naturally has an algebra stru
cture. We prove\, by employing birational geometric techniques\, the finit
e generation of the algebra of conformal blocks for $\\mathfrak{g} = \\mat
hfrak{sl}_r$. This is joint work with Sang-Bum Yoo.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florencia Orosz Hunziker (Harvard University)
DTSTART:20200529T180000Z
DTEND:20200529T190000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/7
DESCRIPTION:Title: Tensor categories arising from the Virasoro algebra\nby Florenci
a Orosz Hunziker (Harvard University) as part of VCU Geometry and Topology
Seminar\n\n\nAbstract\nIn this talk we will discuss the tensor structure
associated to certain representations of the Virasoro algebra. In particul
ar\, we will show that there is a braided tensor category structure on the
category of C1-cofinite modules for the Virasoro vertex operator algebras
of arbitrary central charge.\nThis talk is based on joint work with Jinwe
i Yang\, Thomas Creutzig\, Cuibo Jiang and David Ridout.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Szczesny (Boston University)
DTSTART:20200605T180000Z
DTEND:20200605T190000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/8
DESCRIPTION:Title: Toric Hall Algebras\nby Matt Szczesny (Boston University) as par
t of VCU Geometry and Topology Seminar\n\n\nAbstract\nI will describe a co
nstruction that attaches to a smooth projective toric variety a co-commuta
tive Hopf algebra (in fact\, an enveloping algebra). It arises as a Hall a
lgebra of special coherent sheaves on the associated monoid scheme\, using
a version of algebraic geometry over $\\mathbb{F}_1$. These sheaves are c
ombinatorial in nature\, and look locally like (possibly infinite) n-dimen
sional skew shapes. I will discuss some evidence to suggest that these Hal
l algebras are classical limits of quantum groups\, and in some cases rela
te them to known loop algebras. This is joint work with Jaiung Jun.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olof Bergvall (University of Gävle)
DTSTART:20200911T190000Z
DTEND:20200911T200000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/9
DESCRIPTION:Title: Configurations\, arrangements and moduli spaces\nby Olof Bergval
l (University of Gävle) as part of VCU Geometry and Topology Seminar\n\n\
nAbstract\nIn this talk we will encounter certain configuration spaces of
points in the projective plane and see how they relate to certain moduli s
paces of curves and surfaces (marked with e.g. level structures\, geometri
c markings and anticanonical curves). We will also see how to compute thei
r cohomology\, equivariantly with respect to certain natural group actions
\, by using techniques from the theory of subspace arrangements.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joshua Wang (Harvard)
DTSTART:20201009T190000Z
DTEND:20201009T200000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/10
DESCRIPTION:Title: Floer and Khovanov homologies of band sums\nby Joshua Wang (Har
vard) as part of VCU Geometry and Topology Seminar\n\n\nAbstract\nGiven a
nontrivial band sum of two knots\, we may add full twists to the band to o
btain a family of knots indexed by the integers. In this talk\, I'll show
that the knots in this family have the same Heegaard and instanton knot Fl
oer homology but distinct Khovanov homology\, generalizing a result of M.
Hedden and L. Watson. A key component of the argument is a proof that each
of the three knot homologies detects the trivial band. The main applicati
on is a verification of the generalized cosmetic crossing conjecture for s
plit links.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Sikora (SUNY Buffalo)
DTSTART:20201023T190000Z
DTEND:20201023T200000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/11
DESCRIPTION:Title: Tangle Equations\, the Jones conjecture and quantum rational number
s\nby Adam Sikora (SUNY Buffalo) as part of VCU Geometry and Topology
Seminar\n\n\nAbstract\nWe study systems of 2-tangle equations\, which play
an important role in the analysis of enzyme actions on DNA strands. We sh
ow the benefits of considering such systems in the context of framed tangl
es and\, in particular\, we conjecture uniqueness of solutions in that cas
e. We prove a version of this conjecture for rational tangles and we relat
e this conjecture to the Jones Unknotting conjecture\, which potentially o
pens a door to a purely topological line of attack on the Jones conjecture
. Additionally\, we relate systems of tangle equations to the Cosmetic Sur
gery Conjecture.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joshua Lackman (Toronto)
DTSTART:20201106T200000Z
DTEND:20201106T210000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/12
DESCRIPTION:Title: Quantization of (Holomorphic) Poisson Manifolds\nby Joshua Lack
man (Toronto) as part of VCU Geometry and Topology Seminar\n\n\nAbstract\n
We will discuss how\, starting with a Poisson manifold\, one may produce a
quantization via its symplectic groupoid\, and hopefully a noncommutative
algebra.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iulia Gheorghita (Boston College)
DTSTART:20201120T200000Z
DTEND:20201120T210000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/13
DESCRIPTION:Title: Effective classes in the projectivized k-th Hodge bundle\nby Iu
lia Gheorghita (Boston College) as part of VCU Geometry and Topology Semin
ar\n\n\nAbstract\nThe k-th Hodge bundle over the moduli space of curves pa
rametrizes stable k-differentials. In this talk\, we will discuss several
effective classes in both the projectivized k-th Hodge bundle and the proj
ectivized n-marked k-th Hodge bundle. In the n-marked k-th Hodge bundle we
will show how to compute the locus where the k-differential has zeros at
the n marked points for the cases n=1\, 2\, as well as for the case n <= k
. We will then show how to use these classes to compute the classes of eff
ective divisors in the unmarked projectivized k-th Hodge bundle where the
zeros of the k-differentials satisfy a Brill-Noether condition.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Jose Villarreal
DTSTART:20201211T160000Z
DTEND:20201211T170000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/14
DESCRIPTION:Title: Logarithmic vertex algebras\nby Juan Jose Villarreal as part of
VCU Geometry and Topology Seminar\n\n\nAbstract\nIn this talk\, we will i
ntroduce the notion of logarithmic vertex algebra\, which is a vertex alge
bra with logarithmic singularities in the operator product expansion of qu
antum fields\; thus providing a rigorous formulation of the algebraic prop
erties of quantum fields in logarithmic conformal field theory. We develop
a framework that allows many results about vertex algebras to be transfer
red to logarithmic vertex algebras\, and we describe some examples. This i
s a joint work with Bojko Bakalov.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gage Martin (Boston College)
DTSTART:20201113T200000Z
DTEND:20201113T210000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/16
DESCRIPTION:Title: Khovanov homology\, knot Floer homology\, and link detection\nb
y Gage Martin (Boston College) as part of VCU Geometry and Topology Semina
r\n\n\nAbstract\nKhovanov homology and knot/link Floer homology are invari
ants of links in S^3 categorifying the more classical Jones and Alexander
polynomials respectively. There are many formal similarities between the t
heories but some key differences as well. The relationships between Khovan
ov homology and knot/link Floer homology has been a source of inspiration
in each theory. In this talk\, we will give an overview of both theories
in the context of link detection\, mention some of techniques used in prov
ing detection results in each of the theories\, and sketch proofs that Kho
vanov homology detects the torus link T(2\,6) and link Floer homology dete
cts the torus links T(2\,2n). This is partially joint work with Fraser Bin
ns.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicola Pagani (University of Liverpool)
DTSTART:20210205T200000Z
DTEND:20210205T210000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/17
DESCRIPTION:Title: Geometry of genus 1 fine compactified Jacobians\nby Nicola Pag
ani (University of Liverpool) as part of VCU Geometry and Topology Seminar
\n\n\nAbstract\nA classical construction in algebraic geometry associates
with every nonsingular complex projective curve its Jacobian\, a complex p
rojective variety of dimension equal to the genus of the curve. A similar
construction is available for singular curves\, but the resulting Jacobian
variety fails in general to be compact. In this talk we introduce a gener
al abstract notion of fine compactified Jacobian for nodal curves of arbit
rary genus.\n\nWe focus on genus 1 and discuss combinatorial classificatio
n results for fine compactified Jacobians in the case of a single stable c
urve\, and in the case of the universal family over the moduli space of st
able pointed curves. In the former case\, our abstract notion finds back
objects that had already been constructed by Oda-Seshadri and others. In t
he latter case our complete classification exhibits new examples. If time
permits it\, we will discuss how to calculate the cohomology of these comp
actified Jacobians. \n\nA joint work with Orsola Tommasi.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bin Gui (Rutgers University)
DTSTART:20210305T200000Z
DTEND:20210305T210000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/18
DESCRIPTION:Title: Conjugation and positivity of conformal blocks\nby Bin Gui (Rut
gers University) as part of VCU Geometry and Topology Seminar\n\n\nAbstrac
t\nGiven a strongly rational unitary VOA V\, a Hermitian form on the space
of its intertwining operators was introduced recently to understand the u
nitarity of the representation modular tensor category Rep(V). It was actu
ally shown that\, along with some natural assumptions\, if this Hermitian
form (which is necessarily non-degenerate) is positive\, namely\, if it is
an inner product\, then Rep(V) is unitary. The crucial step of this story
is to prove the positivity of the Hermitian form. In this talk\, I give a
geometric interpretation of this positivity problem using (self)conjugate
Riemann surfaces and (self)conjugate conformal blocks.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oğuz Şavk (Boğaziçi University)
DTSTART:20210319T190000Z
DTEND:20210319T200000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/19
DESCRIPTION:Title: Classical and New Plumbings Bounding Contractible Manifolds and Rat
ional Homology Balls\nby Oğuz Şavk (Boğaziçi University) as part o
f VCU Geometry and Topology Seminar\n\n\nAbstract\nA classical question in
low-dimensional topology asks which homology 3-spheres bound contractible
4-manifolds. In this talk\, we address this question for plumbed 3-manifo
lds and we present two new infinite families. Along the way\, we also simp
ly reprove most of the classical works of Akbulut and Kirby\, Fukuhara\, F
ickle\, Maruyama\, Martin\, Casson and Harer\, and Stern around the ninete
en-eighties. Therefore\, our approach provides a unification of classical
and new results via a modification of Mazur’s famous argument. One can w
eaken the above question and ask which homology 3-spheres bound rational h
omology 4-balls. Surprisingly\, this question still remains hard. Recently
\, significant progress occurred due to Akbulut and Larson. Using their te
chnique\, we exhibit new homology 3-spheres bounding rational homology 4-b
alls but not integral homology 4-balls. These 3-manifolds represent non-tr
ivial elements in the kernel of the natural map from the homology cobordis
m group to the rational homology cobordism group.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan C. Johnson (University of Texas at Austin)
DTSTART:20210402T190000Z
DTEND:20210402T200000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/20
DESCRIPTION:Title: Bi-Orderability Techniques and Double Twist Links\nby Jonathan
C. Johnson (University of Texas at Austin) as part of VCU Geometry and Top
ology Seminar\n\n\nAbstract\nThe bi-orderability of link groups has become
a fascinating research topic. In this talk\, we will survey some useful t
ools that have been developed to investigate the bi-orderabily of link com
plements\, including results of Linnell-Rhemtulla-Rolfsen\, Ito\, and Kin-
Rolfsen. In particular\, we will apply these techniques to the double twis
t link groups.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannah Turner (University of Texas at Austin)
DTSTART:20210212T200000Z
DTEND:20210212T210000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/21
DESCRIPTION:Title: Branched cyclic covers and L-spaces\nby Hannah Turner (Universi
ty of Texas at Austin) as part of VCU Geometry and Topology Seminar\n\nAbs
tract: TBA\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allison Moore (Virginia Commonwealth University)
DTSTART:20210430T190000Z
DTEND:20210430T200000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/22
DESCRIPTION:by Allison Moore (Virginia Commonwealth University) as part of
VCU Geometry and Topology Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vance Blankers (Northeastern University)
DTSTART:20210917T140000Z
DTEND:20210917T145000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/23
DESCRIPTION:Title: Alternative compactifications of the moduli space of curves\nby
Vance Blankers (Northeastern University) as part of VCU Geometry and Topo
logy Seminar\n\n\nAbstract\nThe moduli space of curves is an important obj
ect in modern algebraic geometry\, both interesting in its own right and s
erving as a test space for broader geometric programs. These often require
the space to be compact\, which leads to a variety of choices for compact
ification\, the most well-known of which is the Deligne-Mumford-Knudsen co
mpactification by stable curves\, originally introduced in 1969. Since the
n\, several alternative compactifications have been constructed and studie
d\, and in 2013 David Smyth used a combinatorial framework to make progres
s towards classifying all "sufficiently nice" compactifications. In this t
alk\, I'll discuss some of the most well-studied compactifications\, as we
ll as two new compactifications\, which together classify the Gorenstein c
ompactifications in genus 0 and genus 1.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:César Lozano Huerta (Universidad Nacional Autónoma de México -
Oaxaca)
DTSTART:20210924T140000Z
DTEND:20210924T145000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/24
DESCRIPTION:Title: On the Weak Lefschetz Principle in birational geometry\nby Cés
ar Lozano Huerta (Universidad Nacional Autónoma de México - Oaxaca) as p
art of VCU Geometry and Topology Seminar\n\n\nAbstract\nIn this talk we wi
ll discuss the weak Lefschetz Principle in the context of birational geome
try.\n\nOur departing point will be the influential work of Solomon Lefsch
etz started in 1924. We will look at the original formulation of the Lefsc
hetz hyperplane theorem in algebraic topology and build up to recent devel
opments of it in birational geometry. In doing so\, the slogan of the talk
will be the following: there are many scenarios in geometry in which anal
ogous versions of the Lefschetz hyperplane theorem hold. Such scenarios ar
e somewhat unexpected and have had a profound impact in mathematics.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mara Ungureanu (Albert-Ludwigs-Universität Freiburg)
DTSTART:20211008T140000Z
DTEND:20211008T145000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/25
DESCRIPTION:Title: Counts of secant planes to varieties and universal polynomials\
nby Mara Ungureanu (Albert-Ludwigs-Universität Freiburg) as part of VCU G
eometry and Topology Seminar\n\n\nAbstract\nFor a curve in projective spac
e\, the count of varieties parametrising its secant planes is among the mo
st studied problems in classical enumerative geometry. We shall start wit
h a gentle introduction to secant varieties and then explore the connectio
n between their enumerative geometry and Virasoro algebras on one side\, a
nd tautological integrals on the other.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Mullane (Humboldt Universität zu Berlin)
DTSTART:20211119T150000Z
DTEND:20211119T155000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/26
DESCRIPTION:Title: The birational geometry of the moduli space of pointed hyperellipti
c curves\nby Scott Mullane (Humboldt Universität zu Berlin) as part o
f VCU Geometry and Topology Seminar\n\n\nAbstract\nThe moduli space of poi
nted hyperelliptic curves is a seemingly simple object with perhaps unexpe
ctedly interesting geometry. I will report on joint work with Ignacio Barr
os towards a full classification of both the Kodaira dimension and the str
ucture of the effective cone of these moduli spaces.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Margherita Lelli-Chiesa (Università Roma 3)
DTSTART:20211015T140000Z
DTEND:20211015T145000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/27
DESCRIPTION:Title: Brill-Noether theory of curves on abelian surfaces\nby Margheri
ta Lelli-Chiesa (Università Roma 3) as part of VCU Geometry and Topology
Seminar\n\n\nAbstract\nBrill-Noether theory investigates the ways in which
an algebraic curve can be embedded in some projective space. I will recal
l the most relevant results in the theory and their relation with curves l
ying on K3 surfaces. I will then illustrate more recent results on the Bri
ll-Noether theory of curves on Abelian surfaces highlightening the major d
ifferences with respect to K3 surfaces and some applications to the moduli
space of curves.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seppo Niemi-Colvin (Duke University)
DTSTART:20210910T140000Z
DTEND:20210910T145000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/28
DESCRIPTION:Title: Invariance of Knot Lattice Homology\nby Seppo Niemi-Colvin (Duk
e University) as part of VCU Geometry and Topology Seminar\n\n\nAbstract\n
Links of singularity and generalized algebraic links are ways of construct
ing three-manifolds and smooth links inside them from algebraic surfaces a
nd curves inside them. Némethi created lattice homology as an invariant f
or links of normal surface singularities which developed out of computatio
ns for Heegaard Floer homology. Later Ozsváth\, Stipsicz\, and Szabó def
ined knot lattice homology for generalized algebraic knots in rational hom
ology spheres\, which is known to play a similar role to knot Floer homolo
gy and is known to compute knot Floer in some cases. I discuss a proof tha
t knot lattice is an invariant of the smooth knot type\, which had been pr
eviously suspected but not confirmed.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jingling Yang (The Chinese University of Hong Kong\, Shenzhen)
DTSTART:20211029T140000Z
DTEND:20211029T145000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/29
DESCRIPTION:Title: Distance one surgeries on the lens space L(n\,1) and band surgeries
on the torus knot T(2\,n)\nby Jingling Yang (The Chinese University o
f Hong Kong\, Shenzhen) as part of VCU Geometry and Topology Seminar\n\n\n
Abstract\nIt has been well known that any closed\, orientable 3-manifold c
an be obtained by performing Dehn surgery on a link in $S^3$. One of the m
ost prominent problems in 3-manifold topology is to list all the possible
lens spaces that can be obtained by a Dehn surgery along a knot in $S^3$\,
which has been solved by Greene. A natural generalization of this problem
is to list all the possible lens spaces that can be obtained by a Dehn su
rgery from other lens spaces. Besides\, considering surgeries between lens
spaces is also motivated from DNA topology. In this talk\, we will discus
s distance one surgeries between lens spaces $L(n\, 1)$ with $n \\geq 5$ o
dd and lens spaces $L(s\,1)$ for $s \\neq 0 \\in \\mathbb{Z}$ and correspo
nding band surgeries from $T(2\, n)$ to $T(2\, s)$\, by using Heegaard Flo
er mapping cone formula. We give an almost complete classification of the
above surgeries.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Vitagliano (Universita' di Salerno)
DTSTART:20211105T140000Z
DTEND:20211105T145000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/30
DESCRIPTION:Title: Homogeneous G-structures\nby Luca Vitagliano (Universita' di Sa
lerno) as part of VCU Geometry and Topology Seminar\n\n\nAbstract\nG-struc
tures unify several interesting geometries including: almost complex\, Rie
mannian\, almost symplectic geometry\, etc.\, the integrable versions of w
hich being complex\, flat Riemannian\, symplectic geometry\, etc. Contact
manifolds are odd dimensional analogues of symplectic manifolds but\, desp
ite this\, there is no natural way to understand them as manifolds with an
ordinary integrable G-structure. In this talk\, we present a possible sol
ution to this discrepancy. Our proposal is based on a new notion of homog
eneous G-structures. Interestingly\, besides contact\, the latter include
other nice (old and new) geometries including: cosymplectic\, almost conta
ct\, and a curious “homogeneous version” of Riemannian geometry. This
is joint work with A. G. Tortorella and O. Yudilevich.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert DeYeso (North Carolina State University)
DTSTART:20211001T140000Z
DTEND:20211001T145000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/31
DESCRIPTION:Title: (Heegaard Floer) thin knots satisfy the Cabling Conjecture\nby
Robert DeYeso (North Carolina State University) as part of VCU Geometry an
d Topology Seminar\n\n\nAbstract\nThe Cabling Conjecture of González-Acu
ña and Short holds that only cable knots admit a reducible surgery\, whic
h is Dehn surgery containing an essential 2-sphere. For surgeries along (H
eegaard Floer) thin knots\, we approach this conjecture by comparing the r
elative Maslov gradings and periodicity structure of their Floer homology.
This is primarily done by reinterpreting these objects via immersed curve
s techniques that recover Floer homology\, inspired by Hanselman's approac
h to the Cosmetic Surgery Conjecture.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Villareal
DTSTART:20211210T150000Z
DTEND:20211210T155000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/32
DESCRIPTION:Title: Logarithmic vertex algebras\nby Juan Villareal as part of VCU G
eometry and Topology Seminar\n\n\nAbstract\nIn this talk\, I want to expla
in a generalization of vertex algebras called logarithmic vertex algebras.
In this work\, we develop a framework that allows many results about vert
ex algebras to be extended to logarithmic vertex algebras. In particular\,
I will mention one example which is motivated by physics\, this example
exhibits some unexpected new features that are peculiar to the logarithmic
case. Finally\, I will mention a relation between logarithmic vertex alge
bras and non-local poisson vertex algebras. This is joint work with Bojko
Bakalov.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Samperton (University of Illinois at Urbana-Champaign)
DTSTART:20220128T150000Z
DTEND:20220128T155000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/33
DESCRIPTION:Title: Topological quantum computation is hyperbolic\nby Eric Samperto
n (University of Illinois at Urbana-Champaign) as part of VCU Geometry and
Topology Seminar\n\n\nAbstract\nWe show that a topological quantum comput
er based on the evaluation of a Witten-Reshetikhin-Turaev TQFT invariant o
f knots can always be arranged so that the knot diagrams one compiles are
hyperbolic. Furthermore\, the diagrams can be arranged to have additional
nice properties\, such as being alternating with minimal crossing number.
Various complexity-theoretic hardness results regarding the calculation of
quantum invariants of knots follow as corollaries. In particular\, we arg
ue that the hyperbolic geometry of knots is unlikely to be useful for topo
logical quantum computation.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Balazs Elek (Virginia Commonwealth University)
DTSTART:20220204T180000Z
DTEND:20220204T185000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/34
DESCRIPTION:Title: Heaps\, Crystals and Preprojective Algebra Modules\nby Balazs E
lek (Virginia Commonwealth University) as part of VCU Geometry and Topolog
y Seminar\n\n\nAbstract\nKashiwara crystals are combinatorial gadgets asso
ciated to a representation of a reductive algebraic group that enable us t
o understand the structure of the representation in purely combinatorial t
erms. We will describe a type-independent combinatorial construction of cr
ystals of the form $B(n\\lambda)$\, where $\\lambda$ is a dominant minuscu
le weight\, using the heap associated to a fully commutative element in th
e Weyl group. Then we will discuss how we can use the heap to also define
a module for the preprojective algebra of the underlying Dynkin quiver. Us
ing the work of Savage and Tingley\, we also realize the crystal $B(n\\lam
bda)$ via irreducible components of the quiver Grassmannians of $n$ copies
of this module\, and we describe an explicit crystal isomorphism between
the two models. This is joint work with Anne Dranowski\, Joel Kamnitzer an
d Calder Morton-Ferguson.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Sala (Università di Pisa)
DTSTART:20220218T150000Z
DTEND:20220218T155000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/35
DESCRIPTION:Title: Two-dimensional cohomological Hall algebras\nby Francesco Sala
(Università di Pisa) as part of VCU Geometry and Topology Seminar\n\n\nAb
stract\nThe present talk aims at introducing the theory of 2-dimensional c
ohomological Hall algebras and their relations with moduli spaces in algeb
raic geometry and representation theory. In the second part of the talk\,
I will focus on those associated to curves and surfaces and discuss their
categorification. If time permits\, I will describe in detail the cohomolo
gical Hall algebra of a Kleinian surface singularity.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Swarnava Mukhopadhyay (Tata Institute of Fundamental Research)
DTSTART:20220211T150000Z
DTEND:20220211T155000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/36
DESCRIPTION:Title: Graph potentials and their periods\nby Swarnava Mukhopadhyay (T
ata Institute of Fundamental Research) as part of VCU Geometry and Topolog
y Seminar\n\n\nAbstract\nWe introduce graph potentials\, which are Laurent
polynomials associated to\n(colored) trivalent graphs. These graph potent
ials encode degenerations of the \nmoduli space of rank two bundles with f
ixed determinant. \n\nIn this talk\, we will discuss how the graph potenti
al defines a topological quantum field\ntheory. Applying the TQFT machiner
y gives us an efficient way to compute periods of these potentials. \nIf t
ime permits\, we will explain how these are related to the moduli spaces
of rank two bundles from \nthe perspective of mirror symmetry. This is a
joint work with Pieter Belmans and Sergey Galkin.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele Agostini (Max-Planck-Institut für Mathematik in den Natur
wissenschaften in Leipzig)
DTSTART:20220318T140000Z
DTEND:20220318T145000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/38
DESCRIPTION:Title: Singular curves\, degenerate theta functions and KP solutions\n
by Daniele Agostini (Max-Planck-Institut für Mathematik in den Naturwisse
nschaften in Leipzig) as part of VCU Geometry and Topology Seminar\n\n\nAb
stract\nThe KP equation is a PDE that describes waves in shallow water. Qu
ite surprisingly\, smooth algebraic curves give rise to solutions to the K
P equation via Riemann's theta function. Singular curves produce solutions
as well\, but the theta function in this case becomes degenerate. I will
present some results in this direction\, focusing on soliton and rational
solutions.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alejandro Cabrera (Universidade Federal do Rio de Janeiro\, Brasil
)
DTSTART:20220325T140000Z
DTEND:20220325T145000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/39
DESCRIPTION:Title: Infinite dimensional Dirac structures and moduli spaces\nby Ale
jandro Cabrera (Universidade Federal do Rio de Janeiro\, Brasil) as part o
f VCU Geometry and Topology Seminar\n\n\nAbstract\nIn this talk\, we first
recall a class of geometric structures called Courant algebroids and Dira
c structures. We then proceed to outline their study on infinite dimension
al manifolds and stress their advantage with respect to more traditional g
eometries (notably\, Poisson) in the infinite dimensional context. We then
study their reduction and apply this setting to the description of geomet
ric structures on moduli spaces of principal connections. This is joint wo
rk with M. Gualtieri and E. Meinrenken. Along the way\, we recover several
known results involving moduli on surfaces and comment on possible novel
applications\, including Topological Field Theories.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Konstantinos Varvarezos (Princeton University)
DTSTART:20220401T140000Z
DTEND:20220401T145000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/40
DESCRIPTION:Title: Heegaard Floer homology\, immersed curves\, and chirally cosmetic s
urgeries\nby Konstantinos Varvarezos (Princeton University) as part of
VCU Geometry and Topology Seminar\n\n\nAbstract\nDehn surgery is a common
method for obtaining 3-manifolds from knots. A pair of (Dehn) surgeries o
n a knot is called chirally cosmetic if the resulting manifolds are homeom
orphic with opposite orientations. Making use of immersed curve formulatio
ns of Heegaard Floer invariants\, we discuss new obstructions to the exist
ence of such surgeries\, which we apply to certain families of knots. In p
articular\, it turns out that combined with previously known results\, the
se obstructions are sufficient to completely classify chirally cosmetic su
rgeries on odd alternating pretzel knots. Furthermore\, we are able to rul
e out cosmetic surgeries for L-space knots along slopes with opposite sign
s.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex McCleary (Ohio State University)
DTSTART:20220429T140000Z
DTEND:20220429T145000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/42
DESCRIPTION:Title: An Introduction to Multiparameter Persistent Homology\nby Alex
McCleary (Ohio State University) as part of VCU Geometry and Topology Semi
nar\n\n\nAbstract\nPersistent homology is a method for studying topologica
l features of data sets. Originally developed in the early 2000s\, it has
proven useful for a wide range of applications including neuroscience\, me
dical research\, chemistry\, weather prediction\, and financial modelling.
We will start with a brief introduction to persistent homology and multip
arameter persistent homology followed by some recent results on multiparam
eter persistence.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Aldi (VCU)
DTSTART:20220422T140000Z
DTEND:20220422T145000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/43
DESCRIPTION:Title: Generalized Polynomial Structures\nby Marco Aldi (VCU) as part
of VCU Geometry and Topology Seminar\n\n\nAbstract\nThe generalized tangen
t bundle is a geometric object that appears naturally in both physics and
mathematics. Generalized almost complex structures\, encompassing classica
l almost complex structure and almost symplectic structures\, are an endom
orphisms of the generalized tangent that square to negative the identity.
In this talk we discuss more general endomorphims satisfying an arbitrary
polynomial equation with constant coefficients. As it turns out\, particul
ar care is required in properly formulating the correct integrability cond
itions. This is joint work with Daniele Grandini.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Bud (Humboldt University in Berlin)
DTSTART:20220902T150000Z
DTEND:20220902T155000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/44
DESCRIPTION:Title: Moduli of Prym curves and Prym-Brill-Noether theory\nby Andrei
Bud (Humboldt University in Berlin) as part of VCU Geometry and Topology S
eminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergio Da Silva (Virginia State University)
DTSTART:20220923T150000Z
DTEND:20220923T155000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/45
DESCRIPTION:Title: An Introduction to Geometric Vertex Decomposability\nby Sergio
Da Silva (Virginia State University) as part of VCU Geometry and Topology
Seminar\n\nLecture held in Room 4145 Harris Hall.\n\nAbstract\nA Gröbner
degeneration is a useful method to reduce problems involving ideals to the
monomial ideal setting. In the square-free case\, we can associate a simp
licial complex to a monomial ideal and ask whether this complex is vertex
decomposable. Another tool in this direction\, called a geometric vertex d
ecomposition\, is a generalization of this technique first introduced by K
nutson-Miller-Yong to study diagonal degenerations of Schubert varieties.
Later uses of the concept mostly occurred in the context of Schubert geome
try\, until recent work of Klein-Rajchgot established a connection to liai
son theory. The interplay between these two theories can be used to analyz
e degenerations\, construct Gröbner bases\, and find families of ideals w
hich are glicci (in the Gorenstein liaison class of a complete intersectio
n). In this talk\, I will introduce geometric vertex decomposability and h
ighlight its applications to toric ideals of graphs and Hessenberg varieti
es.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos Marcelo Servan (University of Chicago)
DTSTART:20220930T150000Z
DTEND:20220930T155000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/47
DESCRIPTION:Title: On the uniqueness of the Prym map\nby Carlos Marcelo Servan (Un
iversity of Chicago) as part of VCU Geometry and Topology Seminar\n\n\nAbs
tract\nThe Prym map associates to a double unbranched cover $p:Y \\to X$ o
f a smooth complex curve of X of genus g\, a principally polarized abelian
variety (ppav) Prym(p). Denote by $R_g$ to the moduli space of such doubl
e covers and by $A_h$ the moduli space of ppavs of dimension h. We will sh
ow that for $g \\geq 4$ and $h \\leq g-1$\, Prym is the unique non-constan
t map of complex orbifolds between $R_g \\to A_h$. A key step in the proof
is a classification of homomorphisms at the level of orbifold fundamental
groups\, which uses arguments from low-dimensional topology and geometric
group theory.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samantha Allen (Duquesne University)
DTSTART:20221007T150000Z
DTEND:20221007T155000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/48
DESCRIPTION:Title: Unknotting via null-homologous twists and multi-twists\nby Sama
ntha Allen (Duquesne University) as part of VCU Geometry and Topology Semi
nar\n\n\nAbstract\nThe untwisting number of a knot K is the minimum number
of null-homologous full twists required to unknot K. The surgery descript
ion number of K can be defined similarly\, allowing for multiple full twis
ts in a single twisting region. We can find no examples of knots in the li
terature where these two invariants are not equal. In this talk\, I will p
rovide the first known examples where untwisting number and surgery descri
ption number are not equal and discuss challenges to distinguishing these
invariants in general. While these invariants are defined geometrically\,
our methods will involve several “algebraic” versions of unknotting op
erations. In addition\, we show the surprising result that the untwisting
number of a knot is at most three times its surgery description number. Th
is work is joint with Kenan Ince\, Seungwon Kim\, Benjamin Ruppik\, and Ha
nnah Turner.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pengyu Liu (UC Davis)
DTSTART:20221209T160000Z
DTEND:20221209T165000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/49
DESCRIPTION:Title: A graph polynomial that distinguishes tree topologies and its appli
cations\nby Pengyu Liu (UC Davis) as part of VCU Geometry and Topology
Seminar\n\n\nAbstract\nIn this talk\, I will define a graph polynomial fo
r trees and show that the polynomial is a complete invariant for unlabeled
trees. Then\, we introduce distance-based methods for analyzing tree stru
ctures with the polynomial\, and we demonstrate its applications in molecu
lar evolutionary and structural biology.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fernando Etayo Gordejuela (Universidad de Cantabria)
DTSTART:20220916T170000Z
DTEND:20220916T175000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/50
DESCRIPTION:Title: Structures on Generalized Geometry\nby Fernando Etayo Gordejuel
a (Universidad de Cantabria) as part of VCU Geometry and Topology Seminar\
n\n\nAbstract\nGeneralized Geometry was introduced at the beginning of XXI
century by Hitchin\, Gualtieri and Cavalcanti\, as a mathematical theory
including Complex and Symplectic Geometries. The starting points are the
notion of the big tangent bundle\, which is the sum of the tangent and th
e cotangent bundlles of a manifold\, and the notion of generalized almost
complex structure on the big tangent bundle. We shall show that many other
geometric structures appear in Generalized Geometry. The talk will not re
quire deep knowledge of Differential Geometry.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Minyoung Jeon (University of Georgia)
DTSTART:20221014T170000Z
DTEND:20221014T175000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/51
DESCRIPTION:Title: Euler characteristic of Brill-Noether loci on Prym varieties\nb
y Minyoung Jeon (University of Georgia) as part of VCU Geometry and Topolo
gy Seminar\n\n\nAbstract\nPrym varieties\, named after Friedrich Prym\, ar
e abelian varieties constructed from étale double covers of algebraic cur
ves. In 1985\, Welters subsequently equipped Prym varieties with Brill-Noe
ther loci. In this talk\, we give a formula for the Euler characteristic o
f the Brill-Noether locus in Prym varieties with a vanishing sequence at o
ne marked point.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gretchen Matthews (Virginia Tech)
DTSTART:20230210T150000Z
DTEND:20230210T155000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/53
DESCRIPTION:Title: Coding for distributed storage using algebraic geometry\nby Gre
tchen Matthews (Virginia Tech) as part of VCU Geometry and Topology Semina
r\n\n\nAbstract\nGiven the astonishing rates at which data is generated\,
how can it be stored efficiently? How is access to the stored information
guaranteed? How can it be distributed across a network while also protecti
ng it from distortion\, degradation\, and loss? Answers to some of these q
uestions may be found using algebraic geometry. Algebraic geometry codes a
re constructed using curves over finite fields\, a discovery in the 1980s
that motivated much work on curves over finite fields with many rational p
oints and asymptotically good towers of function fields. Refinements of al
gebraic geometry codes designed from curves and surfaces now play a role i
n coding for distributed storage. In this talk\, we share how studying the
se rich underlying structures provides a window into the powerful local pr
operties that aid in designing codes for local recovery from erasures.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lev Borisov (Rutgers University)
DTSTART:20230217T150000Z
DTEND:20230217T155000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/54
DESCRIPTION:Title: On explicit equations of fake projective planes\nby Lev Borisov
(Rutgers University) as part of VCU Geometry and Topology Seminar\n\n\nAb
stract\nFake projective planes are fascinating complex surfaces (real four
-dimensional manifolds). While they were first discovered about 40 years a
go\, their explicit equations have only been computed recently. I will tal
k about the history of fake projective planes and some of the peculiar con
structions and challenges associated with finding their explicit equations
.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sara Maloni (University of Virginia)
DTSTART:20230224T150000Z
DTEND:20230224T155000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/55
DESCRIPTION:Title: Some new results in Higher Teichmüller Theory\nby Sara Maloni
(University of Virginia) as part of VCU Geometry and Topology Seminar\n\n\
nAbstract\nThe Teichmüller space of a surface S is the space of marked hy
perbolic structure on S\, up to equivalence. By considering the holonomy r
epresentation of such structures\, the Teichmüller space can also be seen
as a connected component of (conjugacy classes of) representations from t
he fundamental group of S into PSL(2\,R)\, consisting entirely of discrete
and faithful representations. Generalizing this point of view\, Higher Te
ichmüller Theory studies connected components of (conjugacy classes of) r
epresentations from the fundamental group of S into more general semisimpl
e Lie groups which consist entirely of discrete and faithful representatio
ns.\n\nWe will give a survey of some aspects of Higher Teichmüller Theory
\, and will make links with the recent powerful notion of Anosov represent
ation. Time permitting\, we will conclude by focusing on two separate ques
tions:\nDo these representations correspond to deformation of geometric st
ructures? \nCan we generalize the important notion of pleated surfaces to
higher rank Lie groups like PSL(d\, C)?\nThe answer to question 1 is joint
work with Alessandrini\, Tholozan and Wienhard\, while the answer to ques
tion 2 is joint work with Martone\, Mazzoli and Zhang.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ralph Gomez (Swarthmore College)
DTSTART:20230303T150000Z
DTEND:20230303T155000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/56
DESCRIPTION:Title: The Berglund-Huebsch Transpose rule and Sasakian Geometry\nby R
alph Gomez (Swarthmore College) as part of VCU Geometry and Topology Semin
ar\n\n\nAbstract\nThe goal of this talk will be to use some ideas from a c
onstruction of mirror Calabi-Yau orbifolds due to Berglund\, Hübsch\, Kra
witz (BHK mirror symmetry) to outline a way to create new examples of Sasa
ki manifolds of positive Ricci curvature. If time permits\, we will say so
me things about the Sasaki-Einstein case and report on (joint with J. Vall
e and J. Vicente) some new examples of Sasaki-Einstein rational homology 7
-spheres.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Beibei Liu (MIT)
DTSTART:20230317T140000Z
DTEND:20230317T145000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/57
DESCRIPTION:Title: Heegaard Floer homology and plane curves with non-cuspidal singular
ities\nby Beibei Liu (MIT) as part of VCU Geometry and Topology Semina
r\n\n\nAbstract\nIt is an interesting question to ask about the possible c
onfigurations of singular points occurring on general algebraic curves. In
this talk\, we use Heegaard Floer homology to study the singularity links
and give some obstructions for the configurations. The main ingredient is
to use the knot Floer complex of the knotification of the singularities l
inks in the algebraic curves. This is joint work with Borodzik and Zemke.\
n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Feride Ceren Köse (University of Georgia)
DTSTART:20230127T160000Z
DTEND:20230127T165000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/58
DESCRIPTION:Title: Symmetric unions and knot invariants\nby Feride Ceren Köse (Un
iversity of Georgia) as part of VCU Geometry and Topology Seminar\n\n\nAbs
tract\nWe study symmetric unions in the context of problems regarding knot
invariants. Recently\, a class of symmetric unions was proposed to constr
uct nontrivial knots with trivial Jones polynomial. We show\, however\, th
at such a knot is always trivial and hence this construction cannot be use
d to answer the open question asking whether the Jones polynomial detects
the unknot. We then discuss why symmetric union is a valuable construction
to study knot invariants and why our result provides strong evidence for
the non-existence of nontrivial knots with trivial Jones polynomial.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicola Tarasca (VCU)
DTSTART:20230324T140000Z
DTEND:20230324T145000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/59
DESCRIPTION:Title: Coinvariants of vertex algebras and abelian varieties\nby Nicol
a Tarasca (VCU) as part of VCU Geometry and Topology Seminar\n\n\nAbstract
\nSpaces of coinvariants have classically been constructed by assigning re
presentations of affine Lie algebras\, and more generally\, vertex operato
r algebras\, to algebraic curves.\nRemoving curves out of the picture\, I
will introduce spaces of coinvariants at abelian varieties with respect to
the action of an infinite-dimensional Lie algebra. I will show how these
spaces globalize to twisted D-modules on moduli of abelian varieties\, ext
ending the classical picture from moduli of curves. This is based on my re
cent preprint arXiv:2301.13227.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Almut Burchard (University of Toronto)
DTSTART:20230331T140000Z
DTEND:20230331T145000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/60
DESCRIPTION:Title: What is the best shape? Geometric problems arising in aggregation m
odels\nby Almut Burchard (University of Toronto) as part of VCU Geomet
ry and Topology Seminar\n\n\nAbstract\nHow do pair interactions shape the
large-scale behaviour of a\ncloud of particles (animals\, social agents ..
.) ? In the most basic\nmodels\, the shape of the cloud is determined by
minimizing an\nattractive-repulsive interaction energy under suitable geom
etric\nconstraints.\nWhen can we expect aggregation to occur? What is the
shape of the\nresulting flock? I will describe recent work on optimal sha
pes in\ncapacitor problems that occur as limiting cases.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ihsan Topaloglu (VCU)
DTSTART:20230407T140000Z
DTEND:20230407T145000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/61
DESCRIPTION:Title: Characterization of regular polygons via an overdetermined problem<
/a>\nby Ihsan Topaloglu (VCU) as part of VCU Geometry and Topology Seminar
\n\n\nAbstract\nIn this talk I will discuss the optimality of regular tria
ngles and quadrilaterals for nonlocal energies of generalized Riesz-type i
n the class of polygons with a fixed number of sides and fixed area\, as w
ell as their characterization as unique stationary points. These results a
re joint work with M. Bonacini and R. Cristoferi. I will also present on r
ecent results by Bogosel\, Bucur and Fragalà where they show that for cer
tain interaction kernels there is symmetry breaking for polygons with numb
er of sides greater than 5.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louisa Liles (UVA)
DTSTART:20230915T170000Z
DTEND:20230915T175000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/62
DESCRIPTION:Title: Quantum modularity of 3-manifold invariants\nby Louisa Liles (U
VA) as part of VCU Geometry and Topology Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Prakash Belkale (UNC Chapel Hill)
DTSTART:20230929T170000Z
DTEND:20230929T175000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/63
DESCRIPTION:Title: Vertices in the multiplicative eigenvalue problem\nby Prakash B
elkale (UNC Chapel Hill) as part of VCU Geometry and Topology Seminar\n\n\
nAbstract\nThe classical problem about the possible eigenvalues of a prod
uct of unitary matrices AB given the eigenvalues of A and B has relations
to many areas of geometry\, representation theory and combinatorics. There
is a polytope controlling this problem whose faces can be described in te
rms of the quantum cohomology of Grassmannians. The problem of determining
the vertices of the polytope remained open for a long time\, but recently
I gave an inductive framework for understanding vertices on a given face
: some vertices come explicitly from cycle classes of geometrically defin
ed loci\, and the remaining vertices come from an induction procedure fro
m smaller groups. I want to describe this method\, and generalization to t
he case of arbitrary groups (joint work with Joshua Kiers). If time permi
ts\, I will state connections to the theory of unitary rigid local systems
.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lutian Zhao (University of Maryland)
DTSTART:20240126T170000Z
DTEND:20240126T175000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/64
DESCRIPTION:Title: Nonabelian Hodge Theory of parahoric torsors\nby Lutian Zhao (U
niversity of Maryland) as part of VCU Geometry and Topology Seminar\n\n\nA
bstract\nModern mathematical research has been enriched by exploring the b
ijection between Higgs bundles and local systems over noncompact Riemann s
urfaces\, an incredible feat accomplished profoundly by C. Simpson by intr
oducing weighted filtrations. In this discussion\, our focus will be on fu
rther unraveling this relationship by delving into the correlation between
the Dolbeault and de Rham moduli spaces for generally complex reductive s
tructure groups\, utilizing the influential language of parahoric group sc
hemes as initially established by Bruhat-Tits. This presentation is based
on collaborative work with Georgios Kydonakis\, Pengfei Huang\, and Hao Su
n.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bojko Bakalov (North Carolina State University)
DTSTART:20240202T180000Z
DTEND:20240202T185000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/65
DESCRIPTION:Title: Dynamical Lie algebras\nby Bojko Bakalov (North Carolina State
University) as part of VCU Geometry and Topology Seminar\n\n\nAbstract\nIn
this talk\, I’ll review the role of Lie algebras in variational quantum
computing and in quantum dynamics and control. One of the main obstacles
to training parameterized quantum circuits is the presence of flat regions
in the parameter landscape\, called barren plateaus. To diagnose such bar
ren plateaus\, we obtain an exact expression for the variance of the cost
function in terms of the dynamical Lie algebra generated by the circuit. S
econd\, we classify all dynamical Lie algebras of 1-dimensional translatio
n-invariant spin chains. The talk will be based on the papers arXiv:2309.0
9342 and arXiv:2309.05690.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatsu Takeuchi (Virginia Tech)
DTSTART:20240209T180000Z
DTEND:20240209T185000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/66
DESCRIPTION:Title: A Toy Quantum Mechanics on a Vector Space over Finite Fields\nb
y Tatsu Takeuchi (Virginia Tech) as part of VCU Geometry and Topology Semi
nar\n\n\nAbstract\nUnlike Relativity\, which can be derived from a few phy
sical postulates\, Quantum Mechanics is defined from a mathematical "recip
e" that is known to "work\," in the sense that it leads to a theory whose
predictions agree with experiment exactly\, but no one really understand w
hat the physical meaning of the recipe is. One approach that has been trie
d to clarify the meaning of the "recipe" is to modify parts of it to see h
ow the resulting theory changes. For instance\, one can change the field o
ver which the state space is defined from the complex numbers to other fie
lds or division algebras\, e.g. real numbers or quaternions. In this talk\
, I will discuss what would happen if we change that field to a finite fie
ld Fq. We find that the correlations in the resulting toy theory do not vi
olate the CHSH inequality though its predictions cannot be reproduced by a
hidden variable theory. Furthermore\, we argue that the q->1 limit\, in w
hich the field becomes the "field with one element\," the theory becomes "
classical."\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Aldi (VCU)
DTSTART:20240216T180000Z
DTEND:20240216T185000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/67
DESCRIPTION:Title: Integrable endomorphisms of the generalized tangent bundle\nby
Marco Aldi (VCU) as part of VCU Geometry and Topology Seminar\n\n\nAbstrac
t\nThe generalized tangent bundle\, the direct sum of the tangent and cota
ngent bundle of a manifold\, is an object of great interest in both differ
ential geometry and physics. Skew-symmetric endomorphisms that square to n
egative the identity are known as generalized almost complex structures an
d their integrability is equivalent to the vanishing of the Courant-Nijenh
uis tensor. Integrability conditions for more general skew-symmetric endom
orphisms are not well-understood. In joint work with Sergio Da Silva and D
aniele Grandini\, we describe all possible tensorial integrability conditi
ons in terms of a shifted version of the Courant-Nijenhuis tensor.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Deepisha Solanki (University of Buffalo)
DTSTART:20240301T180000Z
DTEND:20240301T185000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/68
DESCRIPTION:Title: Studying Links via Plats\nby Deepisha Solanki (University of Bu
ffalo) as part of VCU Geometry and Topology Seminar\n\n\nAbstract\nBetween
1990 and 2006\, Birman and Menasco wrote a sequence of papers with the ru
nning major title “Stabilisation in the braid groups”\, that investiga
ted the question of what stabilisation accomplishes in Markov’s theorem.
One key result coming out of that sequence of papers was the discovery of
a new isotopy -- the exchange move – which also preserves braid index a
nd writhe\, but could jump between conjugacy classes. Thus\, it was establ
ished that using just a sequence of braid isotopies\, exchange moves and d
estabilisations\, one could go from any closed braid representative of the
unlink to the representative of minimal index – the trivial closed brai
d. It was also shown that using just braid isotopies and exchange moves\,
one could take a closed braid representing a split or composite link to on
e where it was “obviously” split or composite\, respectively.\n\nIn th
e setting of plat presentations of links\, we now ask the same question: w
hat does stabilisation accomplish? We introduce two new isotopy moves that
preserve the bridge index: the pocket move and the flip move\, which can
be thought of as being analogous to an exchange move of the closed braid s
etting. Equipped with these isotopies\, we prove results analogous to Birm
an-Menasco’s results\, in the plat setting.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evangelia Gazaki (University of Virginia)
DTSTART:20240412T170000Z
DTEND:20240412T175000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/70
DESCRIPTION:Title: Hyperelliptic Curves mapping to Abelian Surfaces and Applications t
o Beilinson's Conjecture for 0-cycles\nby Evangelia Gazaki (University
of Virginia) as part of VCU Geometry and Topology Seminar\n\n\nAbstract\n
A classical invariant in Algebraic Geometry is the Picard group of a smoot
h projective curve C. This group is the quotient of the group of divisors
on C (aka the free abelian group on all points of the curve) modulo diviso
rs of rational functions on C. Over an algebraically closed field this gro
up can be fully understood by the Abel-Jacobi map\, which gives an isomorp
hism between the degree zero elements of the Picard group and the Jacobian
variety of the curve. In higher dimensions there is an analog of this gro
up\, called the Chow group of 0-cycles\, for which many things generalize
from the case of curves. The main issue that makes the situation much more
chaotic though is that the Abel-Jacobi map is in general no longer an iso
morphism. In fact\, over large fields like the complex numbers and for man
y important classes of varieties (abelian varieties\, K3 surfaces\, produc
ts of curves of positive genus\,...) the kernel of the Abel-Jacobi can be
really enormous. On the other extreme a famous conjecture of Beilinson fro
m the mid 80's predicts that over the algebraic closure of the rational nu
mbers the Abel-Jacobi map is an isomorphism unconditionally on the variety
. This conjecture is very hard to establish and in fact\, there are no in
teresting examples in the literature known to satisfy this conjecture. In
this talk I will present recent joint work with Jonathan Love\, where we m
ake substantial progress on this conjecture for abelian surfaces. First\,
we describe a very rich collection of relations in the kernel of the Abel
-Jacobi arising from hyperelliptic curves\, that is\, curves that are give
n by an equation of the form y^2=f(x). Second\, we will give a geometric c
onstruction that produces large countable collections of such curves mappi
ng to a given abelian surface.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mee Seong Im (USNA)
DTSTART:20240405T170000Z
DTEND:20240405T175000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/71
DESCRIPTION:Title: Diagrammatics of infinitesimal dilogarithms and entropy\nby Mee
Seong Im (USNA) as part of VCU Geometry and Topology Seminar\n\n\nAbstrac
t\nA special case of certain diagrammatics\, when G is the group of affine
transformations of a\nline\, can be related to the infinitesimal dilogari
thm and to the Shannon entropy of finite probability\ndistributions. I wil
l explain the diagrammatics and their connections to infinitesimal dilogar
ithms and\nentropy.\n\nThis is joint work in progress with Mikhail Khovano
v.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eleni Panagiotu (Arizona State University)
DTSTART:20240419T170000Z
DTEND:20240419T175000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/72
DESCRIPTION:Title: Novel measures of complexity of open curves in 3-space\nby Elen
i Panagiotu (Arizona State University) as part of VCU Geometry and Topolog
y Seminar\n\n\nAbstract\nFilamentous material may exhibit structure depend
ent material properties and function that depends on their entanglement. E
ven though intuitively entanglement is often understood in terms of knotti
ng or linking\, many of the filamentous systems in the natural world are n
ot mathematical knots or links. In this talk we will introduce a novel fra
mework in knot theory that can characterize the complexity of (collections
of) open curves in 3-space in general. This leads to novel metrics of ent
anglement of open curves in 3-space that generalize classical topological
invariants\, like\, for example\, the Jones polynomial and Vassiliev invar
iants. For open curves\, these are continuous functions of the curve coord
inates and tend to topological invariants of classical knots and links whe
n the endpoints of the curves tend to coincide. We will apply our methods
to proteins and we will show that these enable us to create a new framewor
k for understanding protein folding\, which is validated by experimental d
ata. When applied to the SARS-CoV-2 spike protein\, we see that the local
native topological landscape can predict residues where mutations can have
an important impact on protein structure and possibly in viral transmissi
bility. These methods thus not only open a new mathematical direction in k
not theory\, but can also help us understand polymer and biopolymer functi
on and material properties in many contexts with the goal of their predict
ion and design.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louisa Liles (University of Virginia)
DTSTART:20240830T170000Z
DTEND:20240830T175000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/73
DESCRIPTION:Title: Thompson's Groups\, Annular Links\, and Tangles\nby Louisa Lile
s (University of Virginia) as part of VCU Geometry and Topology Seminar\n\
nLecture held in Harris Hall 4145.\n\nAbstract\nVaughan Jones showed how t
o associate links in the $3$-sphere to elements of Thompson’s group $F$
and proved that $F$ gives rise to all link types. This talk will discuss t
wo recent extensions of Jones’ work– the first is a method of building
annular links from Thompson’s group $T$\, which contains $F$ as a subgr
oup\, and the second is a method of building $(n\,n)$-tangles from $F$ . A
nnular links from $T$ arise from Jones’s unitary representations of the
Thompson groups\, and tangles from $F$ give rise to an action of $F$ on Kh
ovanov’s chain complexes. This talk includes joint work with Slava Krush
kal and Yangxiao Luo.\n\nThis talk is based on two papers: https://arxiv.o
rg/abs/2403.16838 \; https://arxiv.org/abs/2401.12065 .\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leo Herr (Virginia Tech)
DTSTART:20241025T190000Z
DTEND:20241025T195000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/77
DESCRIPTION:Title: The log Grothendieck group of varieties\nby Leo Herr (Virginia
Tech) as part of VCU Geometry and Topology Seminar\n\nLecture held in Harr
is Hall 4145.\n\nAbstract\nThe ordinary Grothendieck group of varieties is
a group with simple generators and relations built out of varieties analo
gous to the construction of the integers from the natural numbers. Called
the ``poor man's motives\,'' this group recovers Hodge numbers\, even for
open\, singular varieties\, and point counts over finite fields. \nLog sch
emes are morally pairs of a scheme with a divisor (X\, D). Used for compac
tifications and degenerations of varieties\, they admit a log Hodge theory
due to Kato-Usui. This theory is not yet understood for open or singular
varieties\, so we define a log Grothendieck group to get log Hodge numbers
. Unfortunately\, this does not work! We modify log Hodge numbers to get w
eaker well-defined invariants from our theory\, leaving lots of open quest
ions. This is joint with Andreas Gross\, David Holmes\, Pim Spelier\, Jess
e Vogel.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renzo Cavalieri (Colorado State University)
DTSTART:20241101T170000Z
DTEND:20241101T175000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/82
DESCRIPTION:Title: tropical psi classes and tropicalizations of psi classes\nby Re
nzo Cavalieri (Colorado State University) as part of VCU Geometry and Topo
logy Seminar\n\nLecture held in Harris Hall 4145.\n\nAbstract\nthe general
rule for the interactions between tropical geometry and moduli spaces of
course is the following: everything you may wish is going to work like a c
harm in genus zero\, and break down horribly in higher genus. This is the
case for the tautological intersection theory of psi classes\, a class of
fundamental objects in the geometry of moduli spaces of curves: the genera
ting function of their intersection numbers has made waves\, pun intended\
, when it was noticed that it is a tau function for the KdV hierarchy. Bac
k to tropical geometry: in genus zero tropical psi classes have been first
defined by Mikhalkin in the early 2000's\, then through the work of Kerbe
r-Markwig and Katz it was shown that intersection numbers of tropical psi
classes agree with their algebraic counterparts.\nIn work with A.Gross and
H.Markwig (2021)\, we were able to make sense of tropical psi classes in
higher genus\, by making the tropical moduli space of curves into a stack
for families of tropical curves with an affine structure. This is a combin
atorial theory that recovers the algebraic intersection numbers\, but can
also produce results that do not have a counter part in algebraic geometry
. To this end\, in recent work with A.Gross we answer the question of when
we can show that tropical psi classes are tropicalizations. In order to e
ven make sense of the statement\, we had to introduce a notion of tropical
ization for families of curves based on the Picard theory of the base.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joe Boninger (Boston College)
DTSTART:20240920T170000Z
DTEND:20240920T175000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/84
DESCRIPTION:Title: Obstructing Cosmetic Crossing Changes\nby Joe Boninger (Boston
College) as part of VCU Geometry and Topology Seminar\n\nLecture held in H
arris Hall 4145.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tristan Hubsch (Howard University)
DTSTART:20241115T180000Z
DTEND:20241115T185000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/87
DESCRIPTION:Title: Mirror Calabi-Yau Hypersurfaces in Spaces of general Type\nby T
ristan Hubsch (Howard University) as part of VCU Geometry and Topology Sem
inar\n\nLecture held in Harris Hall 4145.\n\nAbstract\nCalabi-Yau hypersur
faces in toric spaces of general type (described by certain non-convex\, f
lip-folded and otherwise multilayered "multitopes") may be smoothed by rat
ional anticanonical sections. Nevertheless\, gauged linear sigma model pha
ses and an increasing number of their classical and quantum data are just
as computable as for their siblings encoded by reflexive polytopes\, and t
hey all have transposition mirrors. Moreover\, explicit deformations of su
ch general-type embeddings are diffeomorphic to regular hypersurfaces in F
ano toric varieties\, jointly realized as generalized complete intersectio
ns in products of projective spaces. Showcasing Calabi-Yau hypersurfaces i
n Hirzebruch scrolls shows this class of constructions to be infinitely va
st\, yet amenable to several well-founded algebro-geometric methods of ana
lysis. This talk will include joint work with Per Berglund\, as reported i
n part: arXiv:1606.07420\, arXiv:1611.10300\, arXiv:2205.12827 and arXiv:2
403.07139.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Machacek (Hampden-Sydney College)
DTSTART:20241206T180000Z
DTEND:20241206T185000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/89
DESCRIPTION:Title: Gorenstein Toric Varieties from Posets\nby John Machacek (Hampd
en-Sydney College) as part of VCU Geometry and Topology Seminar\n\nLecture
held in Harris Hall 4145.\n\nAbstract\nToric varieties are algebraic vari
eties with a group action which can be defined using convex polyhedra. The
y have rich structure due to their combinatorial nature and can be useful
in generating examples and testing conjectures. Gorenstein varieties are v
arieties which can be thought of as being "close to smooth" in many instan
ces. We will study toric varieties coming from partially ordered sets (pos
ets) and determine in many cases when they are Gorenstein. No prior knowle
dge of toric geometry will be assumed\, and in our setting the Gorenstein
property will be reduced to combinatorial\, computational\, and linear alg
ebraic questions.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giuseppe Cotardo (Virginia Tech)
DTSTART:20250124T180000Z
DTEND:20250124T185000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/90
DESCRIPTION:Title: Rank-metric lattices and finite geometry\nby Giuseppe Cotardo (
Virginia Tech) as part of VCU Geometry and Topology Seminar\n\nLecture hel
d in Harris Hall 4145.\n\nAbstract\nRank-Metric Lattices (RML in short) we
re introduced in 2023 as the q-analogue of Higher-Weight Dowling Lattices.
They are special families of geometric lattices whose elements are the $\
\mathbb{F}_{q^m}$-linear subspaces of $\\mathbb{F}_{q^m}^n$ having a basis
of vectors with rank weight bounded from above\, ordered by inclusion.\n\
nIn this talk\, we investigate the properties of RMLs from a finite geomet
ry perspective. We compute the Whitney numbers of the first kind for some
of these lattices\, providing a recursive formula. In the second part of t
he talk\, we present asymptotic results on the density of some classes of
cardinality-optimal rank-metric codes.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilarion Melnikov (James Madison University)
DTSTART:20250207T180000Z
DTEND:20250207T185000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/92
DESCRIPTION:Title: The stringy geometry of integral cohomology in mirror symmetry\
nby Ilarion Melnikov (James Madison University) as part of VCU Geometry an
d Topology Seminar\n\nLecture held in Harris Hall 4145.\n\nAbstract\nI wil
l discuss the physical significance of the torsion subgroups in integral c
ohomology of a mirror pair of Calabi-Yau manifolds. Up to Poincare dualit
y and the universal coefficients theorem\, there are two such independent
groups in the cohomology of a Calabi-Yau 3-fold. I will argue that one of
these corresponds to a quantum symmetry of the underlying conformal theor
y\, and therefore has a direct interpretation in the mirror\; the remainin
g group labels a choice of flat abelian gerbe that can be used to refine t
he mirror correspondence\, and I will present some mirror constructions fo
r the pair (X\, gerbe). This is based on work with Cheng and Minasian\,
ArXiv:2407.07635\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tianyuan Xu (University of Richmond)
DTSTART:20250221T180000Z
DTEND:20250221T185000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/94
DESCRIPTION:Title: On maximal sets of orthogonal roots\nby Tianyuan Xu (University
of Richmond) as part of VCU Geometry and Topology Seminar\n\nLecture held
in Harris Hall 4145.\n\nAbstract\nA root system is a finite subset of a E
uclidean space that satisfies certain\nsimple geometric properties. Each e
lement of a root system is called a root\,\neach root gives rise to a refl
ection map on the ambient Euclidean space\, and\ntogether the reflections
generate a group known as a Weyl group. In this talk we\nwill explore maxi
mal sets of pairwise orthogonal roots in root systems of types\n$E_7$\, $E
_8$ or $D_n$ for $n$ even. We call such maximal sets $n$-roots\, and we\ns
how that the reflections in the Weyl group act on the $n$-roots in a\npart
icularly nice way\, endowing them with the structure of a so-called\nquasi
parabolic set. The quasiparabolic structure can be understood via a\nconne
ction between $n$-roots and perfect matchings\, and we will discuss how th
is\nstructure helps reveal new insights about the Fano plane\, quantum iso
morphisms of\ngraphs\, and certain irreducible representations of the Weyl
group. (Joint work\nwith Richard Green.)\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seppo Niemi-Colvin (Indiana University)
DTSTART:20250228T180000Z
DTEND:20250228T185000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/95
DESCRIPTION:Title: A kitchen sink surgery formula for knot lattice homotopy\nby Se
ppo Niemi-Colvin (Indiana University) as part of VCU Geometry and Topology
Seminar\n\nLecture held in Harris Hall 4145.\n\nAbstract\nI compute the k
not Floer complex for the regular fiber of $\\Sigma(2\,3\,7)$\, and I show
that its Seifert genus and genus in a self homology cobordism agree. A st
ep used for this result was providing upgrades to the surgery formula for
knot lattice homotopy. Ozsv\\'ath\, Stipsicz\, and Szab\\'o showed that kn
ot lattice homology satisfies a surgery formula similar to the one relatin
g knot Floer homology and Heegaard Floer homology. I provide an iterable v
ersion of this formula that given the doubly filtered knot lattice space w
ith involutive maps for a generalized algebraic knot produces the correspo
nding data for the dual knot post-surgery.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bryson Owens (University of Illinois Chicago)
DTSTART:20250328T170000Z
DTEND:20250328T175000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/99
DESCRIPTION:Title: Chern Classes of the Hodge Bundle of Cyclic Admissible Covers\n
by Bryson Owens (University of Illinois Chicago) as part of VCU Geometry a
nd Topology Seminar\n\nLecture held in Harris Hall 4145.\n\nAbstract\nModu
li spaces of marked curves form an important class of examples of moduli s
paces whose geometry can be studied in terms of some combinatorial data. T
here are related moduli spaces of admissible covers of marked curves whose
branch points are the marked points of the base curve\, where the genus\,
degree\, and monodromy data of the covers are fixed. This allows us to st
udy families of such covers in terms of combinatorial data\, yielding a po
werful computation tool for doing intersection theory on these moduli spac
es. In this talk\, I will introduce these moduli spaces and then discuss a
project (joint with Seamus Somerstep and Renzo Cavalieri) in which we com
pute the first Chern class of the Hodge bundle on spaces of cyclic admissi
ble covers.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boya Wen (University of Richmond)
DTSTART:20250404T170000Z
DTEND:20250404T175000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/100
DESCRIPTION:Title: Using heights to find rational points\nby Boya Wen (University
of Richmond) as part of VCU Geometry and Topology Seminar\n\nLecture held
in Harris Hall 4145.\n\nAbstract\nA central question in number theory is
finding the set of integer or rational number solutions to a given system
of polynomial equations. This question\, called the Diophantine problem\,
has more than 1700 years of history and is still an active area of researc
h. In this talk\, we will start with finding rational numbers x and y sati
sfying the equation -139y^2=x^3+10x^2-20x+8. One key ingredient is heights
\, which measure the arithmetic complexity of such rational solutions. Whi
le we explore this question\, I will introduce some key players in number
theory and their interactions: elliptic curves\, modular curves\, modular
forms\, L-functions\, and the more general height theory. In particular\,
we will see a connection between the heights of rational points and the de
rivatives of L-functions\, known as the Gross-Zagier formula. One directio
n of my work is a generalization of this formula\, where a key step involv
es constructing Green’s functions on graphs. Another direction is concre
te computations of rational points on some modular curves when the set of
rational points is known to be finite. I will introduce my past\, current\
, and possible future work in these two directions.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jianqi Liu (University of Pennsylvania)
DTSTART:20250411T170000Z
DTEND:20250411T175000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/101
DESCRIPTION:Title: Applications of the factorization theorem of conformal blocks in v
ertex operator algebras\nby Jianqi Liu (University of Pennsylvania) as
part of VCU Geometry and Topology Seminar\n\nLecture held in Harris Hall
4145.\n\nAbstract\nThe notion of conformal blocks on stable curves defined
by modules over a vertex operator algebra (VOA) is a generalization of th
e WZNW-conformal blocks defined by modules over affine Lie algebras. The r
ecent advances in the theory of VOA-conformal blocks shed new light on the
representation theory of VOAs. The factorization theorem and vector bundl
e property of the sheaves of VOA-conformal blocks lead to new and short pr
oof of some deep theorems in the theory VOAs\, like the associativity of f
usion rules\, generalized Verlinde formula\, and the modular invariance of
intertwining operators. In this talk\, we will briefly discuss these appl
ications. This talk is based on a project with Xu Gao.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicola Tarasca (VCU)
DTSTART:20211203T180000Z
DTEND:20211203T185000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/104
DESCRIPTION:Title: Incident varieties of algebraic curves and canonical divisors\
nby Nicola Tarasca (VCU) as part of VCU Geometry and Topology Seminar\n\nL
ecture held in Harris Hall 4145.\n\nAbstract\nWith roots in the work of Ri
emann\, the theory of canonical divisors on curves has witnessed an explos
ion of interest in recent years\, motivated by the recent developments in
the study of limits of canonical divisors on nodal curves. Imposing condit
ions on canonical divisors allows one to construct natural geometric subva
rieties of moduli spaces of pointed curves\, called strata of canonical di
visors. The strata are in fact the projection on moduli spaces of curves o
f incidence varieties living above moduli spaces of curves. I will present
a graph formula for the restriction of the incident varieties over the lo
cus of pointed curves with rational tails. The formula is expressed as a l
inear combination of tautological classes indexed by decorated stable grap
hs\, with coefficients enumerating appropriate weightings of decorated sta
ble graphs. I will conclude with some applications. Joint work with Iulia
Gheorghita.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Flippen and Essak Seddiq (VCU)
DTSTART:20200925T170000Z
DTEND:20200925T175000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/105
DESCRIPTION:Title: Quotients of the Gordian graph\nby Christopher Flippen and Ess
ak Seddiq (VCU) as part of VCU Geometry and Topology Seminar\n\nLecture he
ld in Harris Hall 4145.\n\nAbstract\nThe Gordian graph and H(2)-Gordian gr
aphs of knots are abstract graphs whose vertex sets represent isotopy clas
ses of unoriented knots\, and whose edge sets record whether pairs of knot
s are related by crossing changes or H(2)-moves\, respectively. We investi
gate the quotients of these graphs under equivalence relations generated b
y several knot invariants including the determinant\, the span of the Jone
s polynomial\, and an invariant related to tricolorability. We show that t
hese quotient graphs are Gromov hyperbolic. We then discuss a collection o
f results about the graph isomorphism type of the quotient graphs\, includ
ing that the H(2)-Gordian graph of links modulo the relation induced by th
e span of Jones polynomial is isomorphic with the complete graph on infini
tely many vertices.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miriam Kuzbary (Georgia Tech)
DTSTART:20200410T170000Z
DTEND:20200410T175000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/106
DESCRIPTION:Title: Pure Braids and Link Concordance\nby Miriam Kuzbary (Georgia T
ech) as part of VCU Geometry and Topology Seminar\n\nLecture held in Harri
s Hall 4145.\n\nAbstract\nThe set of knots in the 3-sphere with the connec
ted sum operation forms a group when its quotient is taken by a 4-dimensio
nal equivalence relation called concordance. This knot concordance group\,
defined by Fox and Milnor in 1966\, can be contextualized as organizing p
roblems about 3- and 4-dimensional spaces and the relationships between th
em. However\, one of its limitations is that every 3-manifold is surgery o
n a link\, not necessarily a knot\, and thus it may be useful to understan
d such a group for links. Unfortunately\, the connected sum of links is no
t well defined\; in 1988\, Le Dimet constructed the string link concordanc
e group for links with n components to get around this problem. Notably\,
the knot concordance group is abelian while\, for each n the string link c
oncordance group on n strands is non-abelian as it contains the pure braid
group on n strands as a subgroup. In this talk\, I will discuss my result
that even the quotient of each string link concordance group by its pure
braid subgroup is non-abelian and explore the structure of this quotient g
roup.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allison Moore (VCU)
DTSTART:20200403T170000Z
DTEND:20200403T175000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/107
DESCRIPTION:Title: Introduction to Khovanov Homology part 2\nby Allison Moore (VC
U) as part of VCU Geometry and Topology Seminar\n\nLecture held in Harris
Hall 4145.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allison Moore (VCU)
DTSTART:20200527T170000Z
DTEND:20200527T175000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/108
DESCRIPTION:Title: Introduction to Khovanov Homology part 1\nby Allison Moore (VC
U) as part of VCU Geometry and Topology Seminar\n\nLecture held in Harris
Hall 4145.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Villareal (VCU)
DTSTART:20200306T180000Z
DTEND:20200306T185000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/109
DESCRIPTION:Title: Introduction to Vertex Algebras\nby Juan Villareal (VCU) as pa
rt of VCU Geometry and Topology Seminar\n\nLecture held in Harris Hall 414
5.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele Grandini (Virginia State University)
DTSTART:20200221T180000Z
DTEND:20200221T185000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/110
DESCRIPTION:Title: Split structures and generalized almost product structures\nby
Daniele Grandini (Virginia State University) as part of VCU Geometry and
Topology Seminar\n\nLecture held in Harris Hall 4145.\n\nAbstract\nThe not
ion of split structure was introduced to capture the idea of transverse ge
ometry in the context of Generalized Geometry. By definition\, a split str
ucture is a subbundle E on the generalized tangent bundle\, such that the
restriction to E of the tautological inner product has split signature. In
particular\, split structures admitting a bi-Lagrangian splitting are equ
ivalent to generalized para-F-structures. A large class of examples of suc
h structures is given by generalized almost product structures\, for which
the projections onto the tangent bundle are complementary distributions.
In this talk I will discuss such structures and operators associated to th
em\, adopting a spinorial formalism.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicola Tarasca (VCU)
DTSTART:20200214T180000Z
DTEND:20200214T185000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/111
DESCRIPTION:Title: 2D TFT's continued\nby Nicola Tarasca (VCU) as part of VCU Geo
metry and Topology Seminar\n\nLecture held in Harris Hall 4145.\nAbstract:
TBA\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicola Tarasca (VCU)
DTSTART:20200207T180000Z
DTEND:20200207T185000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/112
DESCRIPTION:Title: Discussion of 2D modular tensor categories\nby Nicola Tarasca
(VCU) as part of VCU Geometry and Topology Seminar\n\nLecture held in Harr
is Hall 4145.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Aldi (VCU)
DTSTART:20200131T180000Z
DTEND:20200131T185000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/113
DESCRIPTION:Title: Review of Chern Simons theory and TFT\nby Marco Aldi (VCU) as
part of VCU Geometry and Topology Seminar\n\nLecture held in Harris Hall 4
145.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renzo Cavalieri (Colorado State University)
DTSTART:20191206T200000Z
DTEND:20191206T205000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/114
DESCRIPTION:Title: On the elusiveness of hyperelliptic loci\nby Renzo Cavalieri (
Colorado State University) as part of VCU Geometry and Topology Seminar\n\
nLecture held in Harris Hall 4145.\n\nAbstract\nModuli spaces of Riemann s
urfaces of genus g with n marked points are an infinite collection of geom
etric objects\, connected to one another by a number of natural morphisms.
Their full intersection rings being completely out of reach\, we follow M
umford's lead in investigating the tautological rings: the smallest subrin
gs that allow the different moduli spaces to "communicate" with each other
via the natural morphisms. Tautological rings have a combinatorially desc
ribed collection of additive generators\, exhibiting the tautological ring
s as quotients of algebras of appropriately decorated graphs. The hyperell
iptic loci are closed subvarieties of the moduli spaces of curves generica
lly parameterizing surfaces that admit a ramified double cover of a sphere
. Faber and Pandharipande showed their class is tautological\, and a natur
al question is to describe such classes as linear combinations of the comb
inatorial generators of the tautological ring. The answer is to this day o
nly known for genus less than or equal to six. While the computational com
plexity becomes unmanageable for a "brute force" approach\, the collection
of hyperelliptic classes have lots of combinatorial structure that might
lead\, once organized in the appropriate framework\, to a conceptual descr
iption of their formulas. I would describe the current situation as having
a large numbers of pieces of a puzzle\, but still struggling to figure ou
t how to fit them together. In this talk I will give an overview of the pr
oblem\, and discuss some of the recent developments\, results and the ongo
ing work in progress. I will survey the work of many people\, but I wish t
o acknowledge in particular my collaborators Nicola Tarasca and Johannes S
chmitt with whom we are trying to piece together this intriguing puzzle.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ignacio Barros (Northeastern University)
DTSTART:20191122T200000Z
DTEND:20191122T205000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/115
DESCRIPTION:Title: On product identities and the Chow ring of holomorphic symplectic
manifolds\nby Ignacio Barros (Northeastern University) as part of VCU
Geometry and Topology Seminar\n\nLecture held in Harris Hall 4145.\n\nAbst
ract\nWe propose a series of basic conjectural identities in the Chow ring
s of hyperkähler varieties of K3 type that generalizes in higher dimensio
ns a set of key properties of cycles on a K3 surface. We prove that they h
old for the Hilbert scheme of n points on a K3 surface. The talk is based
on joint work with Laure Flapan\, Alina Marian\, and Rob Silversmith.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudius Zibrowius (University of British Columbia)
DTSTART:20191107T180000Z
DTEND:20191107T185000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/116
DESCRIPTION:Title: On symmetries of peculiar modules\; or delta-graded link Floer hom
ology is mutation invariant\nby Claudius Zibrowius (University of Brit
ish Columbia) as part of VCU Geometry and Topology Seminar\n\nLecture held
in Harris Hall 4145.\n\nAbstract\nConway mutation is an operation on link
s that is notoriously difficult to detect: it preserves many link invarian
ts such as the signature\, the Alexander polynomial or\, more generally\,
the HOMFLY polynomial. Baldwin and Levine conjectured that δ-graded link
Floer homology also belongs in this list—despite the fact that *bigraded
* link Floer homology can distinguish some mutant knots such as the famous
Kinoshita-Terasaka and Conway knots. In [arXiv:1909.04267]\, I proved Bal
dwin and Levine's conjecture by studying symmetry properties of peculiar m
odules\, an immersed curve invariant of 4-ended tangles. In this talk\, I
will sketch this proof.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Jose' Villarreal (VCU)
DTSTART:20191101T170000Z
DTEND:20191101T175000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/117
DESCRIPTION:Title: The monodromy representation of the braid group on the space of co
nformal blocks II\nby Juan Jose' Villarreal (VCU) as part of VCU Geome
try and Topology Seminar\n\nLecture held in Harris Hall 4145.\nAbstract: T
BA\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Jose' Villarreal (VCU)
DTSTART:20191025T170000Z
DTEND:20191025T175000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/118
DESCRIPTION:Title: The monodromy representation of the braid group on the space of co
nformal blocks I\nby Juan Jose' Villarreal (VCU) as part of VCU Geomet
ry and Topology Seminar\n\nLecture held in Harris Hall 4145.\nAbstract: TB
A\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicola Tarasca (VCU)
DTSTART:20191004T190000Z
DTEND:20191004T195000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/119
DESCRIPTION:Title: Quantum Algebra and Geometry of Curves\nby Nicola Tarasca (VCU
) as part of VCU Geometry and Topology Seminar\n\nLecture held in Harris H
all 4145.\n\nAbstract\nThis talk will focus on geometric realizations of n
on-commutative\nalgebras. I will discuss how representations of vertex alg
ebras\nencode information about the geometry of algebraic curves. The\nsta
rting point is the Virasoro uniformization\, which provides an\nincarnatio
n of the Virasoro algebra in the tangent space of a\ntautological line bun
dle on families of coordinatized curves. After\nbriefly reviewing vertex a
lgebras and algebraic curves\, I will\ndiscuss how one can construct new v
ector bundles on families of\ncurves using representations of vertex algeb
ras. The new results\nare joint work with Chiara Damiolini and Angela Gibn
ey.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Aldi (VCU)
DTSTART:20191004T170000Z
DTEND:20191004T175000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/120
DESCRIPTION:Title: Abelian Chern-Simons Theory\nby Marco Aldi (VCU) as part of VC
U Geometry and Topology Seminar\n\nLecture held in Harris Hall 4145.\nAbst
ract: TBA\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allison Moore and Marco Aldi (VCU)
DTSTART:20190927T170000Z
DTEND:20190927T175000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/121
DESCRIPTION:Title: Temperley Lieb Algebras / Jones Polynomial in Chern-Simons\nby
Allison Moore and Marco Aldi (VCU) as part of VCU Geometry and Topology S
eminar\n\nLecture held in Harris Hall 4145.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allison Moore (VCU)
DTSTART:20190920T190000Z
DTEND:20190920T195000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/122
DESCRIPTION:Title: Gordian graphs of knots and Gromov hyperbolicity\nby Allison M
oore (VCU) as part of VCU Geometry and Topology Seminar\n\nLecture held in
Harris Hall 4145.\n\nAbstract\nA knot is a closed loop\, smoothly embedde
d in three-dimensional space\nin some potentially interesting way. The set
of isotopy classes of knots\nis a countably infinite set. The Gordian gra
ph G is a construction for\norganizing the set of knots\, in which each ve
rtex represents the isotopy\ntype of a knot\, and two vertices are connect
ed by an edge whenever the\ncorresponding knots are relating by a crossing
change. Other variants\nof this graph (for example\, the H(2)-Gordian gra
ph) can be defined in a\nsimilar manner\, and capture information about ot
her local moves on\nknots. The broad structure of such knot graphs is not
well-understood.\nWe'll discuss a few of the statements that are known\, a
nd mention some\nnew results in this area. Undergrads and grad students ar
e especially\nwelcome to attend this talk\, which will assume no backgroun
d in knot\ntheory.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Aldi (VCU)
DTSTART:20190913T170000Z
DTEND:20190913T175000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/123
DESCRIPTION:Title: Intro to Quantum Field Theory\nby Marco Aldi (VCU) as part of
VCU Geometry and Topology Seminar\n\nLecture held in Harris Hall 4145.\nAb
stract: TBA\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allison Moore (VCU)
DTSTART:20190906T170000Z
DTEND:20190906T175000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/124
DESCRIPTION:Title: Intro to Jones polynomial: skein theory\, Kauffman bracket versus
Jones's perspective via von Neumann algebras\nby Allison Moore (VCU) a
s part of VCU Geometry and Topology Seminar\n\nLecture held in Harris Hall
4145.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruoyu (Tony) Guo (VCU)
DTSTART:20250829T170000Z
DTEND:20250829T175000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/126
DESCRIPTION:Title: Some perspectives on the finitistic dimension conjecture\nby R
uoyu (Tony) Guo (VCU) as part of VCU Geometry and Topology Seminar\n\nLect
ure held in Harris Hall 4145.\n\nAbstract\nThe finitistic dimension conjec
ture\, which serves as a sufficient condition for numerous homological con
jectures\, has been a central topic of research in homological algebra. De
spite over 60 years of study\, the conjecture is only solved in special ca
ses under the context of finite dimensional algebras. In this talk\, we pr
esent three perspectives in studying the finitistic dimension conjecture:
1. the representation theory perspective\, 2. the invariant perspective\,
and 3. the perspective of algebraic operations. These perspectives are clo
sely connected\, and their interaction often leads to new ideas for the co
njecture. We also mention a potential geometric perspective for future stu
dy.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/126/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oliver Hao Wang (University of Virginia)
DTSTART:20251003T170000Z
DTEND:20251003T175000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/131
DESCRIPTION:Title: Chern classes and exotic G-manifolds\nby Oliver Hao Wang (Univ
ersity of Virginia) as part of VCU Geometry and Topology Seminar\n\nLectur
e held in Harris Hall 4145.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/131/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sofia Wood (Columbia University)
DTSTART:20251010T170000Z
DTEND:20251010T175000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/132
DESCRIPTION:Title: Hodge numbers of universal compactified Jacobians\nby Sofia Wo
od (Columbia University) as part of VCU Geometry and Topology Seminar\n\nL
ecture held in Harris Hall 4145.\n\nAbstract\nWe study the universal compa
ctified Jacobians of degree d\, as constructed by Kass and Pagani over the
moduli space of stable curves. These spaces compactify the universal degr
ee-d Jacobian over the moduli of smooth curves\, and depend on a choice of
universal stability condition. We show that the Hodge numbers of these co
mpactified Jacobians are independent of both the degree d and the choice o
f stability condition.\nThis is joint work with Rahul Pandharipande\, Dan
Petersen\, and Johannes Schmidt.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/132/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Blackwell (University of Virginia)
DTSTART:20251031T190000Z
DTEND:20251031T195000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/135
DESCRIPTION:Title: Cornered Skein Lasagna Theory\nby Sarah Blackwell (University
of Virginia) as part of VCU Geometry and Topology Seminar\n\nLecture held
in Harris Hall 4145.\n\nAbstract\nThe theory of skein lasagna modules\, in
itiated by Morrison-Walker-Wedrich\, has been the subject of much interest
in recent years. This theory takes as input Khovanov-Rozansky link homolo
gy and yields invariants of oriented 4-manifolds\, which are generally ver
y powerful yet hard to calculate. Most excitingly\, this theory was used r
ecently to detect exotic compact 4-manifolds by Ren-Willis\, marking the f
irst such result proven without the use of gauge theory. In this talk I wi
ll discuss an extension of skein lasagna theory for cornered 4-manifolds a
nd describe an application to trisections of 4-manifolds\, with an eye tow
ards calculations. This is ongoing joint work with Slava Krushkal and Yang
xiao Luo.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/135/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Levine (Duke University)
DTSTART:20260320T170000Z
DTEND:20260320T175000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/149
DESCRIPTION:Title: Knot Floer Homology\, Bordered Floer Homology\, and Surgery Module
s\nby Adam Levine (Duke University) as part of VCU Geometry and Topolo
gy Seminar\n\nLecture held in Harris Hall 4145.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/149/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Gerhard (VCU)
DTSTART:20260327T170000Z
DTEND:20260327T175000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/150
DESCRIPTION:Title: Counting Abelian Varieties Using Number Theory\nby Jonathan Ge
rhard (VCU) as part of VCU Geometry and Topology Seminar\n\nLecture held i
n Harris Hall 4145.\n\nAbstract\nArithmetic Geometry is the interplay betw
een Algebraic Geometry and Number Theory. As a small introduction to the t
opic\, I will be talking about a research project I did at JMU with Dr. Ca
ssie Williams. There are three main characters in this show: 1) The size o
f isogeny classes of abelian varieties over a finite field\; 2) The class
numbers of certain Galois field extensions\; 3) The average size of conjug
acy classes of matrices in the general symplectic group. In a very surpris
ing connection\, there is a sense in which all three of these numbers are
exactly equal. I will give a general overview of the ideas for this projec
t but will not assume much previous Number Theory knowledge.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/150/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quincy Frias (GMU)
DTSTART:20260403T170000Z
DTEND:20260403T175000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/151
DESCRIPTION:Title: Derived Differential Geometry in Context\nby Quincy Frias (GMU
) as part of VCU Geometry and Topology Seminar\n\nLecture held in Harris H
all 4145.\n\nAbstract\nThe field of Derived Differential Geometry has seen
explosive growth in the past few years\; there is a higher category of de
rived manifolds defined by a universal property and which has several equi
valent models. These models provide us with tools to glean both theoretica
l results about the derived geometry of manifolds as well as computations
of derived manifolds and their associated structures such as cotangent com
plexes.\n\nThis talk will focus on the growth of DDG in the context of der
ived geometry writ large\, and the current progress toward extending class
ical structures on manifolds such as connections and pseudo-differential o
perators to the derived setting.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/151/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Siddarth Kannan (MIT)
DTSTART:20260410T170000Z
DTEND:20260410T175000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/152
DESCRIPTION:Title: Symmetric functions and motivic invariants of moduli spaces\nb
y Siddarth Kannan (MIT) as part of VCU Geometry and Topology Seminar\n\nLe
cture held in Harris Hall 4145.\n\nAbstract\nI will give an introduction t
o moduli spaces of curves and related objects\, including the universal Ja
cobian and the moduli space of maps from curves to projective space. I wil
l also introduce basic aspects of symmetric function theory\, and explain
how symmetric functions provide a powerful algebraic and combinatorial too
lkit for passing geometric information between these spaces. As I will exp
lain in the talk\, the geometric information in question will be “motivi
c” in the sense of constructible invariants such as the topological Eule
r characteristic and its algebro-geometric upgrades. Parts of the talk wil
l be based on joint work with Terry Song.\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/152/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noah Pope (VCU)
DTSTART:20260424T170000Z
DTEND:20260424T175000Z
DTSTAMP:20260422T230717Z
UID:vcugeomandtop/154
DESCRIPTION:Title: Plumbed 3–Manifolds and Neumann moves\nby Noah Pope (VCU) as
part of VCU Geometry and Topology Seminar\n\nLecture held in Harris Hall
4145.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/vcugeomandtop/154/
END:VEVENT
END:VCALENDAR