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BEGIN:VEVENT
SUMMARY:Allison Moore (VCU)
DTSTART:20200417T180000Z
DTEND:20200417T190000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/1
DESCRIPTION:Title: Introduction to Khovanov Homology\, part 3\nby Allison Mo
ore (VCU) as part of VCU Geometry and Topology Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samantha Kirk (NCSU)
DTSTART:20200424T180000Z
DTEND:20200424T190000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/2
DESCRIPTION:Title: Vertex Operator Representations of Twisted Toroidal Lie algeb
ras\nby Samantha Kirk (NCSU) as part of VCU Geometry and Topology Semi
nar\n\n\nAbstract\nA toroidal Lie algebra is the universal central extensi
on of the tensor product of a simple finite-dimensional Lie algebra g and
the ring of Laurent polynomials in 2 or more variables. Given an automorph
ism of the Lie algebra g of finite order\, one can construct a "twisted" v
ersion of a toroidal Lie algebra. In this talk\, we will discuss how to co
nstruct vertex operator representations of twisted toroidal Lie algebras.\
n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katherine Maxwell (University of Minnesota Twin Cities)
DTSTART:20200501T180000Z
DTEND:20200501T190000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/3
DESCRIPTION:Title: The super Mumford form and Sato grassmannian\nby Katherin
e Maxwell (University of Minnesota Twin Cities) as part of VCU Geometry an
d Topology Seminar\n\n\nAbstract\nThe moduli space of curves and represent
ations 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 coinc
idence by involving the infinite-dimensional Sato grassmannian. In this ta
lk\, we will first discuss this construction of Kontsevich and Arbarello\,
De Concini\, Kac\, and Procesi\, and then discuss a supersymmetric genera
lization. Our main result is the existence of a flat holomorphic connectio
n on the line bundle $\\lambda_{3/2}\\otimes\\lambda^{-5}_{1/2}$ on the mo
duli space of triples: a super Riemann surface\, a Neveu-Schwarz puncture\
, and a formal coordinate system.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joshua Sussan (CUNY)
DTSTART:20200508T180000Z
DTEND:20200508T190000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/4
DESCRIPTION:Title: p-DG structures and categorification\nby Joshua Sussan (C
UNY) as part of VCU Geometry and Topology Seminar\n\n\nAbstract\nThe Jones
polynomial is an invariant of links coming from the representation theory
of quantum groups. After reviewing its construction\, we will discuss th
e goals of the categorification program and how the notion of a p-DG algeb
ra naturally arises when looking to categorify the WRT 3-manifold invarian
t.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Taylor (Colby College)
DTSTART:20200515T180000Z
DTEND:20200515T190000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/5
DESCRIPTION:Title: Lower bounds on the tunnel number of composite spatial theta
graphs\nby Scott Taylor (Colby College) as part of VCU Geometry and To
pology Seminar\n\n\nAbstract\nThe tunnel number of a graph embedded in a 3
-dimensional manifold is the fewest number of arcs needed so that the unio
n of the graph with the arcs has handlebody exterior. The behavior of tunn
el number with respect to connected sum of knots can vary dramatically\, d
epending on the knots involved. However\, a classical theorem of Scharlema
nn and Schultens says that the tunnel number of a composite knot is at lea
st the number of factors. For theta graphs\, trivalent vertex sum is the o
peration which most closely resembles the connected sum of knots. The anal
ogous theorem of Scharlemann and Schultens no longer holds\, however. I wi
ll provide a sharp lower bound for the tunnel number of composite theta gr
aphs\, using recent work on a new knot invariant which is additive under c
onnected sum and trivalent vertex sum. This is joint work with Maggy Tomov
a.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Han-Bom Moon (Fordham University)
DTSTART:20200522T180000Z
DTEND:20200522T190000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/6
DESCRIPTION:Title: Finite generation of the algebra of conformal blocks via bira
tional geometry.\nby Han-Bom Moon (Fordham University) as part of VCU
Geometry and Topology Seminar\n\n\nAbstract\nA Conformal block is a repres
entation-theoretic object constructed as an example of two-dimensional con
formal field theory (WZW model). For each simple Lie algebra $\\mathfrak{g
}$ and a stable curve\, the set of conformal blocks naturally has an algeb
ra structure. We prove\, by employing birational geometric techniques\, th
e finite generation of the algebra of conformal blocks for $\\mathfrak{g}
= \\mathfrak{sl}_r$. This is joint work with Sang-Bum Yoo.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florencia Orosz Hunziker (Harvard University)
DTSTART:20200529T180000Z
DTEND:20200529T190000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/7
DESCRIPTION:Title: Tensor categories arising from the Virasoro algebra\nby F
lorencia Orosz Hunziker (Harvard University) as part of VCU Geometry and T
opology Seminar\n\n\nAbstract\nIn this talk we will discuss the tensor str
ucture associated to certain representations of the Virasoro algebra. In p
articular\, we will show that there is a braided tensor category structure
on the category of C1-cofinite modules for the Virasoro vertex operator a
lgebras of arbitrary central charge.\nThis talk is based on joint work wit
h Jinwei Yang\, Thomas Creutzig\, Cuibo Jiang and David Ridout.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Szczesny (Boston University)
DTSTART:20200605T180000Z
DTEND:20200605T190000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/8
DESCRIPTION:Title: Toric Hall Algebras\nby Matt Szczesny (Boston University)
as part of VCU Geometry and Topology Seminar\n\n\nAbstract\nI will descri
be a construction that attaches to a smooth projective toric variety a co-
commutative Hopf algebra (in fact\, an enveloping algebra). It arises as a
Hall algebra of special coherent sheaves on the associated monoid scheme\
, using a version of algebraic geometry over $\\mathbb{F}_1$. These sheave
s are combinatorial in nature\, and look locally like (possibly infinite)
n-dimensional skew shapes. I will discuss some evidence to suggest that th
ese Hall algebras are classical limits of quantum groups\, and in some cas
es relate them to known loop algebras. This is joint work with Jaiung Jun.
\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olof Bergvall (University of Gävle)
DTSTART:20200911T190000Z
DTEND:20200911T200000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/9
DESCRIPTION:Title: Configurations\, arrangements and moduli spaces\nby Olof
Bergvall (University of Gävle) as part of VCU Geometry and Topology Semin
ar\n\n\nAbstract\nIn this talk we will encounter certain configuration spa
ces of points in the projective plane and see how they relate to certain m
oduli spaces of curves and surfaces (marked with e.g. level structures\, g
eometric markings and anticanonical curves). We will also see how to compu
te their cohomology\, equivariantly with respect to certain natural group
actions\, by using techniques from the theory of subspace arrangements.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joshua Wang (Harvard)
DTSTART:20201009T190000Z
DTEND:20201009T200000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/10
DESCRIPTION:Title: Floer and Khovanov homologies of band sums\nby Joshua Wa
ng (Harvard) as part of VCU Geometry and Topology Seminar\n\n\nAbstract\nG
iven a nontrivial band sum of two knots\, we may add full twists to the ba
nd to obtain a family of knots indexed by the integers. In this talk\, I'l
l show that the knots in this family have the same Heegaard and instanton
knot Floer homology but distinct Khovanov homology\, generalizing a result
of M. Hedden and L. Watson. A key component of the argument is a proof th
at each of the three knot homologies detects the trivial band. The main ap
plication is a verification of the generalized cosmetic crossing conjectur
e for split links.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Sikora (SUNY Buffalo)
DTSTART:20201023T190000Z
DTEND:20201023T200000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/11
DESCRIPTION:Title: Tangle Equations\, the Jones conjecture and quantum rational
numbers\nby Adam Sikora (SUNY Buffalo) as part of VCU Geometry and To
pology Seminar\n\n\nAbstract\nWe study systems of 2-tangle equations\, whi
ch play an important role in the analysis of enzyme actions on DNA strands
. We show the benefits of considering such systems in the context of frame
d tangles and\, in particular\, we conjecture uniqueness of solutions in t
hat case. We prove a version of this conjecture for rational tangles and w
e relate this conjecture to the Jones Unknotting conjecture\, which potent
ially opens a door to a purely topological line of attack on the Jones con
jecture. Additionally\, we relate systems of tangle equations to the Cosme
tic Surgery Conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joshua Lackman (Toronto)
DTSTART:20201106T200000Z
DTEND:20201106T210000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/12
DESCRIPTION:Title: Quantization of (Holomorphic) Poisson Manifolds\nby Josh
ua Lackman (Toronto) as part of VCU Geometry and Topology Seminar\n\n\nAbs
tract\nWe will discuss how\, starting with a Poisson manifold\, one may pr
oduce a quantization via its symplectic groupoid\, and hopefully a noncomm
utative algebra.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iulia Gheorghita (Boston College)
DTSTART:20201120T200000Z
DTEND:20201120T210000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/13
DESCRIPTION:Title: Effective classes in the projectivized k-th Hodge bundle
\nby Iulia Gheorghita (Boston College) as part of VCU Geometry and Topolog
y Seminar\n\n\nAbstract\nThe k-th Hodge bundle over the moduli space of cu
rves parametrizes stable k-differentials. In this talk\, we will discuss s
everal effective classes in both the projectivized k-th Hodge bundle and t
he projectivized n-marked k-th Hodge bundle. In the n-marked k-th Hodge bu
ndle we will show how to compute the locus where the k-differential has ze
ros 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 effective divisors in the unmarked projectivized k-th Hodge bundle whe
re the zeros of the k-differentials satisfy a Brill-Noether condition.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Jose Villarreal
DTSTART:20201211T160000Z
DTEND:20201211T170000Z
DTSTAMP:20260404T095038Z
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 introduce the notion of logarithmic vertex algebra\, which is a vert
ex algebra with logarithmic singularities in the operator product expansio
n of quantum fields\; thus providing a rigorous formulation of the algebra
ic properties of quantum fields in logarithmic conformal field theory. We
develop a framework that allows many results about vertex algebras to be t
ransferred to logarithmic vertex algebras\, and we describe some examples.
This is a joint work with Bojko Bakalov.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gage Martin (Boston College)
DTSTART:20201113T200000Z
DTEND:20201113T210000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/16
DESCRIPTION:Title: Khovanov homology\, knot Floer homology\, and link detection
\nby Gage Martin (Boston College) as part of VCU Geometry and Topology
Seminar\n\n\nAbstract\nKhovanov homology and knot/link Floer homology are
invariants of links in S^3 categorifying the more classical Jones and Ale
xander polynomials respectively. There are many formal similarities betwee
n the theories but some key differences as well. The relationships between
Khovanov homology and knot/link Floer homology has been a source of inspi
ration in each theory. In this talk\, we will give an overview of both th
eories in the context of link detection\, mention some of techniques used
in proving detection results in each of the theories\, and sketch proofs t
hat Khovanov homology detects the torus link T(2\,6) and link Floer homolo
gy detects the torus links T(2\,2n). This is partially joint work with Fra
ser Binns.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicola Pagani (University of Liverpool)
DTSTART:20210205T200000Z
DTEND:20210205T210000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/17
DESCRIPTION:Title: Geometry of genus 1 fine compactified Jacobians\nby Nico
la Pagani (University of Liverpool) as part of VCU Geometry and Topology
Seminar\n\n\nAbstract\nA classical construction in algebraic geometry asso
ciates with every nonsingular complex projective curve its Jacobian\, a co
mplex projective variety of dimension equal to the genus of the curve. A s
imilar construction is available for singular curves\, but the resulting J
acobian variety fails in general to be compact. In this talk we introduce
a general abstract notion of fine compactified Jacobian for nodal curves o
f arbitrary genus.\n\nWe focus on genus 1 and discuss combinatorial classi
fication results for fine compactified Jacobians in the case of a single s
table curve\, and in the case of the universal family over the moduli spac
e of stable pointed curves. In the former case\, our abstract notion find
s back objects that had already been constructed by Oda-Seshadri and other
s. In the latter case our complete classification exhibits new examples. I
f time permits it\, we will discuss how to calculate the cohomology of the
se compactified Jacobians. \n\nA joint work with Orsola Tommasi.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bin Gui (Rutgers University)
DTSTART:20210305T200000Z
DTEND:20210305T210000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/18
DESCRIPTION:Title: Conjugation and positivity of conformal blocks\nby Bin G
ui (Rutgers University) as part of VCU Geometry and Topology Seminar\n\n\n
Abstract\nGiven a strongly rational unitary VOA V\, a Hermitian form on th
e space of its intertwining operators was introduced recently to understan
d the unitarity of the representation modular tensor category Rep(V). It w
as actually shown that\, along with some natural assumptions\, if this Her
mitian form (which is necessarily non-degenerate) is positive\, namely\, i
f it is an inner product\, then Rep(V) is unitary. The crucial step of thi
s story is to prove the positivity of the Hermitian form. In this talk\, I
give a geometric interpretation of this positivity problem using (self)co
njugate Riemann surfaces and (self)conjugate conformal blocks.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oğuz Şavk (Boğaziçi University)
DTSTART:20210319T190000Z
DTEND:20210319T200000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/19
DESCRIPTION:Title: Classical and New Plumbings Bounding Contractible Manifolds
and Rational Homology Balls\nby Oğuz Şavk (Boğaziçi University) as
part of VCU Geometry and Topology Seminar\n\n\nAbstract\nA classical ques
tion in low-dimensional topology asks which homology 3-spheres bound contr
actible 4-manifolds. In this talk\, we address this question for plumbed 3
-manifolds and we present two new infinite families. Along the way\, we al
so simply reprove most of the classical works of Akbulut and Kirby\, Fukuh
ara\, Fickle\, Maruyama\, Martin\, Casson and Harer\, and Stern around the
nineteen-eighties. Therefore\, our approach provides a unification of cla
ssical and new results via a modification of Mazur’s famous argument. On
e can weaken the above question and ask which homology 3-spheres bound rat
ional homology 4-balls. Surprisingly\, this question still remains hard. R
ecently\, significant progress occurred due to Akbulut and Larson. Using t
heir technique\, we exhibit new homology 3-spheres bounding rational homol
ogy 4-balls but not integral homology 4-balls. These 3-manifolds represent
non-trivial elements in the kernel of the natural map from the homology c
obordism group to the rational homology cobordism group.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan C. Johnson (University of Texas at Austin)
DTSTART:20210402T190000Z
DTEND:20210402T200000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/20
DESCRIPTION:Title: Bi-Orderability Techniques and Double Twist Links\nby Jo
nathan C. Johnson (University of Texas at Austin) as part of VCU Geometry
and Topology Seminar\n\n\nAbstract\nThe bi-orderability of link groups has
become a fascinating research topic. In this talk\, we will survey some u
seful tools that have been developed to investigate the bi-orderabily of l
ink complements\, including results of Linnell-Rhemtulla-Rolfsen\, Ito\, a
nd Kin-Rolfsen. In particular\, we will apply these techniques to the doub
le twist link groups.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannah Turner (University of Texas at Austin)
DTSTART:20210212T200000Z
DTEND:20210212T210000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/21
DESCRIPTION:Title: Branched cyclic covers and L-spaces\nby Hannah Turner (U
niversity of Texas at Austin) as part of VCU Geometry and Topology Seminar
\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allison Moore (Virginia Commonwealth University)
DTSTART:20210430T190000Z
DTEND:20210430T200000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/22
DESCRIPTION:by Allison Moore (Virginia Commonwealth University) as part of
VCU Geometry and Topology Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vance Blankers (Northeastern University)
DTSTART:20210917T140000Z
DTEND:20210917T145000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/23
DESCRIPTION:Title: Alternative compactifications of the moduli space of curves<
/a>\nby Vance Blankers (Northeastern University) as part of VCU Geometry a
nd Topology Seminar\n\n\nAbstract\nThe moduli space of curves is an import
ant object in modern algebraic geometry\, both interesting in its own righ
t and serving as a test space for broader geometric programs. These often
require the space to be compact\, which leads to a variety of choices for
compactification\, the most well-known of which is the Deligne-Mumford-Knu
dsen compactification by stable curves\, originally introduced in 1969. Si
nce then\, several alternative compactifications have been constructed and
studied\, and in 2013 David Smyth used a combinatorial framework to make
progress towards classifying all "sufficiently nice" compactifications. In
this talk\, I'll discuss some of the most well-studied compactifications\
, as well as two new compactifications\, which together classify the Goren
stein compactifications in genus 0 and genus 1.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:César Lozano Huerta (Universidad Nacional Autónoma de México -
Oaxaca)
DTSTART:20210924T140000Z
DTEND:20210924T145000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/24
DESCRIPTION:Title: On the Weak Lefschetz Principle in birational geometry\n
by César Lozano Huerta (Universidad Nacional Autónoma de México - Oaxac
a) as part of VCU Geometry and Topology Seminar\n\n\nAbstract\nIn this tal
k we will discuss the weak Lefschetz Principle in the context of birationa
l geometry.\n\nOur departing point will be the influential work of Solomon
Lefschetz started in 1924. We will look at the original formulation of th
e Lefschetz hyperplane theorem in algebraic topology and build up to recen
t developments of it in birational geometry. In doing so\, the slogan of t
he talk will be the following: there are many scenarios in geometry in whi
ch analogous versions of the Lefschetz hyperplane theorem hold. Such scena
rios are somewhat unexpected and have had a profound impact in mathematics
.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mara Ungureanu (Albert-Ludwigs-Universität Freiburg)
DTSTART:20211008T140000Z
DTEND:20211008T145000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/25
DESCRIPTION:Title: Counts of secant planes to varieties and universal polynomia
ls\nby Mara Ungureanu (Albert-Ludwigs-Universität Freiburg) as part o
f VCU Geometry and Topology Seminar\n\n\nAbstract\nFor a curve in projecti
ve space\, the count of varieties parametrising its secant planes is among
the most studied problems in classical enumerative geometry. We shall st
art with a gentle introduction to secant varieties and then explore the co
nnection between their enumerative geometry and Virasoro algebras on one s
ide\, and tautological integrals on the other.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Mullane (Humboldt Universität zu Berlin)
DTSTART:20211119T150000Z
DTEND:20211119T155000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/26
DESCRIPTION:Title: The birational geometry of the moduli space of pointed hyper
elliptic curves\nby Scott Mullane (Humboldt Universität zu Berlin) as
part of VCU Geometry and Topology Seminar\n\n\nAbstract\nThe moduli space
of pointed hyperelliptic curves is a seemingly simple object with perhaps
unexpectedly interesting geometry. I will report on joint work with Ignac
io Barros towards a full classification of both the Kodaira dimension and
the structure of the effective cone of these moduli spaces.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Margherita Lelli-Chiesa (Università Roma 3)
DTSTART:20211015T140000Z
DTEND:20211015T145000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/27
DESCRIPTION:Title: Brill-Noether theory of curves on abelian surfaces\nby M
argherita Lelli-Chiesa (Università Roma 3) as part of VCU Geometry and To
pology Seminar\n\n\nAbstract\nBrill-Noether theory investigates the ways i
n which an algebraic curve can be embedded in some projective space. I wil
l recall the most relevant results in the theory and their relation with c
urves lying on K3 surfaces. I will then illustrate more recent results on
the Brill-Noether theory of curves on Abelian surfaces highlightening the
major differences with respect to K3 surfaces and some applications to the
moduli space of curves.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seppo Niemi-Colvin (Duke University)
DTSTART:20210910T140000Z
DTEND:20210910T145000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/28
DESCRIPTION:Title: Invariance of Knot Lattice Homology\nby Seppo Niemi-Colv
in (Duke University) as part of VCU Geometry and Topology Seminar\n\n\nAbs
tract\nLinks of singularity and generalized algebraic links are ways of co
nstructing three-manifolds and smooth links inside them from algebraic sur
faces and curves inside them. Némethi created lattice homology as an inva
riant for links of normal surface singularities which developed out of com
putations for Heegaard Floer homology. Later Ozsváth\, Stipsicz\, and Sza
bó defined knot lattice homology for generalized algebraic knots in ratio
nal homology spheres\, which is known to play a similar role to knot Floer
homology and is known to compute knot Floer in some cases. I discuss a pr
oof that knot lattice is an invariant of the smooth knot type\, which had
been previously suspected but not confirmed.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jingling Yang (The Chinese University of Hong Kong\, Shenzhen)
DTSTART:20211029T140000Z
DTEND:20211029T145000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/29
DESCRIPTION:Title: Distance one surgeries on the lens space L(n\,1) and band su
rgeries on the torus knot T(2\,n)\nby Jingling Yang (The Chinese Unive
rsity of Hong Kong\, Shenzhen) as part of VCU Geometry and Topology Semina
r\n\n\nAbstract\nIt has been well known that any closed\, orientable 3-man
ifold can be obtained by performing Dehn surgery on a link in $S^3$. One o
f the most prominent problems in 3-manifold topology is to list all the po
ssible 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 surgery from other lens spaces. Besides\, considering surgeries betwe
en lens spaces is also motivated from DNA topology. In this talk\, we will
discuss distance one surgeries between lens spaces $L(n\, 1)$ with $n \\g
eq 5$ odd and lens spaces $L(s\,1)$ for $s \\neq 0 \\in \\mathbb{Z}$ and c
orresponding band surgeries from $T(2\, n)$ to $T(2\, s)$\, by using Heega
ard Floer mapping cone formula. We give an almost complete classification
of the above surgeries.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Vitagliano (Universita' di Salerno)
DTSTART:20211105T140000Z
DTEND:20211105T145000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/30
DESCRIPTION:Title: Homogeneous G-structures\nby Luca Vitagliano (Universita
' di Salerno) as part of VCU Geometry and Topology Seminar\n\n\nAbstract\n
G-structures unify several interesting geometries including: almost comple
x\, Riemannian\, almost symplectic geometry\, etc.\, the integrable versio
ns of which being complex\, flat Riemannian\, symplectic geometry\, etc. C
ontact manifolds are odd dimensional analogues of symplectic manifolds but
\, despite this\, there is no natural way to understand them as manifolds
with an ordinary integrable G-structure. In this talk\, we present a possi
ble solution to this discrepancy. Our proposal is based on a new notion o
f homogeneous G-structures. Interestingly\, besides contact\, the latter i
nclude other nice (old and new) geometries including: cosymplectic\, almos
t contact\, and a curious “homogeneous version” of Riemannian geometry
. This is joint work with A. G. Tortorella and O. Yudilevich.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert DeYeso (North Carolina State University)
DTSTART:20211001T140000Z
DTEND:20211001T145000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/31
DESCRIPTION:Title: (Heegaard Floer) thin knots satisfy the Cabling Conjecture\nby Robert DeYeso (North Carolina State University) as part of VCU Geom
etry and Topology Seminar\n\n\nAbstract\nThe Cabling Conjecture of Gonzál
ez-Acuña and Short holds that only cable knots admit a reducible surgery\
, which is Dehn surgery containing an essential 2-sphere. For surgeries al
ong (Heegaard Floer) thin knots\, we approach this conjecture by comparing
the relative Maslov gradings and periodicity structure of their Floer hom
ology. This is primarily done by reinterpreting these objects via immersed
curves techniques that recover Floer homology\, inspired by Hanselman's a
pproach to the Cosmetic Surgery Conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Villareal
DTSTART:20211210T150000Z
DTEND:20211210T155000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/32
DESCRIPTION:Title: Logarithmic vertex algebras\nby Juan Villareal as part o
f VCU Geometry and Topology Seminar\n\n\nAbstract\nIn this talk\, I want t
o explain a generalization of vertex algebras called logarithmic vertex al
gebras. In this work\, we develop a framework that allows many results abo
ut vertex algebras to be extended to logarithmic vertex algebras. In parti
cular\, I will mention one example which is motivated by physics\, this e
xample exhibits some unexpected new features that are peculiar to the loga
rithmic case. Finally\, I will mention a relation between logarithmic vert
ex algebras and non-local poisson vertex algebras. This is joint work with
Bojko Bakalov.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Samperton (University of Illinois at Urbana-Champaign)
DTSTART:20220128T150000Z
DTEND:20220128T155000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/33
DESCRIPTION:Title: Topological quantum computation is hyperbolic\nby Eric S
amperton (University of Illinois at Urbana-Champaign) as part of VCU Geome
try and Topology Seminar\n\n\nAbstract\nWe show that a topological quantum
computer based on the evaluation of a Witten-Reshetikhin-Turaev TQFT inva
riant of knots can always be arranged so that the knot diagrams one compil
es are hyperbolic. Furthermore\, the diagrams can be arranged to have addi
tional nice properties\, such as being alternating with minimal crossing n
umber. Various complexity-theoretic hardness results regarding the calcula
tion of quantum invariants of knots follow as corollaries. In particular\,
we argue that the hyperbolic geometry of knots is unlikely to be useful f
or topological quantum computation.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Balazs Elek (Virginia Commonwealth University)
DTSTART:20220204T180000Z
DTEND:20220204T185000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/34
DESCRIPTION:Title: Heaps\, Crystals and Preprojective Algebra Modules\nby B
alazs Elek (Virginia Commonwealth University) as part of VCU Geometry and
Topology Seminar\n\n\nAbstract\nKashiwara crystals are combinatorial gadge
ts associated to a representation of a reductive algebraic group that enab
le us to understand the structure of the representation in purely combinat
orial terms. We will describe a type-independent combinatorial constructio
n of crystals of the form $B(n\\lambda)$\, where $\\lambda$ is a dominant
minuscule weight\, using the heap associated to a fully commutative elemen
t in the 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 qui
ver. Using the work of Savage and Tingley\, we also realize the crystal $B
(n\\lambda)$ via irreducible components of the quiver Grassmannians of $n$
copies of this module\, and we describe an explicit crystal isomorphism b
etween the two models. This is joint work with Anne Dranowski\, Joel Kamni
tzer and Calder Morton-Ferguson.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Sala (Università di Pisa)
DTSTART:20220218T150000Z
DTEND:20220218T155000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/35
DESCRIPTION:Title: Two-dimensional cohomological Hall algebras\nby Francesc
o Sala (Università di Pisa) as part of VCU Geometry and Topology Seminar\
n\n\nAbstract\nThe present talk aims at introducing the theory of 2-dimens
ional cohomological Hall algebras and their relations with moduli spaces i
n algebraic 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 c
ohomological Hall algebra of a Kleinian surface singularity.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Swarnava Mukhopadhyay (Tata Institute of Fundamental Research)
DTSTART:20220211T150000Z
DTEND:20220211T155000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/36
DESCRIPTION:Title: Graph potentials and their periods\nby Swarnava Mukhopad
hyay (Tata Institute of Fundamental Research) as part of VCU Geometry and
Topology Seminar\n\n\nAbstract\nWe introduce graph potentials\, which are
Laurent polynomials associated to\n(colored) trivalent graphs. These graph
potentials encode degenerations of the \nmoduli space of rank two bundles
with fixed determinant. \n\nIn this talk\, we will discuss how the graph
potential defines a topological quantum field\ntheory. Applying the TQFT m
achinery gives us an efficient way to compute periods of these potentials.
\nIf time permits\, we will explain how these are related to the moduli
spaces of rank two bundles from \nthe perspective of mirror symmetry. Thi
s is a joint work with Pieter Belmans and Sergey Galkin.\n
LOCATION:https://stable.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:20260404T095038Z
UID:vcugeomandtop/38
DESCRIPTION:Title: Singular curves\, degenerate theta functions and KP solution
s\nby Daniele Agostini (Max-Planck-Institut für Mathematik in den Nat
urwissenschaften in Leipzig) as part of VCU Geometry and Topology Seminar\
n\n\nAbstract\nThe KP equation is a PDE that describes waves in shallow wa
ter. Quite surprisingly\, smooth algebraic curves give rise to solutions t
o the KP equation via Riemann's theta function. Singular curves produce so
lutions as well\, but the theta function in this case becomes degenerate.
I will present some results in this direction\, focusing on soliton and ra
tional solutions.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alejandro Cabrera (Universidade Federal do Rio de Janeiro\, Brasil
)
DTSTART:20220325T140000Z
DTEND:20220325T145000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/39
DESCRIPTION:Title: Infinite dimensional Dirac structures and moduli spaces\
nby Alejandro Cabrera (Universidade Federal do Rio de Janeiro\, Brasil) as
part of VCU Geometry and Topology Seminar\n\n\nAbstract\nIn this talk\, w
e first recall a class of geometric structures called Courant algebroids a
nd Dirac structures. We then proceed to outline their study on infinite di
mensional manifolds and stress their advantage with respect to more tradit
ional geometries (notably\, Poisson) in the infinite dimensional context.
We then study their reduction and apply this setting to the description of
geometric structures on moduli spaces of principal connections. This is j
oint work 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://stable.researchseminars.org/talk/vcugeomandtop/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Konstantinos Varvarezos (Princeton University)
DTSTART:20220401T140000Z
DTEND:20220401T145000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/40
DESCRIPTION:Title: Heegaard Floer homology\, immersed curves\, and chirally cos
metic surgeries\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) surg
eries on a knot is called chirally cosmetic if the resulting manifolds are
homeomorphic with opposite orientations. Making use of immersed curve for
mulations of Heegaard Floer invariants\, we discuss new obstructions to th
e existence of such surgeries\, which we apply to certain families of knot
s. In particular\, it turns out that combined with previously known result
s\, these obstructions are sufficient to completely classify chirally cosm
etic surgeries on odd alternating pretzel knots. Furthermore\, we are able
to rule out cosmetic surgeries for L-space knots along slopes with opposi
te signs.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex McCleary (Ohio State University)
DTSTART:20220429T140000Z
DTEND:20220429T145000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/42
DESCRIPTION:Title: An Introduction to Multiparameter Persistent Homology\nb
y Alex McCleary (Ohio State University) as part of VCU Geometry and Topolo
gy Seminar\n\n\nAbstract\nPersistent homology is a method for studying top
ological features of data sets. Originally developed in the early 2000s\,
it has proven useful for a wide range of applications including neuroscien
ce\, medical research\, chemistry\, weather prediction\, and financial mod
elling. We will start with a brief introduction to persistent homology and
multiparameter persistent homology followed by some recent results on mul
tiparameter persistence.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Aldi (VCU)
DTSTART:20220422T140000Z
DTEND:20220422T145000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/43
DESCRIPTION:Title: Generalized Polynomial Structures\nby Marco Aldi (VCU) a
s part of VCU Geometry and Topology Seminar\n\n\nAbstract\nThe generalized
tangent bundle is a geometric object that appears naturally in both physi
cs and mathematics. Generalized almost complex structures\, encompassing c
lassical almost complex structure and almost symplectic structures\, are a
n endomorphisms of the generalized tangent that square to negative the ide
ntity. In this talk we discuss more general endomorphims satisfying an arb
itrary polynomial equation with constant coefficients. As it turns out\, p
articular care is required in properly formulating the correct integrabili
ty conditions. This is joint work with Daniele Grandini.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Bud (Humboldt University in Berlin)
DTSTART:20220902T150000Z
DTEND:20220902T155000Z
DTSTAMP:20260404T095038Z
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 Top
ology Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergio Da Silva (Virginia State University)
DTSTART:20220923T150000Z
DTEND:20220923T155000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/45
DESCRIPTION:Title: An Introduction to Geometric Vertex Decomposability\nby
Sergio Da Silva (Virginia State University) as part of VCU Geometry and To
pology Seminar\n\nLecture held in Room 4145 Harris Hall.\n\nAbstract\nA Gr
öbner degeneration is a useful method to reduce problems involving ideals
to the monomial ideal setting. In the square-free case\, we can associate
a simplicial complex to a monomial ideal and ask whether this complex is
vertex decomposable. Another tool in this direction\, called a geometric v
ertex decomposition\, is a generalization of this technique first introduc
ed by Knutson-Miller-Yong to study diagonal degenerations of Schubert vari
eties. Later uses of the concept mostly occurred in the context of Schuber
t geometry\, until recent work of Klein-Rajchgot established a connection
to liaison theory. The interplay between these two theories can be used to
analyze degenerations\, construct Gröbner bases\, and find families of i
deals which are glicci (in the Gorenstein liaison class of a complete inte
rsection). In this talk\, I will introduce geometric vertex decomposabilit
y and highlight its applications to toric ideals of graphs and Hessenberg
varieties.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos Marcelo Servan (University of Chicago)
DTSTART:20220930T150000Z
DTEND:20220930T155000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/47
DESCRIPTION:Title: On the uniqueness of the Prym map\nby Carlos Marcelo Ser
van (University of Chicago) as part of VCU Geometry and Topology Seminar\n
\n\nAbstract\nThe Prym map associates to a double unbranched cover $p:Y \\
to X$ of 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 suc
h double covers and by $A_h$ the moduli space of ppavs of dimension h. We
will show that for $g \\geq 4$ and $h \\leq g-1$\, Prym is the unique non-
constant map of complex orbifolds between $R_g \\to A_h$. A key step in th
e proof is a classification of homomorphisms at the level of orbifold fund
amental groups\, which uses arguments from low-dimensional topology and ge
ometric group theory.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samantha Allen (Duquesne University)
DTSTART:20221007T150000Z
DTEND:20221007T155000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/48
DESCRIPTION:Title: Unknotting via null-homologous twists and multi-twists\n
by Samantha Allen (Duquesne University) as part of VCU Geometry and Topolo
gy Seminar\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 d
escription number of K can be defined similarly\, allowing for multiple fu
ll twists in a single twisting region. We can find no examples of knots in
the literature where these two invariants are not equal. In this talk\, I
will provide the first known examples where untwisting number and surgery
description number are not equal and discuss challenges to distinguishing
these invariants in general. While these invariants are defined geometric
ally\, our methods will involve several “algebraic” versions of unknot
ting operations. In addition\, we show the surprising result that the untw
isting number of a knot is at most three times its surgery description num
ber. This work is joint with Kenan Ince\, Seungwon Kim\, Benjamin Ruppik\,
and Hannah Turner.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pengyu Liu (UC Davis)
DTSTART:20221209T160000Z
DTEND:20221209T165000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/49
DESCRIPTION:Title: A graph polynomial that distinguishes tree topologies and it
s applications\nby Pengyu Liu (UC Davis) as part of VCU Geometry and T
opology Seminar\n\n\nAbstract\nIn this talk\, I will define a graph polyno
mial for trees and show that the polynomial is a complete invariant for un
labeled trees. Then\, we introduce distance-based methods for analyzing tr
ee structures with the polynomial\, and we demonstrate its applications in
molecular evolutionary and structural biology.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fernando Etayo Gordejuela (Universidad de Cantabria)
DTSTART:20220916T170000Z
DTEND:20220916T175000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/50
DESCRIPTION:Title: Structures on Generalized Geometry\nby Fernando Etayo Go
rdejuela (Universidad de Cantabria) as part of VCU Geometry and Topology S
eminar\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 the cotangent bundlles of a manifold\, and the notion of generalized
almost complex structure on the big tangent bundle. We shall show that man
y other geometric structures appear in Generalized Geometry. The talk will
not require deep knowledge of Differential Geometry.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Minyoung Jeon (University of Georgia)
DTSTART:20221014T170000Z
DTEND:20221014T175000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/51
DESCRIPTION:Title: Euler characteristic of Brill-Noether loci on Prym varieties
\nby Minyoung Jeon (University of Georgia) as part of VCU Geometry and
Topology Seminar\n\n\nAbstract\nPrym varieties\, named after Friedrich Pr
ym\, are abelian varieties constructed from étale double covers of algebr
aic curves. In 1985\, Welters subsequently equipped Prym varieties with Br
ill-Noether loci. In this talk\, we give a formula for the Euler character
istic of the Brill-Noether locus in Prym varieties with a vanishing sequen
ce at one marked point.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gretchen Matthews (Virginia Tech)
DTSTART:20230210T150000Z
DTEND:20230210T155000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/53
DESCRIPTION:Title: Coding for distributed storage using algebraic geometry\
nby Gretchen Matthews (Virginia Tech) as part of VCU Geometry and Topology
Seminar\n\n\nAbstract\nGiven the astonishing rates at which data is gener
ated\, how can it be stored efficiently? How is access to the stored infor
mation guaranteed? How can it be distributed across a network while also p
rotecting it from distortion\, degradation\, and loss? Answers to some of
these questions may be found using algebraic geometry. Algebraic geometry
codes are constructed using curves over finite fields\, a discovery in the
1980s that motivated much work on curves over finite fields with many rat
ional points and asymptotically good towers of function fields. Refinement
s of algebraic geometry codes designed from curves and surfaces now play a
role in coding for distributed storage. In this talk\, we share how study
ing these rich underlying structures provides a window into the powerful l
ocal properties that aid in designing codes for local recovery from erasur
es.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lev Borisov (Rutgers University)
DTSTART:20230217T150000Z
DTEND:20230217T155000Z
DTSTAMP:20260404T095038Z
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\nAbstract\nFake projective planes are fascinating complex surfaces (re
al four-dimensional manifolds). While they were first discovered about 40
years ago\, their explicit equations have only been computed recently. I w
ill talk about the history of fake projective planes and some of the pecul
iar constructions and challenges associated with finding their explicit eq
uations.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sara Maloni (University of Virginia)
DTSTART:20230224T150000Z
DTEND:20230224T155000Z
DTSTAMP:20260404T095038Z
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 Semin
ar\n\n\nAbstract\nThe Teichmüller space of a surface S is the space of ma
rked hyperbolic structure on S\, up to equivalence. By considering the hol
onomy representation of such structures\, the Teichmüller space can also
be seen as a connected component of (conjugacy classes of) representations
from the fundamental group of S into PSL(2\,R)\, consisting entirely of d
iscrete and faithful representations. Generalizing this point of view\, Hi
gher Teichmüller Theory studies connected components of (conjugacy classe
s of) representations from the fundamental group of S into more general se
misimple Lie groups which consist entirely of discrete and faithful repres
entations.\n\nWe will give a survey of some aspects of Higher Teichmüller
Theory\, and will make links with the recent powerful notion of Anosov re
presentation. Time permitting\, we will conclude by focusing on two separa
te questions:\nDo these representations correspond to deformation of geome
tric structures? \nCan we generalize the important notion of pleated surfa
ces to higher rank Lie groups like PSL(d\, C)?\nThe answer to question 1 i
s joint work with Alessandrini\, Tholozan and Wienhard\, while the answer
to question 2 is joint work with Martone\, Mazzoli and Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ralph Gomez (Swarthmore College)
DTSTART:20230303T150000Z
DTEND:20230303T155000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/56
DESCRIPTION:Title: The Berglund-Huebsch Transpose rule and Sasakian Geometry\nby Ralph Gomez (Swarthmore College) as part of VCU Geometry and Topolog
y Seminar\n\n\nAbstract\nThe goal of this talk will be to use some ideas f
rom a construction of mirror Calabi-Yau orbifolds due to Berglund\, Hübsc
h\, Krawitz (BHK mirror symmetry) to outline a way to create new examples
of Sasaki manifolds of positive Ricci curvature. If time permits\, we will
say some things about the Sasaki-Einstein case and report on (joint with
J. Valle and J. Vicente) some new examples of Sasaki-Einstein rational hom
ology 7-spheres.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Beibei Liu (MIT)
DTSTART:20230317T140000Z
DTEND:20230317T145000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/57
DESCRIPTION:Title: Heegaard Floer homology and plane curves with non-cuspidal s
ingularities\nby Beibei Liu (MIT) as part of VCU Geometry and Topology
Seminar\n\n\nAbstract\nIt is an interesting question to ask about the pos
sible configurations of singular points occurring on general algebraic cur
ves. In this talk\, we use Heegaard Floer homology to study the singularit
y links and give some obstructions for the configurations. The main ingred
ient is to use the knot Floer complex of the knotification of the singular
ities links in the algebraic curves. This is joint work with Borodzik and
Zemke.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Feride Ceren Köse (University of Georgia)
DTSTART:20230127T160000Z
DTEND:20230127T165000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/58
DESCRIPTION:Title: Symmetric unions and knot invariants\nby Feride Ceren K
öse (University of Georgia) as part of VCU Geometry and Topology Seminar\
n\n\nAbstract\nWe study symmetric unions in the context of problems regard
ing knot invariants. Recently\, a class of symmetric unions was proposed t
o construct nontrivial knots with trivial Jones polynomial. We show\, howe
ver\, that such a knot is always trivial and hence this construction canno
t be used to answer the open question asking whether the Jones polynomial
detects the unknot. We then discuss why symmetric union is a valuable cons
truction to study knot invariants and why our result provides strong evide
nce for the non-existence of nontrivial knots with trivial Jones polynomia
l.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicola Tarasca (VCU)
DTSTART:20230324T140000Z
DTEND:20230324T145000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/59
DESCRIPTION:Title: Coinvariants of vertex algebras and abelian varieties\nb
y Nicola Tarasca (VCU) as part of VCU Geometry and Topology Seminar\n\n\nA
bstract\nSpaces of coinvariants have classically been constructed by assig
ning representations of affine Lie algebras\, and more generally\, vertex
operator algebras\, to algebraic curves.\nRemoving curves out of the pictu
re\, I will introduce spaces of coinvariants at abelian varieties with res
pect to the action of an infinite-dimensional Lie algebra. I will show how
these spaces globalize to twisted D-modules on moduli of abelian varietie
s\, extending the classical picture from moduli of curves. This is based o
n my recent preprint arXiv:2301.13227.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Almut Burchard (University of Toronto)
DTSTART:20230331T140000Z
DTEND:20230331T145000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/60
DESCRIPTION:Title: What is the best shape? Geometric problems arising in aggreg
ation models\nby Almut Burchard (University of Toronto) as part of VCU
Geometry and Topology Seminar\n\n\nAbstract\nHow do pair interactions sha
pe the large-scale behaviour of a\ncloud of particles (animals\, social ag
ents ...) ? In the most basic\nmodels\, the shape of the cloud is determi
ned by minimizing an\nattractive-repulsive interaction energy under suitab
le geometric\nconstraints.\nWhen can we expect aggregation to occur? What
is the shape of the\nresulting flock? I will describe recent work on opti
mal shapes in\ncapacitor problems that occur as limiting cases.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ihsan Topaloglu (VCU)
DTSTART:20230407T140000Z
DTEND:20230407T145000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/61
DESCRIPTION:Title: Characterization of regular polygons via an overdetermined p
roblem\nby Ihsan Topaloglu (VCU) as part of VCU Geometry and Topology
Seminar\n\n\nAbstract\nIn this talk I will discuss the optimality of regul
ar triangles and quadrilaterals for nonlocal energies of generalized Riesz
-type in the class of polygons with a fixed number of sides and fixed area
\, as well as their characterization as unique stationary points. These re
sults are joint work with M. Bonacini and R. Cristoferi. I will also prese
nt on recent results by Bogosel\, Bucur and Fragalà where they show that
for certain interaction kernels there is symmetry breaking for polygons wi
th number of sides greater than 5.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louisa Liles (UVA)
DTSTART:20230915T170000Z
DTEND:20230915T175000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/62
DESCRIPTION:Title: Quantum modularity of 3-manifold invariants\nby Louisa L
iles (UVA) as part of VCU Geometry and Topology Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Prakash Belkale (UNC Chapel Hill)
DTSTART:20230929T170000Z
DTEND:20230929T175000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/63
DESCRIPTION:Title: Vertices in the multiplicative eigenvalue problem\nby Pr
akash Belkale (UNC Chapel Hill) as part of VCU Geometry and Topology Semin
ar\n\n\nAbstract\nThe classical problem about the possible eigenvalues of
a product of unitary matrices AB given the eigenvalues of A and B has rel
ations to many areas of geometry\, representation theory and combinatorics
. There is a polytope controlling this problem whose faces can be describe
d in terms of the quantum cohomology of Grassmannians. The problem of dete
rmining the vertices of the polytope remained open for a long time\, but r
ecently I gave an inductive framework for understanding vertices on a giv
en face: some vertices come explicitly from cycle classes of geometricall
y defined loci\, and the remaining vertices come from an induction proced
ure from smaller groups. I want to describe this method\, and generalizati
on to the case of arbitrary groups (joint work with Joshua Kiers). If tim
e permits\, I will state connections to the theory of unitary rigid local
systems.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lutian Zhao (University of Maryland)
DTSTART:20240126T170000Z
DTEND:20240126T175000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/64
DESCRIPTION:Title: Nonabelian Hodge Theory of parahoric torsors\nby Lutian
Zhao (University of Maryland) as part of VCU Geometry and Topology Seminar
\n\n\nAbstract\nModern mathematical research has been enriched by explorin
g the bijection between Higgs bundles and local systems over noncompact Ri
emann surfaces\, an incredible feat accomplished profoundly by C. Simpson
by introducing weighted filtrations. In this discussion\, our focus will b
e on further unraveling this relationship by delving into the correlation
between the Dolbeault and de Rham moduli spaces for generally complex redu
ctive structure groups\, utilizing the influential language of parahoric g
roup schemes as initially established by Bruhat-Tits. This presentation is
based on collaborative work with Georgios Kydonakis\, Pengfei Huang\, and
Hao Sun.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bojko Bakalov (North Carolina State University)
DTSTART:20240202T180000Z
DTEND:20240202T185000Z
DTSTAMP:20260404T095038Z
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\nAbstr
act\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 obs
tacles to training parameterized quantum circuits is the presence of flat
regions in the parameter landscape\, called barren plateaus. To diagnose s
uch barren plateaus\, we obtain an exact expression for the variance of th
e cost function in terms of the dynamical Lie algebra generated by the cir
cuit. Second\, we classify all dynamical Lie algebras of 1-dimensional tra
nslation-invariant spin chains. The talk will be based on the papers arXiv
:2309.09342 and arXiv:2309.05690.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatsu Takeuchi (Virginia Tech)
DTSTART:20240209T180000Z
DTEND:20240209T185000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/66
DESCRIPTION:Title: A Toy Quantum Mechanics on a Vector Space over Finite Fields
\nby Tatsu Takeuchi (Virginia Tech) as part of VCU Geometry and Topolo
gy Seminar\n\n\nAbstract\nUnlike Relativity\, which can be derived from a
few physical postulates\, Quantum Mechanics is defined from a mathematical
"recipe" that is known to "work\," in the sense that it leads to a theory
whose predictions agree with experiment exactly\, but no one really under
stand what the physical meaning of the recipe is. One approach that has be
en tried to clarify the meaning of the "recipe" is to modify parts of it t
o see how the resulting theory changes. For instance\, one can change the
field over which the state space is defined from the complex numbers to ot
her fields or division algebras\, e.g. real numbers or quaternions. In thi
s talk\, I will discuss what would happen if we change that field to a fin
ite field Fq. We find that the correlations in the resulting toy theory do
not violate the CHSH inequality though its predictions cannot be reproduc
ed by a hidden variable theory. Furthermore\, we argue that the q->1 limit
\, in which the field becomes the "field with one element\," the theory be
comes "classical."\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Aldi (VCU)
DTSTART:20240216T180000Z
DTEND:20240216T185000Z
DTSTAMP:20260404T095038Z
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\n
Abstract\nThe generalized tangent bundle\, the direct sum of the tangent a
nd cotangent bundle of a manifold\, is an object of great interest in both
differential geometry and physics. Skew-symmetric endomorphisms that squa
re to negative the identity are known as generalized almost complex struct
ures and their integrability is equivalent to the vanishing of the Courant
-Nijenhuis tensor. Integrability conditions for more general skew-symmetri
c endomorphisms are not well-understood. In joint work with Sergio Da Silv
a and Daniele Grandini\, we describe all possible tensorial integrability
conditions in terms of a shifted version of the Courant-Nijenhuis tensor.\
n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Deepisha Solanki (University of Buffalo)
DTSTART:20240301T180000Z
DTEND:20240301T185000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/68
DESCRIPTION:Title: Studying Links via Plats\nby Deepisha Solanki (Universit
y of Buffalo) as part of VCU Geometry and Topology Seminar\n\n\nAbstract\n
Between 1990 and 2006\, Birman and Menasco wrote a sequence of papers with
the running major title “Stabilisation in the braid groups”\, that in
vestigated the question of what stabilisation accomplishes in Markov’s t
heorem. One key result coming out of that sequence of papers was the disco
very of a new isotopy -- the exchange move – which also preserves braid
index and writhe\, but could jump between conjugacy classes. Thus\, it was
established that using just a sequence of braid isotopies\, exchange move
s and destabilisations\, one could go from any closed braid representative
of the unlink to the representative of minimal index – the trivial clos
ed braid. It was also shown that using just braid isotopies and exchange m
oves\, one could take a closed braid representing a split or composite lin
k to one where it was “obviously” split or composite\, respectively.\n
\nIn the setting of plat presentations of links\, we now ask the same ques
tion: what does stabilisation accomplish? We introduce two new isotopy mov
es that preserve the bridge index: the pocket move and the flip move\, whi
ch can be thought of as being analogous to an exchange move of the closed
braid setting. Equipped with these isotopies\, we prove results analogous
to Birman-Menasco’s results\, in the plat setting.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evangelia Gazaki (University of Virginia)
DTSTART:20240412T170000Z
DTEND:20240412T175000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/70
DESCRIPTION:Title: Hyperelliptic Curves mapping to Abelian Surfaces and Applica
tions to Beilinson's Conjecture for 0-cycles\nby Evangelia Gazaki (Uni
versity of Virginia) as part of VCU Geometry and Topology Seminar\n\n\nAbs
tract\nA classical invariant in Algebraic Geometry is the Picard group of
a smooth projective curve C. This group is the quotient of the group of di
visors on C (aka the free abelian group on all points of the curve) modulo
divisors of rational functions on C. Over an algebraically closed field t
his group can be fully understood by the Abel-Jacobi map\, which gives an
isomorphism between the degree zero elements of the Picard group and the J
acobian variety of the curve. In higher dimensions there is an analog of t
his group\, called the Chow group of 0-cycles\, for which many things gene
ralize from the case of curves. The main issue that makes the situation mu
ch more chaotic though is that the Abel-Jacobi map is in general no longer
an isomorphism. In fact\, over large fields like the complex numbers and
for many important classes of varieties (abelian varieties\, K3 surfaces\,
products of curves of positive genus\,...) the kernel of the Abel-Jacobi
can be really enormous. On the other extreme a famous conjecture of Beilin
son from the mid 80's predicts that over the algebraic closure of the rati
onal numbers the Abel-Jacobi map is an isomorphism unconditionally on the
variety. This conjecture is very hard to establish and in fact\, there ar
e no interesting examples in the literature known to satisfy this conjectu
re. In this talk I will present recent joint work with Jonathan Love\, whe
re we make substantial progress on this conjecture for abelian surfaces.
First\, we describe a very rich collection of relations in the kernel of t
he Abel-Jacobi arising from hyperelliptic curves\, that is\, curves that a
re given by an equation of the form y^2=f(x). Second\, we will give a geom
etric construction that produces large countable collections of such curve
s mapping to a given abelian surface.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mee Seong Im (USNA)
DTSTART:20240405T170000Z
DTEND:20240405T175000Z
DTSTAMP:20260404T095038Z
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\n
Abstract\nA special case of certain diagrammatics\, when G is the group of
affine transformations of a\nline\, can be related to the infinitesimal d
ilogarithm and to the Shannon entropy of finite probability\ndistributions
. I will explain the diagrammatics and their connections to infinitesimal
dilogarithms and\nentropy.\n\nThis is joint work in progress with Mikhail
Khovanov.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eleni Panagiotu (Arizona State University)
DTSTART:20240419T170000Z
DTEND:20240419T175000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/72
DESCRIPTION:Title: Novel measures of complexity of open curves in 3-space\n
by Eleni Panagiotu (Arizona State University) as part of VCU Geometry and
Topology Seminar\n\n\nAbstract\nFilamentous material may exhibit structure
dependent material properties and function that depends on their entangle
ment. Even though intuitively entanglement is often understood in terms of
knotting or linking\, many of the filamentous systems in the natural worl
d are not mathematical knots or links. In this talk we will introduce a no
vel framework in knot theory that can characterize the complexity of (coll
ections of) open curves in 3-space in general. This leads to novel metrics
of entanglement of open curves in 3-space that generalize classical topol
ogical invariants\, like\, for example\, the Jones polynomial and Vassilie
v invariants. For open curves\, these are continuous functions of the curv
e coordinates and tend to topological invariants of classical knots and li
nks when the endpoints of the curves tend to coincide. We will apply our m
ethods to proteins and we will show that these enable us to create a new f
ramework for understanding protein folding\, which is validated by experim
ental data. When applied to the SARS-CoV-2 spike protein\, we see that the
local native topological landscape can predict residues where mutations c
an have an important impact on protein structure and possibly in viral tra
nsmissibility. These methods thus not only open a new mathematical directi
on in knot theory\, but can also help us understand polymer and biopolymer
function and material properties in many contexts with the goal of their
prediction and design.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louisa Liles (University of Virginia)
DTSTART:20240830T170000Z
DTEND:20240830T175000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/73
DESCRIPTION:Title: Thompson's Groups\, Annular Links\, and Tangles\nby Loui
sa Liles (University of Virginia) as part of VCU Geometry and Topology Sem
inar\n\nLecture held in Harris Hall 4145.\n\nAbstract\nVaughan Jones showe
d how to associate links in the $3$-sphere to elements of Thompson’s gro
up $F$ and proved that $F$ gives rise to all link types. This talk will di
scuss two recent extensions of Jones’ work– the first is a method of b
uilding annular links from Thompson’s group $T$\, which contains $F$ as
a subgroup\, and the second is a method of building $(n\,n)$-tangles from
$F$ . Annular 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 Khovanov’s chain complexes. This talk includes joint work with Slav
a Krushkal and Yangxiao Luo.\n\nThis talk is based on two papers: https://
arxiv.org/abs/2403.16838 \; https://arxiv.org/abs/2401.12065 .\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leo Herr (Virginia Tech)
DTSTART:20241025T190000Z
DTEND:20241025T195000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/77
DESCRIPTION:Title: The log Grothendieck group of varieties\nby Leo Herr (Vi
rginia Tech) as part of VCU Geometry and Topology Seminar\n\nLecture held
in Harris Hall 4145.\n\nAbstract\nThe ordinary Grothendieck group of varie
ties is a group with simple generators and relations built out of varietie
s analogous to the construction of the integers from the natural numbers.
Called the ``poor man's motives\,'' this group recovers Hodge numbers\, ev
en for open\, singular varieties\, and point counts over finite fields. \n
Log schemes are morally pairs of a scheme with a divisor (X\, D). Used for
compactifications and degenerations of varieties\, they admit a log Hodge
theory due to Kato-Usui. This theory is not yet understood for open or si
ngular varieties\, so we define a log Grothendieck group to get log Hodge
numbers. Unfortunately\, this does not work! We modify log Hodge numbers t
o get weaker well-defined invariants from our theory\, leaving lots of ope
n questions. This is joint with Andreas Gross\, David Holmes\, Pim Spelier
\, Jesse Vogel.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renzo Cavalieri (Colorado State University)
DTSTART:20241101T170000Z
DTEND:20241101T175000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/82
DESCRIPTION:Title: tropical psi classes and tropicalizations of psi classes
\nby Renzo Cavalieri (Colorado State University) as part of VCU Geometry a
nd Topology Seminar\n\nLecture held in Harris Hall 4145.\n\nAbstract\nthe
general rule for the interactions between tropical geometry and moduli spa
ces of course is the following: everything you may wish is going to work l
ike a charm in genus zero\, and break down horribly in higher genus. This
is the case for the tautological intersection theory of psi classes\, a cl
ass of fundamental objects in the geometry of moduli spaces of curves: the
generating function of their intersection numbers has made waves\, pun in
tended\, when it was noticed that it is a tau function for the KdV hierarc
hy. Back to tropical geometry: in genus zero tropical psi classes have bee
n first defined by Mikhalkin in the early 2000's\, then through the work o
f Kerber-Markwig and Katz it was shown that intersection numbers of tropic
al psi classes agree with their algebraic counterparts.\nIn work with A.Gr
oss and H.Markwig (2021)\, we were able to make sense of tropical psi clas
ses 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
combinatorial theory that recovers the algebraic intersection numbers\, b
ut can also produce results that do not have a counter part in algebraic g
eometry. 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 ord
er to even make sense of the statement\, we had to introduce a notion of t
ropicalization for families of curves based on the Picard theory of the ba
se.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joe Boninger (Boston College)
DTSTART:20240920T170000Z
DTEND:20240920T175000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/84
DESCRIPTION:Title: Obstructing Cosmetic Crossing Changes\nby Joe Boninger (
Boston College) as part of VCU Geometry and Topology Seminar\n\nLecture he
ld in Harris Hall 4145.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tristan Hubsch (Howard University)
DTSTART:20241115T180000Z
DTEND:20241115T185000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/87
DESCRIPTION:Title: Mirror Calabi-Yau Hypersurfaces in Spaces of general Type\nby Tristan Hubsch (Howard University) as part of VCU Geometry and Topol
ogy Seminar\n\nLecture held in Harris Hall 4145.\n\nAbstract\nCalabi-Yau h
ypersurfaces in toric spaces of general type (described by certain non-con
vex\, flip-folded and otherwise multilayered "multitopes") may be smoothed
by rational anticanonical sections. Nevertheless\, gauged linear sigma mo
del phases and an increasing number of their classical and quantum data ar
e just as computable as for their siblings encoded by reflexive polytopes\
, and they all have transposition mirrors. Moreover\, explicit deformation
s of such general-type embeddings are diffeomorphic to regular hypersurfac
es in Fano toric varieties\, jointly realized as generalized complete inte
rsections in products of projective spaces. Showcasing Calabi-Yau hypersur
faces in Hirzebruch scrolls shows this class of constructions to be infini
tely vast\, yet amenable to several well-founded algebro-geometric methods
of analysis. This talk will include joint work with Per Berglund\, as rep
orted in part: arXiv:1606.07420\, arXiv:1611.10300\, arXiv:2205.12827 and
arXiv:2403.07139.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Machacek (Hampden-Sydney College)
DTSTART:20241206T180000Z
DTEND:20241206T185000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/89
DESCRIPTION:Title: Gorenstein Toric Varieties from Posets\nby John Machacek
(Hampden-Sydney College) as part of VCU Geometry and Topology Seminar\n\n
Lecture held in Harris Hall 4145.\n\nAbstract\nToric varieties are algebra
ic varieties with a group action which can be defined using convex polyhed
ra. They have rich structure due to their combinatorial nature and can be
useful in generating examples and testing conjectures. Gorenstein varietie
s are varieties which can be thought of as being "close to smooth" in many
instances. We will study toric varieties coming from partially ordered se
ts (posets) and determine in many cases when they are Gorenstein. No prior
knowledge of toric geometry will be assumed\, and in our setting the Gore
nstein property will be reduced to combinatorial\, computational\, and lin
ear algebraic questions.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giuseppe Cotardo (Virginia Tech)
DTSTART:20250124T180000Z
DTEND:20250124T185000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/90
DESCRIPTION:Title: Rank-metric lattices and finite geometry\nby Giuseppe Co
tardo (Virginia Tech) as part of VCU Geometry and Topology Seminar\n\nLect
ure held in Harris Hall 4145.\n\nAbstract\nRank-Metric Lattices (RML in sh
ort) were introduced in 2023 as the q-analogue of Higher-Weight Dowling La
ttices. 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 inclus
ion.\n\nIn this talk\, we investigate the properties of RMLs from a finite
geometry perspective. We compute the Whitney numbers of the first kind fo
r some of these lattices\, providing a recursive formula. In the second pa
rt of the talk\, we present asymptotic results on the density of some clas
ses of cardinality-optimal rank-metric codes.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilarion Melnikov (James Madison University)
DTSTART:20250207T180000Z
DTEND:20250207T185000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/92
DESCRIPTION:Title: The stringy geometry of integral cohomology in mirror symmet
ry\nby Ilarion Melnikov (James Madison University) as part of VCU Geom
etry and Topology Seminar\n\nLecture held in Harris Hall 4145.\n\nAbstract
\nI will discuss the physical significance of the torsion subgroups in int
egral cohomology of a mirror pair of Calabi-Yau manifolds. Up to Poincare
duality and the universal coefficients theorem\, there are two such indep
endent 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 conforma
l theory\, and therefore has a direct interpretation in the mirror\; the r
emaining group labels a choice of flat abelian gerbe that can be used to r
efine the mirror correspondence\, and I will present some mirror construct
ions for the pair (X\, gerbe). This is based on work with Cheng and Mina
sian\, ArXiv:2407.07635\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tianyuan Xu (University of Richmond)
DTSTART:20250221T180000Z
DTEND:20250221T185000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/94
DESCRIPTION:Title: On maximal sets of orthogonal roots\nby Tianyuan Xu (Uni
versity of Richmond) as part of VCU Geometry and Topology Seminar\n\nLectu
re held in Harris Hall 4145.\n\nAbstract\nA root system is a finite subset
of a Euclidean space that satisfies certain\nsimple geometric properties.
Each element of a root system is called a root\,\neach root gives rise to
a reflection map on the ambient Euclidean space\, and\ntogether the refle
ctions generate a group known as a Weyl group. In this talk we\nwill explo
re maximal 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\, an
d we\nshow that the reflections in the Weyl group act on the $n$-roots in
a\nparticularly nice way\, endowing them with the structure of a so-called
\nquasiparabolic set. The quasiparabolic structure can be understood via a
\nconnection between $n$-roots and perfect matchings\, and we will discuss
how this\nstructure helps reveal new insights about the Fano plane\, quan
tum isomorphisms of\ngraphs\, and certain irreducible representations of t
he Weyl group. (Joint work\nwith Richard Green.)\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seppo Niemi-Colvin (Indiana University)
DTSTART:20250228T180000Z
DTEND:20250228T185000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/95
DESCRIPTION:Title: A kitchen sink surgery formula for knot lattice homotopy
\nby Seppo Niemi-Colvin (Indiana University) as part of VCU Geometry and T
opology Seminar\n\nLecture held in Harris Hall 4145.\n\nAbstract\nI comput
e the knot 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 agre
e. A step used for this result was providing upgrades to the surgery formu
la for knot lattice homotopy. Ozsv\\'ath\, Stipsicz\, and Szab\\'o showed
that knot lattice homology satisfies a surgery formula similar to the one
relating knot Floer homology and Heegaard Floer homology. I provide an ite
rable version of this formula that given the doubly filtered knot lattice
space with involutive maps for a generalized algebraic knot produces the c
orresponding data for the dual knot post-surgery.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bryson Owens (University of Illinois Chicago)
DTSTART:20250328T170000Z
DTEND:20250328T175000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/99
DESCRIPTION:Title: Chern Classes of the Hodge Bundle of Cyclic Admissible Cover
s\nby Bryson Owens (University of Illinois Chicago) as part of VCU Geo
metry and Topology Seminar\n\nLecture held in Harris Hall 4145.\n\nAbstrac
t\nModuli spaces of marked curves form an important class of examples of m
oduli spaces whose geometry can be studied in terms of some combinatorial
data. There are related moduli spaces of admissible covers of marked curve
s 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 u
s to study families of such covers in terms of combinatorial data\, yieldi
ng a powerful computation tool for doing intersection theory on these modu
li spaces. In this talk\, I will introduce these moduli spaces and then di
scuss a project (joint with Seamus Somerstep and Renzo Cavalieri) in which
we compute the first Chern class of the Hodge bundle on spaces of cyclic
admissible covers.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boya Wen (University of Richmond)
DTSTART:20250404T170000Z
DTEND:20250404T175000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/100
DESCRIPTION:Title: Using heights to find rational points\nby Boya Wen (Uni
versity of Richmond) as part of VCU Geometry and Topology Seminar\n\nLectu
re held in Harris Hall 4145.\n\nAbstract\nA central question in number the
ory is finding the set of integer or rational number solutions to a given
system of polynomial equations. This question\, called the Diophantine pro
blem\, has more than 1700 years of history and is still an active area of
research. In this talk\, we will start with finding rational numbers x and
y satisfying the equation -139y^2=x^3+10x^2-20x+8. One key ingredient is
heights\, which measure the arithmetic complexity of such rational solutio
ns. While we explore this question\, I will introduce some key players in
number theory and their interactions: elliptic curves\, modular curves\, m
odular forms\, L-functions\, and the more general height theory. In partic
ular\, we will see a connection between the heights of rational points and
the derivatives of L-functions\, known as the Gross-Zagier formula. One d
irection of my work is a generalization of this formula\, where a key step
involves constructing Green’s functions on graphs. Another direction is
concrete computations of rational points on some modular curves when the
set of rational points is known to be finite. I will introduce my past\, c
urrent\, and possible future work in these two directions.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jianqi Liu (University of Pennsylvania)
DTSTART:20250411T170000Z
DTEND:20250411T175000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/101
DESCRIPTION:Title: Applications of the factorization theorem of conformal bloc
ks in vertex operator algebras\nby Jianqi Liu (University of Pennsylva
nia) as part of VCU Geometry and Topology Seminar\n\nLecture held in Harri
s Hall 4145.\n\nAbstract\nThe notion of conformal blocks on stable curves
defined by modules over a vertex operator algebra (VOA) is a generalizatio
n of the WZNW-conformal blocks defined by modules over affine Lie algebras
. The recent advances in the theory of VOA-conformal blocks shed new light
on the representation theory of VOAs. The factorization theorem and vecto
r bundle property of the sheaves of VOA-conformal blocks lead to new and s
hort proof of some deep theorems in the theory VOAs\, like the associativi
ty of fusion rules\, generalized Verlinde formula\, and the modular invari
ance of intertwining operators. In this talk\, we will briefly discuss the
se applications. This talk is based on a project with Xu Gao.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicola Tarasca (VCU)
DTSTART:20211203T180000Z
DTEND:20211203T185000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/104
DESCRIPTION:Title: Incident varieties of algebraic curves and canonical diviso
rs\nby Nicola Tarasca (VCU) as part of VCU Geometry and Topology Semin
ar\n\nLecture held in Harris Hall 4145.\n\nAbstract\nWith roots in the wor
k of Riemann\, the theory of canonical divisors on curves has witnessed an
explosion of interest in recent years\, motivated by the recent developme
nts in the study of limits of canonical divisors on nodal curves. Imposing
conditions on canonical divisors allows one to construct natural geometri
c subvarieties of moduli spaces of pointed curves\, called strata of canon
ical divisors. The strata are in fact the projection on moduli spaces of c
urves of incidence varieties living above moduli spaces of curves. I will
present a graph formula for the restriction of the incident varieties over
the locus of pointed curves with rational tails. The formula is expressed
as a linear combination of tautological classes indexed by decorated stab
le graphs\, with coefficients enumerating appropriate weightings of decora
ted stable graphs. I will conclude with some applications. Joint work with
Iulia Gheorghita.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Flippen and Essak Seddiq (VCU)
DTSTART:20200925T170000Z
DTEND:20200925T175000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/105
DESCRIPTION:Title: Quotients of the Gordian graph\nby Christopher Flippen
and Essak Seddiq (VCU) as part of VCU Geometry and Topology Seminar\n\nLec
ture held in Harris Hall 4145.\n\nAbstract\nThe Gordian graph and H(2)-Gor
dian graphs of knots are abstract graphs whose vertex sets represent isoto
py classes of unoriented knots\, and whose edge sets record whether pairs
of knots are related by crossing changes or H(2)-moves\, respectively. We
investigate the quotients of these graphs under equivalence relations gene
rated by several knot invariants including the determinant\, the span of t
he Jones polynomial\, and an invariant related to tricolorability. We show
that these quotient graphs are Gromov hyperbolic. We then discuss a colle
ction of results about the graph isomorphism type of the quotient graphs\,
including that the H(2)-Gordian graph of links modulo the relation induce
d by the span of Jones polynomial is isomorphic with the complete graph on
infinitely many vertices.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miriam Kuzbary (Georgia Tech)
DTSTART:20200410T170000Z
DTEND:20200410T175000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/106
DESCRIPTION:Title: Pure Braids and Link Concordance\nby Miriam Kuzbary (Ge
orgia Tech) as part of VCU Geometry and Topology Seminar\n\nLecture held i
n Harris Hall 4145.\n\nAbstract\nThe set of knots in the 3-sphere with the
connected sum operation forms a group when its quotient is taken by a 4-d
imensional equivalence relation called concordance. This knot concordance
group\, defined by Fox and Milnor in 1966\, can be contextualized as organ
izing problems about 3- and 4-dimensional spaces and the relationships bet
ween them. However\, one of its limitations is that every 3-manifold is su
rgery on a link\, not necessarily a knot\, and thus it may be useful to un
derstand such a group for links. Unfortunately\, the connected sum of link
s is not well defined\; in 1988\, Le Dimet constructed the string link con
cordance group for links with n components to get around this problem. Not
ably\, the knot concordance group is abelian while\, for each n the string
link concordance group on n strands is non-abelian as it contains the pur
e 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 it
s pure braid subgroup is non-abelian and explore the structure of this quo
tient group.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allison Moore (VCU)
DTSTART:20200403T170000Z
DTEND:20200403T175000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/107
DESCRIPTION:Title: Introduction to Khovanov Homology part 2\nby Allison Mo
ore (VCU) as part of VCU Geometry and Topology Seminar\n\nLecture held in
Harris Hall 4145.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allison Moore (VCU)
DTSTART:20200527T170000Z
DTEND:20200527T175000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/108
DESCRIPTION:Title: Introduction to Khovanov Homology part 1\nby Allison Mo
ore (VCU) as part of VCU Geometry and Topology Seminar\n\nLecture held in
Harris Hall 4145.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Villareal (VCU)
DTSTART:20200306T180000Z
DTEND:20200306T185000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/109
DESCRIPTION:Title: Introduction to Vertex Algebras\nby Juan Villareal (VCU
) as part of VCU Geometry and Topology Seminar\n\nLecture held in Harris H
all 4145.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele Grandini (Virginia State University)
DTSTART:20200221T180000Z
DTEND:20200221T185000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/110
DESCRIPTION:Title: Split structures and generalized almost product structures<
/a>\nby Daniele Grandini (Virginia State University) as part of VCU Geomet
ry and Topology Seminar\n\nLecture held in Harris Hall 4145.\n\nAbstract\n
The notion of split structure was introduced to capture the idea of transv
erse geometry in the context of Generalized Geometry. By definition\, a sp
lit structure is a subbundle E on the generalized tangent bundle\, such th
at the restriction to E of the tautological inner product has split signat
ure. In particular\, split structures admitting a bi-Lagrangian splitting
are equivalent to generalized para-F-structures. A large class of examples
of such structures is given by generalized almost product structures\, fo
r which the projections onto the tangent bundle are complementary distribu
tions. In this talk I will discuss such structures and operators associate
d to them\, adopting a spinorial formalism.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicola Tarasca (VCU)
DTSTART:20200214T180000Z
DTEND:20200214T185000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/111
DESCRIPTION:Title: 2D TFT's continued\nby Nicola Tarasca (VCU) as part of
VCU Geometry and Topology Seminar\n\nLecture held in Harris Hall 4145.\nAb
stract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicola Tarasca (VCU)
DTSTART:20200207T180000Z
DTEND:20200207T185000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/112
DESCRIPTION:Title: Discussion of 2D modular tensor categories\nby Nicola T
arasca (VCU) as part of VCU Geometry and Topology Seminar\n\nLecture held
in Harris Hall 4145.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Aldi (VCU)
DTSTART:20200131T180000Z
DTEND:20200131T185000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/113
DESCRIPTION:Title: Review of Chern Simons theory and TFT\nby Marco Aldi (V
CU) as part of VCU Geometry and Topology Seminar\n\nLecture held in Harris
Hall 4145.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renzo Cavalieri (Colorado State University)
DTSTART:20191206T200000Z
DTEND:20191206T205000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/114
DESCRIPTION:Title: On the elusiveness of hyperelliptic loci\nby Renzo Cava
lieri (Colorado State University) as part of VCU Geometry and Topology Sem
inar\n\nLecture held in Harris Hall 4145.\n\nAbstract\nModuli spaces of Ri
emann surfaces of genus g with n marked points are an infinite collection
of geometric objects\, connected to one another by a number of natural mor
phisms. Their full intersection rings being completely out of reach\, we f
ollow Mumford's lead in investigating the tautological rings: the smallest
subrings that allow the different moduli spaces to "communicate" with eac
h other via the natural morphisms. Tautological rings have a combinatorial
ly described collection of additive generators\, exhibiting the tautologic
al rings as quotients of algebras of appropriately decorated graphs. The h
yperelliptic loci are closed subvarieties of the moduli spaces of curves g
enerically parameterizing surfaces that admit a ramified double cover of a
sphere. Faber and Pandharipande showed their class is tautological\, and
a natural question is to describe such classes as linear combinations of t
he combinatorial generators of the tautological ring. The answer is to thi
s day only known for genus less than or equal to six. While the computatio
nal complexity becomes unmanageable for a "brute force" approach\, the col
lection of hyperelliptic classes have lots of combinatorial structure that
might lead\, once organized in the appropriate framework\, to a conceptua
l description of their formulas. I would describe the current situation as
having a large numbers of pieces of a puzzle\, but still struggling to fi
gure out how to fit them together. In this talk I will give an overview of
the problem\, and discuss some of the recent developments\, results and t
he ongoing work in progress. I will survey the work of many people\, but I
wish to acknowledge in particular my collaborators Nicola Tarasca and Joh
annes Schmitt with whom we are trying to piece together this intriguing pu
zzle.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ignacio Barros (Northeastern University)
DTSTART:20191122T200000Z
DTEND:20191122T205000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/115
DESCRIPTION:Title: On product identities and the Chow ring of holomorphic symp
lectic manifolds\nby Ignacio Barros (Northeastern University) as part
of VCU Geometry and Topology Seminar\n\nLecture held in Harris Hall 4145.\
n\nAbstract\nWe propose a series of basic conjectural identities in the Ch
ow rings of hyperkähler varieties of K3 type that generalizes in higher d
imensions a set of key properties of cycles on a K3 surface. We prove that
they hold 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 Silversmit
h.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudius Zibrowius (University of British Columbia)
DTSTART:20191107T180000Z
DTEND:20191107T185000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/116
DESCRIPTION:Title: On symmetries of peculiar modules\; or delta-graded link Fl
oer homology is mutation invariant\nby Claudius Zibrowius (University
of British Columbia) as part of VCU Geometry and Topology Seminar\n\nLectu
re held in Harris Hall 4145.\n\nAbstract\nConway mutation is an operation
on links that is notoriously difficult to detect: it preserves many link i
nvariants such as the signature\, the Alexander polynomial or\, more gener
ally\, the HOMFLY polynomial. Baldwin and Levine conjectured that δ-grade
d link Floer homology also belongs in this list—despite the fact that *b
igraded* link Floer homology can distinguish some mutant knots such as the
famous Kinoshita-Terasaka and Conway knots. In [arXiv:1909.04267]\, I pro
ved Baldwin and Levine's conjecture by studying symmetry properties of pec
uliar modules\, an immersed curve invariant of 4-ended tangles. In this ta
lk\, I will sketch this proof.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Jose' Villarreal (VCU)
DTSTART:20191101T170000Z
DTEND:20191101T175000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/117
DESCRIPTION:Title: The monodromy representation of the braid group on the spac
e of conformal blocks II\nby Juan Jose' Villarreal (VCU) as part of VC
U Geometry and Topology Seminar\n\nLecture held in Harris Hall 4145.\nAbst
ract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Jose' Villarreal (VCU)
DTSTART:20191025T170000Z
DTEND:20191025T175000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/118
DESCRIPTION:Title: The monodromy representation of the braid group on the spac
e of conformal blocks I\nby Juan Jose' Villarreal (VCU) as part of VCU
Geometry and Topology Seminar\n\nLecture held in Harris Hall 4145.\nAbstr
act: TBA\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicola Tarasca (VCU)
DTSTART:20191004T190000Z
DTEND:20191004T195000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/119
DESCRIPTION:Title: Quantum Algebra and Geometry of Curves\nby Nicola Taras
ca (VCU) as part of VCU Geometry and Topology Seminar\n\nLecture held in H
arris Hall 4145.\n\nAbstract\nThis talk will focus on geometric realizatio
ns of non-commutative\nalgebras. I will discuss how representations of ver
tex algebras\nencode information about the geometry of algebraic curves. T
he\nstarting point is the Virasoro uniformization\, which provides an\ninc
arnation of the Virasoro algebra in the tangent space of a\ntautological l
ine bundle on families of coordinatized curves. After\nbriefly reviewing v
ertex algebras and algebraic curves\, I will\ndiscuss how one can construc
t new vector bundles on families of\ncurves using representations of verte
x algebras. The new results\nare joint work with Chiara Damiolini and Ange
la Gibney.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Aldi (VCU)
DTSTART:20191004T170000Z
DTEND:20191004T175000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/120
DESCRIPTION:Title: Abelian Chern-Simons Theory\nby Marco Aldi (VCU) as par
t of VCU Geometry and Topology Seminar\n\nLecture held in Harris Hall 4145
.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allison Moore and Marco Aldi (VCU)
DTSTART:20190927T170000Z
DTEND:20190927T175000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/121
DESCRIPTION:Title: Temperley Lieb Algebras / Jones Polynomial in Chern-Simons<
/a>\nby Allison Moore and Marco Aldi (VCU) as part of VCU Geometry and Top
ology Seminar\n\nLecture held in Harris Hall 4145.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allison Moore (VCU)
DTSTART:20190920T190000Z
DTEND:20190920T195000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/122
DESCRIPTION:Title: Gordian graphs of knots and Gromov hyperbolicity\nby Al
lison Moore (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
embedded in three-dimensional space\nin some potentially interesting way.
The set of isotopy classes of knots\nis a countably infinite set. The Gord
ian graph G is a construction for\norganizing the set of knots\, in which
each vertex represents the isotopy\ntype of a knot\, and two vertices are
connected by an edge whenever the\ncorresponding knots are relating by a c
rossing change. Other variants\nof this graph (for example\, the H(2)-Gord
ian graph) can be defined in a\nsimilar manner\, and capture information a
bout other 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 kn
own\, and mention some\nnew results in this area. Undergrads and grad stud
ents are especially\nwelcome to attend this talk\, which will assume no ba
ckground in knot\ntheory.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Aldi (VCU)
DTSTART:20190913T170000Z
DTEND:20190913T175000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/123
DESCRIPTION:Title: Intro to Quantum Field Theory\nby Marco Aldi (VCU) as p
art of VCU Geometry and Topology Seminar\n\nLecture held in Harris Hall 41
45.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allison Moore (VCU)
DTSTART:20190906T170000Z
DTEND:20190906T175000Z
DTSTAMP:20260404T095038Z
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) as part of VCU Geometry and Topology Seminar\n\nLecture held in Harr
is Hall 4145.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruoyu (Tony) Guo (VCU)
DTSTART:20250829T170000Z
DTEND:20250829T175000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/126
DESCRIPTION:Title: Some perspectives on the finitistic dimension conjecture\nby Ruoyu (Tony) Guo (VCU) as part of VCU Geometry and Topology Seminar\
n\nLecture held in Harris Hall 4145.\n\nAbstract\nThe finitistic dimension
conjecture\, which serves as a sufficient condition for numerous homologi
cal conjectures\, has been a central topic of research in homological alge
bra. Despite over 60 years of study\, the conjecture is only solved in spe
cial cases under the context of finite dimensional algebras. In this talk\
, we present three perspectives in studying the finitistic dimension conje
cture: 1. the representation theory perspective\, 2. the invariant perspec
tive\, and 3. the perspective of algebraic operations. These perspectives
are closely connected\, and their interaction often leads to new ideas for
the conjecture. We also mention a potential geometric perspective for fut
ure study.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/126/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oliver Hao Wang (University of Virginia)
DTSTART:20251003T170000Z
DTEND:20251003T175000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/131
DESCRIPTION:Title: Chern classes and exotic G-manifolds\nby Oliver Hao Wan
g (University of Virginia) as part of VCU Geometry and Topology Seminar\n\
nLecture held in Harris Hall 4145.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/131/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sofia Wood (Columbia University)
DTSTART:20251010T170000Z
DTEND:20251010T175000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/132
DESCRIPTION:Title: Hodge numbers of universal compactified Jacobians\nby S
ofia Wood (Columbia University) as part of VCU Geometry and Topology Semin
ar\n\nLecture held in Harris Hall 4145.\n\nAbstract\nWe study the universa
l compactified Jacobians of degree d\, as constructed by Kass and Pagani o
ver the moduli space of stable curves. These spaces compactify the univers
al degree-d Jacobian over the moduli of smooth curves\, and depend on a ch
oice of universal stability condition. We show that the Hodge numbers of t
hese compactified Jacobians are independent of both the degree d and the c
hoice of stability condition.\nThis is joint work with Rahul Pandharipande
\, Dan Petersen\, and Johannes Schmidt.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/132/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Blackwell (University of Virginia)
DTSTART:20251031T190000Z
DTEND:20251031T195000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/135
DESCRIPTION:Title: Cornered Skein Lasagna Theory\nby Sarah Blackwell (Univ
ersity of Virginia) as part of VCU Geometry and Topology Seminar\n\nLectur
e held in Harris Hall 4145.\n\nAbstract\nThe theory of skein lasagna modul
es\, initiated by Morrison-Walker-Wedrich\, has been the subject of much i
nterest in recent years. This theory takes as input Khovanov-Rozansky link
homology and yields invariants of oriented 4-manifolds\, which are genera
lly very powerful yet hard to calculate. Most excitingly\, this theory was
used recently to detect exotic compact 4-manifolds by Ren-Willis\, markin
g the first such result proven without the use of gauge theory. In this ta
lk I will discuss an extension of skein lasagna theory for cornered 4-mani
folds and describe an application to trisections of 4-manifolds\, with an
eye towards calculations. This is ongoing joint work with Slava Krushkal a
nd Yangxiao Luo.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/135/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Levine (Duke University)
DTSTART:20260320T170000Z
DTEND:20260320T175000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/149
DESCRIPTION:Title: Knot Floer Homology\, Bordered Floer Homology\, and Surgery
Modules\nby Adam Levine (Duke University) as part of VCU Geometry and
Topology Seminar\n\nLecture held in Harris Hall 4145.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/149/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Gerhard (VCU)
DTSTART:20260327T170000Z
DTEND:20260327T175000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/150
DESCRIPTION:Title: Counting Abelian Varieties Using Number Theory\nby Jona
than Gerhard (VCU) as part of VCU Geometry and Topology Seminar\n\nLecture
held in Harris Hall 4145.\n\nAbstract\nArithmetic Geometry is the interpl
ay between Algebraic Geometry and Number Theory. As a small introduction t
o the topic\, I will be talking about a research project I did at JMU with
Dr. Cassie Williams. There are three main characters in this show: 1) The
size of isogeny classes of abelian varieties over a finite field\; 2) The
class numbers of certain Galois field extensions\; 3) The average size of
conjugacy classes of matrices in the general symplectic group. In a very
surprising connection\, there is a sense in which all three of these numbe
rs are exactly equal. I will give a general overview of the ideas for this
project but will not assume much previous Number Theory knowledge.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/150/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quincy Frias (GMU)
DTSTART:20260403T170000Z
DTEND:20260403T175000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/151
DESCRIPTION:Title: Derived Differential Geometry in Context\nby Quincy Fri
as (GMU) as part of VCU Geometry and Topology Seminar\n\nLecture held in H
arris Hall 4145.\n\nAbstract\nThe field of Derived Differential Geometry h
as seen explosive growth in the past few years\; there is a higher categor
y of derived manifolds defined by a universal property and which has sever
al equivalent models. These models provide us with tools to glean both the
oretical results about the derived geometry of manifolds as well as comput
ations of derived manifolds and their associated structures such as cotang
ent complexes.\n\nThis talk will focus on the growth of DDG in the context
of derived geometry writ large\, and the current progress toward extendin
g classical structures on manifolds such as connections and pseudo-differe
ntial operators to the derived setting.\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/151/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Siddarth Kannan (MIT)
DTSTART:20260410T170000Z
DTEND:20260410T175000Z
DTSTAMP:20260404T095038Z
UID:vcugeomandtop/152
DESCRIPTION:by Siddarth Kannan (MIT) as part of VCU Geometry and Topology
Seminar\n\nInteractive livestream: https://vcu.zoom.us/j/96499775895?pwd=Q
1IrcVlGdk1GRUt5TUdRdFZjWCtodz09\nLecture held in Harris Hall 4145.\nAbstra
ct: TBA\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/152/
URL:https://vcu.zoom.us/j/96499775895?pwd=Q1IrcVlGdk1GRUt5TUdRdFZjWCtodz09
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noah Pope (VCU)
DTSTART:20260424T170000Z
DTEND:20260424T175000Z
DTSTAMP:20260404T095038Z
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 Harri
s Hall 4145.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/vcugeomandtop/154/
END:VEVENT
END:VCALENDAR