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BEGIN:VEVENT
SUMMARY:Alexandru Oancea (Sorbonne\, Paris)
DTSTART:20200505T150000Z
DTEND:20200505T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/1
DESCRIPTION:Title: Duality for Rabinowitz-Floer homology\nby Alexandru Oancea (So
rbonne\, Paris) as part of Free Mathematics Seminar\n\n\nAbstract\nI will
explain a duality theorem with products in Rabinowitz-Floer homology. This
has a bearing on string topology and explains a number of dualities that
have been observed in that setting. Joint work in progress with Kai Cielie
bak and Nancy Hingston.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jenny August (MPIM\, Bonn)
DTSTART:20200512T140000Z
DTEND:20200512T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/2
DESCRIPTION:Title: Stability for contraction algebras\nby Jenny August (MPIM\, Bo
nn) as part of Free Mathematics Seminar\n\n\nAbstract\nFor a finite dimens
ional algebra\, Bridgeland stability conditions can be viewed as a continu
ous generalisation of tilting theory\, providing a geometric way to study
the derived category. Describing this stability manifold is often very cha
llenging but in this talk\, I’ll look at a special class of symmetr
ic algebras whose tilting theory is very well behaved\, allowing us to des
cribe the entire stability manifold of such an algebra. This is joint work
with Michael Wemyss.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gleb Smirnov (ETH\, Zurich)
DTSTART:20200519T140000Z
DTEND:20200519T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/3
DESCRIPTION:Title: Isotopy problem for symplectic forms in the presence of an anti-ho
lomorphic involution\nby Gleb Smirnov (ETH\, Zurich) as part of Free M
athematics Seminar\n\n\nAbstract\nSuppose we are given an algebraic surfac
e equipped with an anti-holomorphic involution. From the symplectic viewpo
int\, a natural question to ask is: are there cohomologous anti-invariant
symplectic forms on this manifold which are not isotopic within anti-invar
iant forms? And\, if so\, how many? During the talk\, we will look at a pa
rticularly simple case of complex quadrics and do some explicit computatio
ns.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kazushi Ueda (Univ of Tokyo\, Japan)
DTSTART:20200526T090000Z
DTEND:20200526T100000Z
DTSTAMP:20260404T131153Z
UID:Freemath/4
DESCRIPTION:Title: Noncommutative del Pezzo surfaces\nby Kazushi Ueda (Univ of To
kyo\, Japan) as part of Free Mathematics Seminar\n\n\nAbstract\nIt is know
n after the works of Artin-Tate-Van den Bergh and Bondal-Polishchuk that n
oncommutative deformations of the projective plane are classified by tripl
es consisting of a cubic curve and two line bundles. Similarly\, Van den B
ergh gave a classification of noncommutative quadric surfaces in terms of
quadruples consisting of (a degeneration of) an elliptic curve and three l
ine bundles. In the talk\, I will discuss a joint work in progress with Ta
rig Abdelgadir and Shinnosuke Okawa on classifications of noncommutative d
el Pezzo surfaces.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuhan Sun (Stony Brook)
DTSTART:20200609T140000Z
DTEND:20200609T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/5
DESCRIPTION:Title: Displacement energy of Lagrangian 3-spheres\nby Yuhan Sun (Sto
ny Brook) as part of Free Mathematics Seminar\n\n\nAbstract\nWe study loca
l and global Hamiltonian dynamical behaviours of some Lagrangian submanifo
lds near a Lagrangian sphere S in a symplectic manifold X. When dim S = 2\
, we show that there is a one-parameter family of Lagrangian tori near S\,
which are nondisplaceable in X. When dim S = 3\, we obtain a new estimate
of the displacement energy of S\, by estimating the displacement energy o
f a one-parameter family of Lagrangian tori near S.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Octav Cornea (Univ of Montreal)
DTSTART:20200602T140000Z
DTEND:20200602T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/6
DESCRIPTION:Title: Lagrangians\, surgery and rigidity\nby Octav Cornea (Univ of M
ontreal) as part of Free Mathematics Seminar\n\n\nAbstract\nI will discuss
a framework for analyzing classes of Lagrangian submanifolds\nthat aims t
o endow them with a metric structure. The tools involve certain Floer type
\nmachinery for immersed Lagrangians. Part of the picture is a corresponde
nce\nbetween certain cobordism categories endowed with surgery models and
derived\nFukaya categories. The talks is based on joint work with Paul Bir
an.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Kuznetsov (Steklov)
DTSTART:20200623T150000Z
DTEND:20200623T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/7
DESCRIPTION:Title: Residual categories and quantum cohomology\nby Alexander Kuzne
tsov (Steklov) as part of Free Mathematics Seminar\n\n\nAbstract\nDubrovin
's conjecture predicts that a smooth projective variety has a full excepti
onal collection in the derived category of coherent sheaves if and only if
its big quantum cohomology ring is generically semisimple. However\, the
big quantum cohomology is very hard to compute. We suggest a conjecture\,
where the big quantum cohomology is replaced by the small quantum cohomolo
gy (which is much more easy to compute)\, and a full exceptional collectio
n is replaced by a semiorthogonal decomposition of a special form. We supp
ort this conjecture by a number of examples provided by homogeneous variet
ies of simple algebraic groups. This is a joint work with Maxim Smirnov.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatsuki Kuwagaki (IPMU)
DTSTART:20200616T090000Z
DTEND:20200616T100000Z
DTSTAMP:20260404T131153Z
UID:Freemath/8
DESCRIPTION:Title: Symplectic geometry of exact WKB analysis\nby Tatsuki Kuwagaki
(IPMU) as part of Free Mathematics Seminar\n\n\nAbstract\nA sheaf quantiz
ation is a sheaf associated to a Lagrangian brane. This sheaf conjecturall
y has information as much as Floer theory of the Lagrangian. On the other
hand\, exact WKB analysis is an analysis of differential equations contain
ing \\hbar (the Planck constant).\n\nIn this talk\, I will explain how to
construct a sheaf quantization over the Novikov ring of the spectral curve
of an \\hbar-differential equation by using exact WKB method. In the cons
truction\, one can see how (conjecturally) the convergence in WKB analysis
is related to the convergence in Fukaya category. In degree 2\, there is
an application to cluster theory: the sheaf quantization associates a clus
ter coordinate which is the same as the Voros-Iwaki-Nakanishi-Fock-Gonchar
ov coordinate. I will also mention about some relationships to Riemann-Hil
bert correspondence of D'Agnolo-Kashiwara and Kontsevich-Soibelman.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Sheridan (Edinburgh)
DTSTART:20200630T140000Z
DTEND:20200630T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/9
DESCRIPTION:Title: Symplectic mapping class groups and homological mirror symmetry\nby Nick Sheridan (Edinburgh) as part of Free Mathematics Seminar\n\n\nA
bstract\nI will explain how one can get new information about symplectic m
apping class groups by combining two recent results: a proof of homologica
l mirror symmetry for a new collection of K3 surfaces (joint work with Iva
n Smith)\, together with the computation of the derived autoequivalence gr
oup of a K3 surface of Picard rank one (Bayer--Bridgeland). For example\,
it is possible to give an example of a symplectic K3 whose smoothly trivia
l symplectic mapping class group (the group of isotopy classes of symplect
ic automorphisms which are smoothly isotopic to the identity) is infinitel
y-generated. This is joint work with Ivan Smith.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mohammed Abouzaid (Columbia)
DTSTART:20200707T140000Z
DTEND:20200707T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/10
DESCRIPTION:Title: Floer homotopy without spectra\nby Mohammed Abouzaid (Columbi
a) as part of Free Mathematics Seminar\n\n\nAbstract\nThe construction of
Cohen-Jones-Segal of Floer homotopy types associated to appropriately orie
nted flow categories extracts from the morphisms of such a category the da
ta required to assemble an iterated extension of free modules (in an appro
priate category of spectra). I will explain a direct (geometric) way for d
efining the Floer homotopy groups which completely bypasses stable homotop
y theory. The key point is to work on the geometric topology side of the P
ontryagin-Thom construction. Time permitting\, I will also explain joint w
ork in progress with Blumberg for building a spectrum from the new point o
f view\, as well as various generalisations which are relevant to Floer th
eory.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sheel Ganatra
DTSTART:20200714T140000Z
DTEND:20200714T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/11
DESCRIPTION:Title: On Rabinowitz wrapped Fukaya categories\nby Sheel Ganatra as
part of Free Mathematics Seminar\n\n\nAbstract\nThis talk develops the ope
n-string categorical analogue of Rabinowitz Floer homology\, which we term
the Rabinowitz (wrapped) Fukaya category. Following a conjecture of Abou
zaid\, we relate the Rabinowitz Fukaya category to the usual wrapped Fukay
a category by way of a general categorical construction introduced by Efim
ov\, the "categorical formal punctured neighborhood of infinity". Using t
his result\, we show how Rabinowitz Fukaya categories can be fit into - an
d therefore computed in terms of - mirror symmetry. Joint work (in progre
ss) with Yuan Gao and Sara Venkatesh.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alastair Craw
DTSTART:20200721T140000Z
DTEND:20200721T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/12
DESCRIPTION:Title: Hilbert schemes of ADE singularities as quiver varieties\nby
Alastair Craw as part of Free Mathematics Seminar\n\n\nAbstract\nThe nth s
ymmetric product of a ADE surface singularity is well known to be a Nakaji
ma quiver variety. I will describe recent work with Gammelgaard\, Gyenge a
nd Szendroi in which the Hilbert scheme of n points on the ADE singularity
is constructed as a Nakajima quiver variety. This result provided the cat
alyst for the description of the generating function of Euler numbers on p
unctual Hilbert schemes of an ADE surface singularity by Nakajima earlier
this year.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Catherine Cannizzo
DTSTART:20200728T140000Z
DTEND:20200728T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/13
DESCRIPTION:Title: Towards global homological mirror symmetry for genus 2 curves
\nby Catherine Cannizzo as part of Free Mathematics Seminar\n\n\nAbstract\
nThe first part of the talk will discuss work in https://arxiv.org/abs/190
8.04227 on constructing a Donaldson-Fukaya-Seidel type category for the ge
neralized SYZ mirror of a genus 2 curve. We will explain the categorical m
irror correspondence on the cohomological level. The key idea uses that a
4-torus is SYZ mirror to a 4-torus. So if we view the complex genus 2 curv
e as a hypersurface of a 4-torus V\, a mirror can be constructed as a symp
lectic fibration with fiber given by the dual 4-torus V^. Hence on categor
ies\, line bundles on V are restricted to the genus 2 curve while fiber La
grangians of V^ are parallel transported over U-shapes in the base of the
mirror. Next we describe ongoing work with H. Azam\, H. Lee\, and C-C. M.
Liu on extending the result to a global statement\, namely allowing the co
mplex and symplectic structures to vary in their real six-dimensional fami
lies. The mirror statement for this more general result relies on work of
A. Kanazawa and S-C. Lau.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Baris Kartal
DTSTART:20200804T140000Z
DTEND:20200804T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/14
DESCRIPTION:Title: p-adic analytic actions on the Fukaya category and iterates of s
ymplectomorphisms\nby Baris Kartal as part of Free Mathematics Seminar
\n\n\nAbstract\nA theorem of J. Bell states that given a complex affine \n
variety $X$ with an automorphism $\\phi$\, and a subvariety $Y\\subset \nX
$\, the set of numbers $k$ such that $\\phi^k(x)\\in Y$ is a union of \nfi
nitely many arithmetic progressions and finitely many numbers. \nMotivated
by this statement\, Seidel asked whether there is a \nsymplectic analogue
of this theorem. In this talk\, we give an answer \nto a version of this
question in the case $M$ is monotone\, \nnon-degenerate and $\\phi$ is sym
plectically isotopic to identity. The \nmain tool is analogous to the main
tool in Bell's proof: namely we \ninterpolate the powers of $\\phi$ by a
p-adic arc\, constructing an \nanalytic action of $\\mathbb{Z}_p$ on the F
ukaya category.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dougal Davis
DTSTART:20200811T090000Z
DTEND:20200811T100000Z
DTSTAMP:20260404T131153Z
UID:Freemath/15
DESCRIPTION:Title: Surface singularities and their deformations via principal bundle
s on elliptic curves\nby Dougal Davis as part of Free Mathematics Semi
nar\n\n\nAbstract\nIt is well known that du Val (aka simple\, Kleinian\, A
DE\, ...) singularities of algebraic surfaces are classified by Dynkin dia
grams of type ADE. A geometric link between the singularity and the Lie al
gebra of the same type was given by Brieskorn in the 70s\, who showed that
the singularity can be recovered by intersecting the nilpotent cone insid
e the Lie algebra with a transversal slice through a subregular nilpotent
element. Brieskorn's construction also realises the entire transversal sli
ce as the total space of a miniversal deformation of the singularity. In t
his talk\, I will discuss an elliptic version of this story\, where the Li
e algebra is replaced with the stack of principal bundles on an elliptic c
urve. There is still a notion of subregular slice in this stack\, and one
gets a singular surface by intersecting such a thing with the locus of uns
table bundles. I will explain which surfaces arise in this way\, and in wh
at sense the subregular slice is still the total space of a miniversal def
ormation. Time permitting\, I will also touch on how the BCFG types are re
lated to the ADE ones (in a different way to the story for Lie algebras!)\
, and on some questions about Poisson structures and their quantisations.\
n
LOCATION:https://stable.researchseminars.org/talk/Freemath/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giancarlo Urzúa
DTSTART:20200820T140000Z
DTEND:20200820T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/16
DESCRIPTION:Title: On the geography of complex surfaces of general type with an arbi
trary fundamental group\nby Giancarlo Urzúa as part of Free Mathemati
cs Seminar\n\n\nAbstract\nSurfaces of general type are lovely unclassifiab
le objects in algebraic geometry. Geography refers to the problem of const
ruction of such surfaces for a given set of invariants\, classically the C
hern numbers \\(c_1^2\\) (self-intersection of canonical class) and \\(c_2
\\) (topological Euler characteristic). In this talk\, we treat the questi
on: What can be said about the distribution of Chern slopes \\(c_1^2/c_2\\
) of surfaces of general type when we fix the fundamental group? It turns
out that there are various well-known constraints\, which will be pointed
out during the talk\, but at least we can prove the following theorem (joi
nt with Sergio Troncoso): "Let \\(G\\) be the fundamental group of some no
nsingular complex projective variety. Then Chern slopes of surfaces of ge
neral type with fundamental group isomorphic to \\(G\\) are dense in the i
nterval \\([1\,3]\\).". Remember that for complex surfaces of general type
we have that \\(c_1^2/c_2\\) is a rational number in \\([1/5\,3]\\)\, and
so most open questions now refer to slopes in \\([1/5\,1]\\). On the othe
r hand\, it is known that every finite group is the fundamental group of s
ome nonsingular projective variety\, and so a lot is going on for high slo
pes.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Inbar Klang
DTSTART:20200825T140000Z
DTEND:20200825T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/17
DESCRIPTION:Title: Twisted Calabi-Yau algebras and categories\nby Inbar Klang as
part of Free Mathematics Seminar\n\n\nAbstract\nThis talk will begin with
a discussion of the string topology category of a manifold $M$\; this was
shown by Cohen and Ganatra to be equivalent as a Calabi-Yau category to t
he wrapped Fukaya category of $T^*M$. In joint work with Ralph Cohen\, we
generalize the Calabi-Yau condition from chain complexes to spectra. I'll
talk about these Calabi-Yau ring spectra and discuss examples of interest.
\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wai Kit Yeung
DTSTART:20200901T140000Z
DTEND:20200901T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/18
DESCRIPTION:Title: Pre-Calabi-Yau categories\nby Wai Kit Yeung as part of Free M
athematics Seminar\n\n\nAbstract\nPre-Calabi-Yau categories are algebraic
structures first studied by Kontsevich and Vlassopoulos. They can be viewe
d as a noncommutative analogue of Poisson structures\, just like Calabi-Ya
u structures are a noncommutative analogue of symplectic structures. It is
expected that disk-counting with more than one output endows Fukaya categ
ories with pre-Calabi-Yau structures. In this talk\, we discuss several as
pects of this notion.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Macpherson
DTSTART:20200908T090000Z
DTEND:20200908T100000Z
DTSTAMP:20260404T131153Z
UID:Freemath/19
DESCRIPTION:Title: A bivariant Yoneda lemma and (infinity\, 2)-categories of corresp
ondences\nby Andrew Macpherson as part of Free Mathematics Seminar\n\n
\nAbstract\nThe notion of the *category of correspondences* of a category
D with a specified\, base change stable\, class of morphisms S --- whose o
bjects are those of D and whose morphisms are "spans" in D\, one side of w
hich belongs to S --- will be familiar to practitioners of Grothendieck's
theory of motives. Perhaps less familiar is the fact that an obvious 2-cat
egorical upgrade of correspondences has a universal property: it is the un
iversal way to attach right adjoints to members of S subject to a base cha
nge formula.\n\nI will explain a little about the state of the art on enri
ched and iterated higher categories and show that they can be used to prov
ide a conceptual (that is\, no explicit homotopy- or simplex-chasing) proo
f of this phenomenon for (infinity\, 2)-categories. This enhancement opens
the door to direct constructions of bivariant homology theories in motivi
c homotopy theory and beyond.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Golla
DTSTART:20200915T140000Z
DTEND:20200915T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/20
DESCRIPTION:Title: Symplectic hats\nby Marco Golla as part of Free Mathematics S
eminar\n\n\nAbstract\nA hat for a transverse knot in a symplectic cap of a
contact 3-manifold is a symplectic surface in the cap whose boundary is t
he knot. I will talk about existence\, obstructions\, and properties of ha
ts\, with an emphasis on the standard 3-sphere\, and about an application
to Stein fillings. This is joint work with John Etnyre.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Damien Gayet
DTSTART:20200922T140000Z
DTEND:20200922T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/21
DESCRIPTION:Title: Lagrangians of (random) projective hypersurfaces\nby Damien G
ayet as part of Free Mathematics Seminar\n\n\nAbstract\nI will explain tha
t any smooth compact hypersurface in $\\mathbb R^n$ appears (up to diffeom
orphism) a very large number of times as disjoint Lagrangians in any compl
ex hypersurface of $\\mathbb C P^n$\, if the degree of the hypersurface is
high enough. Suprisingly\, the proof holds on probabilistic arguments.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Manion
DTSTART:20201020T140000Z
DTEND:20201020T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/23
DESCRIPTION:Title: Higher representations and cornered Floer homology\nby Andrew
Manion as part of Free Mathematics Seminar\n\n\nAbstract\nI will discuss
recent work with Raphael Rouquier\, focusing on a higher tensor product op
eration for 2-representations of Khovanov's categorification of U(gl(1|1)^
+)\, examples of such 2-representations that arise as strands algebras in
bordered and cornered Heegaard Floer homology\, and a tensor-product-based
gluing formula for these 2-representations expanding on work of Douglas-M
anolescu.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francois Greer
DTSTART:20201027T150000Z
DTEND:20201027T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/24
DESCRIPTION:Title: Cycle-valued quasi-modular forms on Kontsevich space\nby Fran
cois Greer as part of Free Mathematics Seminar\n\n\nAbstract\nOn a general
rational elliptic surface (fibered over $\\mathbb{P}^1$)\, the number of
sections of height $n$ is equal to the coefficient of the Eisenstein serie
s $E_4(q)$ at order $n+1$. I will describe a conjectural generalization of
this fact\, which associates to any smooth projective variety a quasi-mod
ular form valued in the Chow group of its Kontsevich moduli space. The pro
of is in progress.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pieter Belmans
DTSTART:20201006T140000Z
DTEND:20201006T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/25
DESCRIPTION:Title: Graph potentials as mirrors to moduli of vector bundles on curves
\nby Pieter Belmans as part of Free Mathematics Seminar\n\n\nAbstract\
nIn a joint work with Sergey Galkin and Swarnava Mukhopadhyay we have a cl
ass of Laurent polynomials associated to decorated trivalent graphs which
we called graph potentials. These Laurent polynomials satisfy interesting
symmetry and compatibility properties. Under mirror symmetry they are rela
ted to moduli spaces of rank 2 bundles (with fixed determinant of odd degr
ee) on a curve of genus $g\\geq 2$\, which is a class of Fano varieties of
dimension $3g-3$. I will discuss (parts of) the (enumerative / homologica
l) mirror symmetry picture for Fano varieties\, and then explain what we u
nderstand for this class of varieties and what we can say about the (conje
ctural) semiorthogonal decomposition of the derived category.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kenji Fukaya
DTSTART:20201208T150000Z
DTEND:20201208T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/26
DESCRIPTION:Title: Atiyah-Floer type conjecture and Virtual fundamental chain\nb
y Kenji Fukaya as part of Free Mathematics Seminar\n\n\nAbstract\nThis is
a report on my work in progress with Aliakbar Daemi\n\nWe are studying an
SO(3) version of Atiyah-Floer conjecture relating Instanton Floer homology
to Lagrangian Floer homology\, via cobordism method. In the case when the
moduli space of flat connections on 3 manifold is an {\\it embedded} Lagr
angian submanifold of the space of flat connections on 2 manifold\, we can
perturb Lipyanskiy type mixed moduli space using geometric perturbation.
In the case it is an immersed Lagrangian submanifold\, we need abstract pe
rturbation and virtual technique. The singularity of the instanton moduli
space is wilder than the case of pseudo-holomorphic curve and we need cert
ain `stratified' version of Kuranishi structure. I will explain how we can
define such a notion\, show the existence of such structure and use it to
obtain virtual fundamental chain.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hansol Hong
DTSTART:20201013T090000Z
DTEND:20201013T100000Z
DTSTAMP:20260404T131153Z
UID:Freemath/27
DESCRIPTION:Title: Maurer-Cartan deformation of a Lagrangian\nby Hansol Hong as
part of Free Mathematics Seminar\n\n\nAbstract\nThe Maurer-Cartan algebra
of a Lagrangian is the algebra that encodes the deformation of its Floer c
omplex as an A-infinity algebra. I will give a convenient description of t
he Maurer-Cartan algebra through a natural homological algebra language\,
and relate it with (a version of) Koszul duality for the Floer complex. It
helps us to obtain the mirror-symmetry interpretation for the Maurer-Cart
an deformation and its locality in SYZ situation. Namely\, the Maurer-Cart
an algebra provides a neighborhood of the point mirror to the Lagrangian\,
which varies in size depending on geometric types of Floer generators inv
olved in the deformation.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Bridgeland
DTSTART:20201110T150000Z
DTEND:20201110T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/28
DESCRIPTION:Title: Donaldson-Thomas invariants and a non-perturbative topological st
ring partition function\nby Tom Bridgeland as part of Free Mathematics
Seminar\n\n\nAbstract\nI will introduce a class of Riemann-Hilbert proble
ms which (I claim) arise naturally in Donaldson-Thomas theory. I will star
t with the simplest example (corresponding to the DT theory of the A1 quiv
er) which leads via undergraduate mathematics to the gamma function. Then
I will explain how the same procedure applied to the DT theory of coherent
sheaves on the resolved conifold leads to a non-perturbative version of t
he Gromov-Witten generating series\, i.e. a particular choice of holomorph
ic function having this series as its asymptotic expansion (in fact the sa
me result holds for any non-compact CY threefold having no compact divisor
s). If there is time left at the end (which there never is) I will discuss
recent attempts to go beyond these results.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laurent Côté
DTSTART:20201103T150000Z
DTEND:20201103T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/29
DESCRIPTION:Title: Homological invariants of codimension 2 contact embeddings\nb
y Laurent Côté as part of Free Mathematics Seminar\n\n\nAbstract\nThere
is a rich theory of transverse knots in 3-dimensional contact manifolds. I
t was a major open question in contact topology whether non-trivial transv
erse knots (i.e. codimension 2 contact embeddings) also exist in higher di
mensions. This question was recently settled in the affirmative by Casals
and Etnyre. Motivated by their result\, I will talk about recent work with
Francois-Simon Fauteux-Chapleau in which we develop invariants of codimen
sion 2 contact embeddings using the machinery of symplectic field theory.\
n
LOCATION:https://stable.researchseminars.org/talk/Freemath/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kyler Siegel
DTSTART:20201117T150000Z
DTEND:20201117T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/30
DESCRIPTION:Title: On the embedding complexity of Liouville manifolds\nby Kyler
Siegel as part of Free Mathematics Seminar\n\n\nAbstract\nI will describe
a new framework for obstructing exact symplectic embeddings between Liouvi
lle manifolds\, based on L-infinity structures in symplectic field theory.
As a main application\, we study embeddings between normal crossing divis
or complements in complex projective space\, giving a complete characteriz
ation in many cases. This is based on joint work in preparation with S. Ga
natra.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Mclean
DTSTART:20201124T150000Z
DTEND:20201124T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/31
DESCRIPTION:Title: Floer Cohomology and Arc Spaces\nby Mark Mclean as part of Fr
ee Mathematics Seminar\n\n\nAbstract\nLet f be a polynomial over the compl
ex numbers with an isolated singular point at the origin and let d be a po
sitive integer. To such a polynomial we can assign a variety called the dt
h contact locus of f. Morally\, this corresponds to the space of d-jets of
holomorphic disks in complex affine space whose boundary `wraps' around t
he singularity d times. We show that Floer cohomology of the dth power of
the Milnor monodromy map is isomorphic to compactly supported cohomology o
f the dth contact locus. This answers a question of Paul Seidel and it als
o proves a conjecture of Nero Budur\, Javier Fernández de Bobadilla\, Q
uy Thuong Lê and Hong Duc Nguyen. The key idea of the proof is to use a
jet space version of the PSS map together with a filtration argument.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Lin
DTSTART:20201201T150000Z
DTEND:20201201T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/32
DESCRIPTION:Title: Floer homology and closed geodesics of hyperbolic three-manifolds
\nby Francesco Lin as part of Free Mathematics Seminar\n\n\nAbstract\n
Floer homology and hyperbolic geometry are fundamental tools in the study
of three-dimensional topology. Despite this\, it remains an outstanding pr
oblem to understand whether there is any relationship between them. I will
discuss some results in this direction that use as stepping stone the spe
ctral geometry of coexact 1-forms. This is joint work with M. Lipnowski.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Álvarez-Gavela
DTSTART:20201215T150000Z
DTEND:20201215T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/33
DESCRIPTION:Title: Polarized Weinstein manifolds and their positive arboreal skeleta
\nby Daniel Álvarez-Gavela as part of Free Mathematics Seminar\n\n\nA
bstract\nThe goal of this talk is to give a geometric introduction to arbo
real singularities\, as well as to the distinguished subclass of *positive
* arboreal singularities\, and to state precisely the theorem joint with Y
. Eliashberg and D. Nadler that a Weinstein manifold admits a global field
of Lagrangian planes if and only if the Weinstein structure can be deform
ed so that the skeleton becomes positive arboreal. In particular it follow
s that complete intersections in complex affine space can be arborealized.
\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Halpern-Leistner
DTSTART:20210112T150000Z
DTEND:20210112T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/34
DESCRIPTION:Title: Derived Theta-stratifications and the D-equivalence conjecture\nby Daniel Halpern-Leistner as part of Free Mathematics Seminar\n\n\nAbs
tract\nEvery vector bundle on a smooth curve has a canonical filtration\,
called the Harder-Narasimhan filtration\, and the moduli of all vector bun
dles admits a stratification based on the properties of the Harder-Narasim
han filtration at each point. The theory of Theta-stratifications formulat
es this structure on a general algebraic stack. I will discuss how to char
acterize stratifications of this kind\, and why their local cohomology is
particularly well-behaved. I will then explain how Theta-stratifications a
re part of a recent proof of a case of the D-equivalence conjecture: for a
ny projective Calabi-Yau manifold X that is birationally equivalent to a m
oduli space of semistable coherent sheaves on a K3 surface\, the derived c
ategory of coherent sheaves on X is equivalent to the derived category of
this moduli space. This confirms a prediction from homological mirror symm
etry for this class of compact Calabi-Yau manifold\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sylvain Courte
DTSTART:20210119T150000Z
DTEND:20210119T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/35
DESCRIPTION:Title: Twisted generating functions and the nearby Lagrangian conjecture
\nby Sylvain Courte as part of Free Mathematics Seminar\n\n\nAbstract\
nI will explain the notion of twisted generating function and show that a
closed exact Lagrangian submanifold L in the cotangent bundle of M admits
such a thing. The type of function arising in our construction is related
to Waldhausen's tube space from his manifold approach to algebraic K-theor
y of spaces. Using the rational equivalence of this space with BO\, as pro
ved by Bökstedt\, we conclude that the stable Lagrangian Gauss map of L v
anishes on all homotopy groups. In particular when M is a homotopy sphere\
, we obtain the triviality of the stable Lagrangian Gauss map and a genuin
e generating function for L. This is a joint work with M. Abouzaid\, S. Gu
illermou and T. Kragh.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Gammage
DTSTART:20210126T150000Z
DTEND:20210126T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/36
DESCRIPTION:Title: Mirror symmetry for Berglund-Hübsch Milnor fibers\nby Benjam
in Gammage as part of Free Mathematics Seminar\n\n\nAbstract\nAfter recall
ing some joint work with Jack Smith proving homological Berglund-Hübsch m
irror symmetry\, we explain the calculation of the Fukaya category of a Be
rglund-Hübsch Milnor fiber\, proving a conjecture of Yankı Lekili and Ka
zushi Ueda\; the main technical trick is the reduction of the calculation
to a certain extension of perverse schobers\, essentially already computed
by David Nadler.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Jeffs
DTSTART:20210202T150000Z
DTEND:20210202T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/37
DESCRIPTION:Title: Mirror symmetry and Fukaya categories of singular varieties\n
by Maxim Jeffs as part of Free Mathematics Seminar\n\n\nAbstract\nIn this
talk I will explain Auroux' definition of the Fukaya category of a singula
r hypersurface and two results about this definition\, illustrated with so
me examples. The first result is that Auroux' category is equivalent to th
e Fukaya-Seidel category of a Landau-Ginzburg model on a smooth variety\;
the second result is a homological mirror symmetry equivalence at certain
large complex structure limits. I will also discuss ongoing work on genera
lizations.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junwu Tu
DTSTART:20210209T150000Z
DTEND:20210209T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/38
DESCRIPTION:Title: On the categorical enumerative invariants of a point\nby Junw
u Tu as part of Free Mathematics Seminar\n\n\nAbstract\nWe briefly recall
the definition of categorical enumerative invariants (CEI) first introduce
d by Costello around 2005. Costello's construction relies fundamentally on
Sen-Zwiebach's notion of string vertices V_{g\,n}'s which are chains on m
oduli space of smooth curves M_{g\,n}'s. In this talk\, we explain the rel
ationship between string vertices and the fundamental classes of the Delig
ne-Mumford compactification of M_{g\,n}. More precisely\, we obtain a Feyn
man sum formula expressing the fundamental classes in terms of string vert
ices. As an immediate application\, we prove a comparison result that the
CEI of the field \\mathbb{Q} is the same as the Gromov-Witten invariants o
f a point.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Habermann
DTSTART:20210216T150000Z
DTEND:20210216T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/39
DESCRIPTION:Title: Homological mirror symmetry for nodal stacky curves\nby Matth
ew Habermann as part of Free Mathematics Seminar\n\n\nAbstract\nIn this ta
lk I will explain the proof of homological mirror symmetry where the B-sid
e is a ring or chain of stacky projective lines joined nodally\, and where
each irreducible component is allowed to have a non-trivial generic stabi
liser\, generalising the work of Lekili and Polishchuk. The key ingredient
is to match categorical resolutions on the A- and B-sides with an interme
diary category given by the derived category of modules of a gentle algebr
a. I will begin by explaining how to construct this category from the data
of the A- and B-models before moving on to applications. In particular\,
one can show homological mirror symmetry where the B-model is taken to be
an invertible polynomial in two variables\, but where the grading group is
not necessarily maximal. In the maximally graded case the mirror is shown
to be graded symplectomorphic to the Milnor fibre of the transpose invert
ible polynomial\, thus establishing the Lekili-Ueda conjecture in dimensio
n one.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleksander Doan
DTSTART:20210223T140000Z
DTEND:20210223T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/40
DESCRIPTION:Title: Counting pseudo-holomorphic curves in symplectic six-manifolds\nby Aleksander Doan as part of Free Mathematics Seminar\n\n\nAbstract\nT
he signed count of embedded pseudo-holomorphic curves in a symplectic mani
fold typically depends on the choice of an almost complex structure on the
manifold and so does not lead to a symplectic invariant. However\, I will
discuss two instances in which such naive counting does define a symplect
ic invariant. The proof of invariance combines methods of symplectic geome
try with results of geometric measure theory\, especially regularity theor
y for calibrated currents. The talk is based on joint work with Thomas Wal
puski. Time permitting\, I will also discuss a related project\, joint wit
h Eleny Ionel and Thomas Walpuski\, whose goal is to use geometric measure
theory to prove the Gopakumar-Vafa finiteness conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicholas Wilkins
DTSTART:20210302T150000Z
DTEND:20210302T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/41
DESCRIPTION:Title: Quantum Steenrod operations are covariant constant\nby Nichol
as Wilkins as part of Free Mathematics Seminar\n\n\nAbstract\nWe explore t
he quantum Steenrod operations (which are quantum cohomology operations th
at utilise a symmetry under the cyclic group of order p)\, and observe tha
t these operations are covariant constant with respect to the quantum conn
ection. In particular\, they can be partially calculated in a variety of c
ases (and fully calculated in a subset). This work is joint with Paul Seid
el.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Egor Shelukhin
DTSTART:20210316T150000Z
DTEND:20210316T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/42
DESCRIPTION:Title: Lagrangian configurations and Hamiltonian maps\nby Egor Shelu
khin as part of Free Mathematics Seminar\n\n\nAbstract\nWe study configura
tions of disjoint Lagrangian submanifolds in certain low-dimensional sympl
ectic manifolds from the perspective of the geometry of Hamiltonian maps.
We detect infinite-dimensional flats in the Hamiltonian group of the two-s
phere equipped with Hofer's metric\, showing in particular that this group
is not quasi-isometric to a line. This answers a well-known question of K
apovich-Polterovich from 2006. We show that these flats in Ham(S^2) stabi
lize to certain product four-manifolds\, prove constraints on Lagrangian p
acking\, find new instances of Lagrangian Poincare recurrence\, and presen
t a new hierarchy of normal subgroups of area-preserving homeomorphisms of
the two-sphere. The technology involves Lagrangian spectral invariants wi
th Hamiltonian term in symmetric product orbifolds. This is joint work wit
h Leonid Polterovich.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abigail Ward
DTSTART:20210309T150000Z
DTEND:20210309T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/43
DESCRIPTION:Title: Mirror symmetry for certain non-Kähler elliptic surfaces\nby
Abigail Ward as part of Free Mathematics Seminar\n\n\nAbstract\nThe logar
ithmic transformation is an operation on complex elliptic surfaces which c
an be used to produce interesting spaces from more familiar ones. I will f
irst give homological mirror symmetry results for surfaces which are const
ructed by performing two logarithmic transformations to the product of P^1
with an elliptic curve\, a class of surfaces which includes the classical
Hopf surface (S^1 x S^3). I will then use this work\, along with work of
Auroux\, Efimov and Katzarkov on the Fukaya category of singular curves\,
to describe some work in progress on a potential mirror operation to the l
ogarithmic transformation and some applications.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charlotte Kirchhoff-Lukat
DTSTART:20210323T150000Z
DTEND:20210323T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/44
DESCRIPTION:Title: Towards Floer theory and Fukaya categories for Generalized Comple
x Manifolds: Some first ideas\nby Charlotte Kirchhoff-Lukat as part of
Free Mathematics Seminar\n\n\nAbstract\nGeneralized complex (GC) manifold
s encompass both symplectic and complex manifolds as examples. From the in
ception of the field of GC geometry in the early 2000s\, questions have th
us been raised about its relation to mirror symmetry: Can mirror symmetry
be understood as a generalized complex duality\, and if so\, how? An answe
r to this general question currently seems out of reach both from the poin
t of view of mirror symmetry\, as well as GC geometry -- general GC manifo
lds are so far relatively poorly understood. However\, I have identified a
number specific initial questions and approaches which I hope will ultima
tely help a more general understanding. These ideas -- currently still in
their infancy -- are what I would like to outline in this talk.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Conan Leung
DTSTART:20210330T140000Z
DTEND:20210330T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/45
DESCRIPTION:Title: Quantum cohomology of flag varieties via wonderful compactificati
ons\nby Conan Leung as part of Free Mathematics Seminar\n\n\nAbstract\
nPeterson conjectured that quantum cohomlogy ring of G/T is isomorphic to
the homology of the based loop space of G after localization. Lam and Shim
ozono proved the conjecture by combinatorial method. We studied the wrappe
d Floer theory of the complexification of G and used the geometry of its w
onderful compactification to give a geometric proof of this result.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Le
DTSTART:20210413T090000Z
DTEND:20210413T100000Z
DTSTAMP:20260404T131153Z
UID:Freemath/46
DESCRIPTION:Title: Mirror Symmetry for Truncated Cluster Varieties\nby Ian Le as
part of Free Mathematics Seminar\n\n\nAbstract\nGross\, Hacking and Keel
gave an algebro-geometric construction of cluster varieties: take a toric
variety\, blow up appropriate subvarieties in the boundary\, and then remo
ve the strict transform of the boundary. We work with a modification of th
is construction\, which we call a truncated cluster variety--roughly\, thi
s comes from performing the same procedure on the toric variety with all t
he codimension 2 strata removed. The resulting variety differs from the cl
uster variety in codimension 2. I will describe a construction of a Weinst
ein manifold mirror to a truncated cluster variety and explain how to prov
e a mirror symmetry via Lagrangian skeleta. We hope that this is a first s
tep towards understanding mirror symmetry for the entire cluster variety.
This is joint work with Benjamin Gammage.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Pomerleano
DTSTART:20210420T140000Z
DTEND:20210420T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/47
DESCRIPTION:Title: Intrinsic Mirror Symmetry and Categorical Crepant Resolutions
\nby Dan Pomerleano as part of Free Mathematics Seminar\n\n\nAbstract\nA g
eneral expectation in mirror symmetry is that the mirror partner to an aff
ine log Calabi-Yau variety is "semi-affine" (meaning it is proper over its
affinization). We will discuss how the semi-affineness of the mirror can
be seen directly as certain finiteness properties of Floer theoretic invar
iants of X (the symplectic cohomology and wrapped Fukaya category). One in
teresting consequence of these finiteness results is that\, under fairly g
eneral circumstances\, the wrapped Fukaya of X gives an ("intrinsic") cate
gorical crepant resolution of the affine variety Spec(SH^0(X)). This is ba
sed on https://arxiv.org/pdf/2103.01200.pdf.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolo Sibilla
DTSTART:20210427T140000Z
DTEND:20210427T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/48
DESCRIPTION:Title: Fukaya category of surfaces and pants decomposition\nby Nicol
o Sibilla as part of Free Mathematics Seminar\n\n\nAbstract\nIn this talk
I will explain some results joint with James Pascaleff on the Fukaya categ
ory of Riemann surfaces. I will explain a local-to-global principle which
allows us to reduce the calculation of the Fukaya category of surfaces of
genus g greater than one to the case of the pair-of-pants\, and which hold
s both in the punctured and in the compact case. The starting point are th
e sheaf-theoretic methods which are available in the exact setting\, and w
hich I will review at the beginning of the talk. This result has several i
nteresting consequences for HMS and geometrization of objects in the Fukay
a category. The talk is based on 1604.06448 and 2103.03366.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julie Rana
DTSTART:20210504T140000Z
DTEND:20210504T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/49
DESCRIPTION:Title: T-singular surfaces of general type\nby Julie Rana as part of
Free Mathematics Seminar\n\n\nAbstract\nWe explore the moduli space of st
able surfaces\, where the simplest of questions continue to remain open fo
r almost all invariants. A few such questions: Of the allowable singularit
ies\, which ones actually occur on a stable surface? Which of these deform
to smooth surfaces? How can we use this knowledge to find divisors in the
moduli spaces? Can we develop a stratification of these moduli spaces by
singularity type? Our focus will be on cyclic quotient singularities\, wit
h an emphasis on discussing concrete visual examples built out of rational
\, K3\, and elliptic surfaces.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yin Li
DTSTART:20210511T140000Z
DTEND:20210511T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/50
DESCRIPTION:Title: Exact Lagrangian tori in affine varieties\nby Yin Li as part
of Free Mathematics Seminar\n\n\nAbstract\nWe will discuss what is known a
nd unknown about the existence of exact Lagrangian tori in smooth affine v
arieties. Based on homological mirror symmetry and computations of Hochsch
ild cohomology\, we prove the nonexistence of exact Lagrangian tori in a c
lass of affine conic bundles over C^n\, which cannot in general be embedde
d in the complement of ample divisors in smooth Fano varieties. This resul
t should be regarded as evidence for the existence of dilations.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emre Sertöz
DTSTART:20210518T140000Z
DTEND:20210518T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/51
DESCRIPTION:Title: Separating periods of quartic surfaces\nby Emre Sertöz as pa
rt of Free Mathematics Seminar\n\n\nAbstract\nKontsevich--Zagier periods f
orm a natural number system that extends the algebraic numbers by adding c
onstants coming from geometry and physics. Because there are countably man
y periods\, one would expect it to be possible to compute effectively in t
his number system. This would require an effective height function and the
ability to separate periods of bounded height\, neither of which are curr
ently possible.\n\nIn this talk\, we introduce an effective height functio
n for periods of quartic surfaces defined over algebraic numbers. We also
determine the minimal distance between periods of bounded height on a sing
le surface. We use these results to prove heuristic computations of Picard
groups that rely on approximations of periods. Moreover\, we give explici
t Liouville type numbers that can not be the ratio of two periods of a qua
rtic surface. This is joint work with Pierre Lairez (Inria\, France).\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernhard Keller
DTSTART:20210525T140000Z
DTEND:20210525T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/52
DESCRIPTION:Title: Singular Hochschild cohomology and reconstruction of singularitie
s\nby Bernhard Keller as part of Free Mathematics Seminar\n\n\nAbstrac
t\nWe show that under a mild regularity assumption\, singular Hochschild c
ohomology (also known as Tate-Hochschild cohomology) identifies with Hochs
child cohomology of the (dg enhanced) singularity category. In joint work
with Zheng Hua\, we apply this to the reconstruction of a (complete isolat
ed) compound Du Val singularity from its contraction algebra together with
the additional datum of a class in its zeroth Hochschild homology. This p
rovides some evidence towards a conjecture by Donovan-Wemyss according to
which the contraction algebra alone determines such a singularity.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richard Hind
DTSTART:20210601T140000Z
DTEND:20210601T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/53
DESCRIPTION:Title: The shape invariant and path lifting\nby Richard Hind as part
of Free Mathematics Seminar\n\n\nAbstract\nThe shape invariant of a sympl
ectic manifold encodes the area classes of Lagrangian submanifolds. This t
alk describes joint work with Jun Zhang computing the shape for some simpl
e domains in 4-dimensional Euclidean space. We then consider the path lift
ing problem\, which amounts to finding Lagrangian isotopies with specified
flux. Finally we discuss possible relations to stabilized symplectic embe
ddings.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Smith
DTSTART:20210608T140000Z
DTEND:20210608T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/54
DESCRIPTION:Title: Lagrangian links on surfaces and the Calabi invariant\nby Iva
n Smith as part of Free Mathematics Seminar\n\n\nAbstract\nThe identity co
mponent in the group of area-preserving homeomorphisms of a compact surfac
e admits a `mass-flow’ (or flux) homomorphism to the reals. We will pro
ve that the kernel of this homomorphism is not simple (extending earlier r
esults of Cristofaro-Gardiner\, Humilière and Seyfaddini in the genus zer
o case)\, resolving a question of Fathi from the late 1970s. The proof ap
peals to a new family of Lagrangian spectral invariants associated to Lagr
angian links on the surface\, which are used to probe the small-scale geom
etry of the surface\; their crucial feature is that they can be used to re
cover the classical Calabi invariant of a Hamiltonian. The Floer cohomolo
gy theory behind these spectral invariants is a close cousin of the knot F
loer homology of Ozsváth-Szabó and Rasmussen. This talk reports on join
t work with Dan Cristofaro-Gardiner\, Vincent Humilière\, Cheuk Yu Mak an
d Sobhan Seyfaddini.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johan Asplund
DTSTART:20210615T140000Z
DTEND:20210615T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/55
DESCRIPTION:Title: Chekanov-Eliashberg dg-algebras for singular Legendrians\nby
Johan Asplund as part of Free Mathematics Seminar\n\n\nAbstract\nThe Cheka
nov-Eliashberg dg-algebra is a holomorphic curve invariant associated to a
Legendrian submanifold of a contact manifold. In this talk we explain how
to extend the definition to singular Legendrian submanifolds admitting a
Weinstein neighborhood. Via the Bourgeois-Ekholm-Eliashberg surgery formul
a\, the new definition gives direct geometric proof of the pushout diagram
s and stop removal formulas in partially wrapped Floer cohomology of Ganat
ra-Pardon-Shende. It furthermore leads to a proof of the conjectured surge
ry formula relating partially wrapped Floer cohomology to Chekanov--Eliash
berg dg-algebras with coefficients in chains on the based loop space. This
talk is based on joint work with Tobias Ekholm.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Zemke
DTSTART:20210622T140000Z
DTEND:20210622T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/56
DESCRIPTION:Title: Heegaard Floer homology and complex curves with non-cuspidal sing
ularities\nby Ian Zemke as part of Free Mathematics Seminar\n\n\nAbstr
act\nWe will discuss joint work with B. Liu and M. Borodzik\, concerning a
pplications of Heegaard Floer d-invariants to the study of complex curves
in $\\mathbb{CP}^2$ with non-cuspidal singularities. We focus on the simpl
est such singularity\, which is a double point.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xin Jin
DTSTART:20210921T140000Z
DTEND:20210921T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/57
DESCRIPTION:Title: Homological mirror symmetry for the universal centralizers\nb
y Xin Jin as part of Free Mathematics Seminar\n\n\nAbstract\nI will presen
t my recent result on homological mirror symmetry for the universal centra
lizer (a.k.a Toda space) associated to a complex semisimple Lie group.\n
The A-side is a partially wrapped Fukaya category on the universal centr
alizer\, and the B-side is the category of coherent sheaves on the categor
ical quotient of the dual maximal torus by the Weyl group (with some modif
ications if the group has nontrivial center). I will illustrate many of th
e geometry and ideas of the proof using the example of SL_2 or PGL_2.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Umut Varolgunes (University of Edinburgh)
DTSTART:20210928T140000Z
DTEND:20210928T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/58
DESCRIPTION:Title: Quantum cohomology as a deformation of symplectic cohomology\
nby Umut Varolgunes (University of Edinburgh) as part of Free Mathematics
Seminar\n\n\nAbstract\nConsider a positively monotone closed symplectic ma
nifold $M$ and a symplectic simple crossings divisor $D$ in it. Assume tha
t the Poincare dual of the anti-canonical class is a positive rational lin
ear combination of the classes $[D_i]$\, where $D_i$ are the components of
$D$ with their symplectic orientation. A choice of such coefficients\, ca
lled the weights\, (roughly speaking) equips $M-D$ with a Liouville struct
ure. I will start by discussing results relating the symplectic cohomology
of $M-D$ with quantum cohomology of $M$. These results are particularly s
harp when the weights are all at most 1 (hypothesis A). Then\, I will disc
uss certain rigidity results (inside $M$) for skeleton type subsets of $M-
D$\, which will also demonstrate the geometric meaning of hypothesis A in
examples. The talk will be mainly based on joint work with Strom Borman an
d Nick Sheridan.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Rains
DTSTART:20211019T160000Z
DTEND:20211019T170000Z
DTSTAMP:20260404T131153Z
UID:Freemath/59
DESCRIPTION:Title: The birational geometry of noncommutative surfaces\nby Eric R
ains as part of Free Mathematics Seminar\n\n\nAbstract\nIn commutative alg
ebraic geometry\, the theory of smooth projective surfaces is\, of course\
, very highly developed\, with a major result being the birational classif
ication of such surfaces. For the noncommutative analogue\, much less is k
nown\, with even the notion of "birational" not being very well understood
. In particular\, although several constructions have been known (noncommu
tative projective planes\, noncommutative ruled surfaces\, and noncommutat
ive blowups)\, many basic isomorphisms have proved elusive (e.g.\, that bl
owups in distinct points commute). I'll discuss a new approach to the prob
lem via derived categories that not only makes it easy to construct the de
sired isomorphisms but also to prove a number of other results\, in partic
ular that anything birational to a ruled surface is either ruled or a proj
ective plane\, and the corresponding moduli spaces of simple sheaves are P
oisson\, with smooth symplectic leaves.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Takahiro Oba
DTSTART:20211102T100000Z
DTEND:20211102T110000Z
DTSTAMP:20260404T131153Z
UID:Freemath/60
DESCRIPTION:Title: A four-dimensional mapping class group relation\nby Takahiro
Oba as part of Free Mathematics Seminar\n\n\nAbstract\nRelations between D
ehn twists on mapping class groups of surfaces play an important role in t
he study of symplectic manifolds via Lefschetz fibrations. In higher dimen
sions\, as little is known about symplectic mapping class groups\, fibrati
on-like structures are not so powerful yet. In this talk\, I will give a r
elation between 4-dimensional Dehn twists on a Weinstein domain. One of th
e key ingredients in the construction is a solution to the symplectic isot
opy problem for symplectic surfaces in a Del Pezzo surface.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chi Hong Chow
DTSTART:20211005T140000Z
DTEND:20211005T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/61
DESCRIPTION:Title: Homology of based loop groups and quantum cohomology of flag vari
eties\nby Chi Hong Chow as part of Free Mathematics Seminar\n\n\nAbstr
act\nK be a compact Lie group and G its complexification. There are three
ring maps with the same source H_*(\\Omega K) and target QH(G/P) which ari
se from the work of (1) Peterson/Lam-Shimozono\, (2) Seidel/Savelyev and (
3) Ma'u-Wehrheim-Woodward/Evans-Lekili respectively. In this talk\, I will
discuss how these maps are related and the applications.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philip Engel
DTSTART:20211012T140000Z
DTEND:20211012T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/62
DESCRIPTION:Title: Compact K3 moduli\nby Philip Engel as part of Free Mathematic
s Seminar\n\n\nAbstract\nThe moduli space of polarized K3 surfaces is a no
n-compact quotient of a symmetric space by an arithmetic group. In this ca
pacity\, it has an infinite class of combinatorially-defined "semitoroidal
compactifications." I will discuss joint work with Valery Alexeev that so
metimes semitoroidal compactifications have geometric meaning: they parame
terize "stable K3 surfaces" in a way similar to how the Deligne-Mumford co
mpactification of curves parameterizes "stable curves." Inspired by ideas
from mirror symmetry\, the semifan of such a compactification can sometime
s be computed\, using symplectic and integral-affine geometry.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jie Min
DTSTART:20211026T140000Z
DTEND:20211026T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/63
DESCRIPTION:Title: Moduli space of symplectic log Calabi-Yau divisors and torus fibr
ations\nby Jie Min as part of Free Mathematics Seminar\n\n\nAbstract\n
Symplectic log Calabi-Yau divisors are the symplectic analogue of anti-can
onical divisors in algebraic geometry. We study the rigidity of such divis
ors. In particular we prove a Torelli type theorem and form an equivalent
moduli space of homology configurations which is more suitable for countin
g. We also discuss their relations to toric actions and almost toric fibra
tions\, reprove a finiteness result and an upper bound for toric actions b
y Karshon-Kessler-Pinsonnault\, and prove a new stability result.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angelica Simonetti
DTSTART:20211109T150000Z
DTEND:20211109T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/64
DESCRIPTION:by Angelica Simonetti as part of Free Mathematics Seminar\n\nA
bstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Pertusi
DTSTART:20211116T150000Z
DTEND:20211116T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/65
DESCRIPTION:Title: Serre-invariant stability conditions and cubic threefolds\nby
Laura Pertusi as part of Free Mathematics Seminar\n\n\nAbstract\nStabilit
y conditions on the Kuznetsov component of a Fano threefold of Picard rank
1\, index 1 and 2 have been constructed by Bayer\, Lahoz\, Macrì and Ste
llari\, making possible to study moduli spaces of stable objects and their
geometric properties. In this talk we investigate the action of the Serre
functor on these stability conditions. In the index 2 case and in the cas
e of GM threefolds\, we show that they are Serre-invariant. Then we prove
a general criterion which ensures the existence of a unique Serre-invarian
t stability condition and applies to some of these Fano threefolds. Finall
y\, we apply these results to the study of moduli spaces in the case of a
cubic threefold X. In particular\, we prove the smoothness of moduli space
s of stable objects in the Kuznetsov component of X and the irreducibility
of the moduli space of stable Ulrich bundles on X. These results come fro
m joint works with Song Yang and with Soheyla Feyzbakhsh and in preparatio
n with Ethan Robinett.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Navid Nabijou
DTSTART:20211123T150000Z
DTEND:20211123T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/66
DESCRIPTION:Title: Enumerative invariants of 3-fold flops: hyperplane arrangements a
nd wall-crossing\nby Navid Nabijou as part of Free Mathematics Seminar
\n\n\nAbstract\n3-fold flopping contractions form a fundamental building b
lock of the higher-dimensional Minimal Model Program. They exhibit extreme
ly rich geometry\, which has been investigated by many people over the pas
t half-century. I will present an elegant and visually-pleasing relationsh
ip between enumerative invariants of flopping contractions and certain hyp
erplane arrangements constructed combinatorially from root system data. I
will discuss both Gopakumar-Vafa (GV) and Gromov-Witten (GW) invariants\,
explaining how these are related to one another and how they are encoded i
n finite and infinite arrangements\, respectively. Finally\, I will discus
s wall-crossing: our combinatorial approach allows us to explicitly constr
uct flops from root system data\, leading to a new “direct” proof of t
he Crepant Transformation Conjecture\, with a very explicit formulation. T
his is joint work with Michael Wemyss.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dogancan Karabas
DTSTART:20211130T150000Z
DTEND:20211130T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/67
DESCRIPTION:Title: Homotopy colimit formula for gluing wrapped Fukaya categories\, a
nd lens spaces\nby Dogancan Karabas as part of Free Mathematics Semina
r\n\n\nAbstract\nGanatra\, Pardon\, and Shende introduced a way to compute
wrapped Fukaya categories of Weinstein domains by taking the homotopy col
imit of wrapped Fukaya categories of their sectorial coverings. However\,
homotopy colimits are hard to compute in general. In this talk\, I will de
scribe a practical formula for homotopy colimit when the categories are pr
esented as semifree dg categories. As an application\, I will show that th
e homotopy type of lens spaces is detected by the wrapped Fukaya category
of their cotangent bundles. If time permits\, I will talk about other appl
ications of the formula\, such as the calculation of the wrapped Fukaya ca
tegory of plumbing spaces. This is joint work with Sangjin Lee.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Barbacovi
DTSTART:20211207T150000Z
DTEND:20211207T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/68
DESCRIPTION:Title: Entropy of autoequivalences and holomorphicity\nby Federico B
arbacovi as part of Free Mathematics Seminar\n\n\nAbstract\nThe notion of
entropy of an endofunctor categorifies the notion of topological entropy o
f a continuous map. However\, while the latter is a number\, the former is
a function of a real variable. The value at zero of this function takes t
he name of categorical entropy and makes the connection between the catego
rical and the topological framework. In this talk I will report on joint w
ork with Jongmyeong Kim in which we give sufficient conditions for a conje
cture in categorical dynamics (that mirrors a theorem of Gromov and Yomdin
) to be satisfied. Of particular interest is the fact that such conditions
arise\, through the philosophy of homological mirror symmetry\, as a cate
gorification of one of the properties of holomorphic functions.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Seidel
DTSTART:20220125T150000Z
DTEND:20220125T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/69
DESCRIPTION:Title: Twisted open-closed string maps and applications\nby Paul Sei
del as part of Free Mathematics Seminar\n\n\nAbstract\n(This is joint work
in progress with Shaoyun Bai\, expanding on an idea of Sheel Ganatra). Th
e nondegeneracy of the Shklyarov pairing gives an easy way to prove inject
ivity of the open-closed string map for Fukaya categories which are cohomo
logically smooth\, and that is also true in the case when it's twisted by
a symplectic automorphism. We will discuss some implications of this for L
efschetz fibrations.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesca Carocci
DTSTART:20220208T150000Z
DTEND:20220208T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/70
DESCRIPTION:Title: BPS invariant from non Archimedean integrals\nby Francesca Ca
rocci as part of Free Mathematics Seminar\n\n\nAbstract\nWe consider modul
i spaces M(ß\,χ) of one-dimensional semistable sheaves on del Pezzo and
K3 surfaces supported on ample curve classes. \nWorking over a non-archim
edean local field F\, we define a natural measure on the F-points of such
moduli spaces. We prove that the integral of a certain naturally defined g
erbe on M(ß\,χ) with respect to this measure is independent of the Euler
characteristic.\nAnalogous statements hold for (meromorphic or not) Higgs
bundles.\nRecent results of Maulik-Shen and Kinjo-Coseki imply that these
integrals compute the BPS invariants for the del Pezzo case and for Higgs
bundles.\nThis is a joint work with Giulio Orecchia and Dimitri Wyss.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Woodward
DTSTART:20220301T150000Z
DTEND:20220301T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/71
DESCRIPTION:Title: Quantum stable manifolds for nearby Lagrangians\nby Chris Woo
dward as part of Free Mathematics Seminar\n\n\nAbstract\nAnalogs of Cohen-
Jones-Segal spaces for Lagrangian Floer cohomology of nearby Lagrangians n
aturally arise through a choice of quasi-isomorphisms\, and are cell compl
exes with degree one evaluation maps to either Lagrangian. I will discuss
some results on the problem of desingularizing these classifying spaces.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adrian Petr
DTSTART:20220201T150000Z
DTEND:20220201T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/72
DESCRIPTION:Title: Invariant of the Legendrian lift of an exact Lagrangian submanifo
ld in the circular contactization of a Liouville manifold\nby Adrian P
etr as part of Free Mathematics Seminar\n\n\nAbstract\nAny exact Lagrangia
n submanifold in a Liouville manifold lifts to a Legendrian submanifold in
the circular contactization. For the standard contact form\, this Legendr
ian admits countably many Reeb chords (indexed by their winding number aro
und the fiber) above each point\, thus yielding a degenerate situation. In
this talk\, we will slightly perturb the contact form and compute the Che
kanov-Eliashberg DG-algebra of the Legendrian lift in term of the Floer A_
{\\infty}-algebra of the Lagrangian. The main idea will be to view the Kos
zul dual of the DG-algebra as a particular homotopy colimit (as defined by
Ganatra-Pardon-Shende) of A_{\\infty}-categories.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Travis Mandel
DTSTART:20220215T150000Z
DTEND:20220215T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/73
DESCRIPTION:by Travis Mandel as part of Free Mathematics Seminar\n\nAbstra
ct: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kristin DeVleming
DTSTART:20220222T150000Z
DTEND:20220222T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/74
DESCRIPTION:Title: K-stability and birational geometry of moduli spaces of quartic K
3 surfaces\nby Kristin DeVleming as part of Free Mathematics Seminar\n
\n\nAbstract\nRecently it has been shown that K-stability provides well-be
haved moduli spaces of Fano varieties and log Fano pairs\, and allows one
to naturally interpolate between other geometric compactifications. I wil
l discuss the picture for quartic K3 surfaces\, relating compactifications
coming from geometric invariant theory (GIT)\, Hodge theory\, and K-stabi
lity via wall crossings in K-moduli. This is joint work with Kenneth Asch
er and Yuchen Liu.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ezra Getzler
DTSTART:20220308T150000Z
DTEND:20220308T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/75
DESCRIPTION:by Ezra Getzler as part of Free Mathematics Seminar\n\nAbstrac
t: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Semon Rezchikov
DTSTART:20220315T150000Z
DTEND:20220315T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/76
DESCRIPTION:Title: Holomorphic Floer Theory and the Fueter Equation\nby Semon Re
zchikov as part of Free Mathematics Seminar\n\n\nAbstract\nThe Lagrangian
Floer homology of a pair of holomorphic Lagrangian submanifolds of a hyper
kahler manifold is expected to simplify\, by work of Solomon-Verbitsky and
others. This occurs in part because\, in this setting\, the symplectic ac
tion functional\, the gradient flow of which computes Lagrangian Floer hom
ology\, is the real part of a holomorphic function. As noted by Haydys\, t
hinking of this holomorphic function as a superpotential on an infinite-di
mensional symplectic manifold gives rise to a quaternionic analog of Floer
's equation for holomorphic strips: the Fueter equation. I will explain ho
w this line of thought gives rise to a `complexification' of Floer's theor
em identifying Fueter maps in cotangent bundles to Kahler manifolds with h
olomorphic planes in the base. This complexification has a conjectural cat
egorical interpretation\, giving a model for Fukaya-Seidel categories of L
efshetz fibrations\, which should have algebraic implications for the stud
y of Fukaya categories. This is a report on upcoming joint work with Aleks
ander Doan.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin Hilburn
DTSTART:20220322T150000Z
DTEND:20220322T160000Z
DTSTAMP:20260404T131153Z
UID:Freemath/77
DESCRIPTION:Title: Perverse Schobers and 2-Categorical 3d Mirror Symmetry\nby Ju
stin Hilburn as part of Free Mathematics Seminar\n\n\nAbstract\n3d mirror
symmetry predicts an equivalence between 2-categories associated to dual h
olomorphic symplectic stacks. The first 2-category is of an algebro-geomet
ric flavor and has constructions due to Kapustin/Rozansky/Saulina and Arin
kin. The second category depends on symplectic topology and has a conjectu
ral description in terms of the 3d generalized Seiberg-Witten equations (a
lso known as the gauged Fueter equations). \n\nIn this talk I will describ
e joint work with Ben Gammage and Aaron Mazel-Gee proving a variant of 3d
mirror symmetry for Gale dual toric cotangent stacks. In particular\, we d
efine a combinatorial model for the symplectic 2-category using equivarian
t perverse schobers. If time permits I will explain work in progress exten
ding our equivalence from toric cotangent stacks to hypertoric varieties.
This will provide a categorification of previous results on Koszul duality
for hypertoric categories O.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joel Fine
DTSTART:20220503T140000Z
DTEND:20220503T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/78
DESCRIPTION:Title: Knots\, minimal surfaces and J-holomorphic curves\nby Joel Fi
ne as part of Free Mathematics Seminar\n\n\nAbstract\nLet K be a knot or l
ink in the 3-sphere\, thought of as the ideal boundary of hyperbolic 4-spa
ce\, H^4. The main theme of my talk is that it should be possible to count
minimal surfaces in H^4 which fill K and obtain a link invariant. In othe
r words\, the count doesn’t change under isotopies of K. When one counts
minimal disks\, this is a theorem. Unfortunately there is currently a gap
in the proof for more complicated surfaces. I will explain “morally”
why the result should be true and how I intend to fill the gap. In fact\,
this (currently conjectural) invariant is a kind of Gromov—Witten invari
ant\, counting J-holomorphic curves in a certain symplectic 6-manifold dif
feomorphic to S^2xH^4. The symplectic structure becomes singular at infini
ty\, in directions transverse to the S^2 fibres. These singularities mean
that both the Fredholm and compactness theories have fundamentally new fea
tures\, which I will describe. Finally\, there is a whole class of infinit
e-volume symplectic 6-manifolds which have singularities modelled on the a
bove situation. I will explain how it should be possible to count J-holomo
rphic curves in these manifolds too\, and obtain invariants for links in o
ther 3-manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilaria di Dedda
DTSTART:20220510T140000Z
DTEND:20220510T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/79
DESCRIPTION:Title: Realising perfect derived categories of Auslander algebras of typ
e A as Fukaya-Seidel categories\nby Ilaria di Dedda as part of Free Ma
thematics Seminar\n\n\nAbstract\nThe theme of this talk will be to build a
bridge between two areas of mathematics: representation theory and symple
ctic geometry. Our objects of interest on the representation theoretical s
ide are Auslander algebras of type A. This family of non-commutative algeb
ras arises very naturally as endomorphism algebras of indecomposable modul
es of quivers of finite type. They were given a symplectic interpretation
by Dyckerhoff-Jasso-Lekili\, who proved the equivalence (as $A_{\\infty}$-
categories) between perfect derived categories of Auslander algebras of ty
pe A and certain partially wrapped Fukaya categories. We use their result
to prove an equivalence between the categories in question and the Fukaya-
Seidel categories of a certain family of Lefschetz fibrations. In this tal
k\, we will observe this result in some key examples.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Riccardo Pedrotti
DTSTART:20220517T140000Z
DTEND:20220517T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/80
DESCRIPTION:Title: Fixed point Floer cohomology of a Dehn twist in a monotone settin
g and in more general contexts\nby Riccardo Pedrotti as part of Free M
athematics Seminar\n\n\nAbstract\nIn this talk we will talk about the fixe
d point Floer cohomology of a Dehn twist. Nowadays there are several metho
ds to compute it\, for example by using the Seidel exact triangle. Inspire
d by an early result of P. Seidel (1996) for twists on surfaces\, we gave
an explicit description of the Floer cohomology of a Dehn twist in terms o
f Morse cohomology of some “sub-quotients” of M. The main step will be
to use a neck-stretching argument to establish some energy lower bounds o
n certain trajectories realising differentials. We will start by studying
the rather restricting yet convenient “strongly - monotone” case and t
hen show how to generalise it to more general settings using an energy fil
tration argument due to K. Ono. Time permitting\, we will sketch an applic
ation of our techniques in the context of ongoing joint work with T. Perut
z\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marc Kegel
DTSTART:20220524T140000Z
DTEND:20220524T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/81
DESCRIPTION:Title: Stein traces\nby Marc Kegel as part of Free Mathematics Semin
ar\n\n\nAbstract\nEvery Legendrian knot leaves a traces in the 4-dimension
al symplectic world. In this talk we will investigate whether a 4-dimensio
nal tracker (with the necessary mathematical education) can determine the
3-dimensional creature that left the trace. This is based on joint work wi
th Roger Casals and John Etnyre.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yang Li
DTSTART:20220614T140000Z
DTEND:20220614T150000Z
DTSTAMP:20260404T131153Z
UID:Freemath/82
DESCRIPTION:Title: The Thomas-Yau conjecture\nby Yang Li as part of Free Mathema
tics Seminar\n\n\nAbstract\nThe Thomas-Yau conjecture is an open-ended pro
gram to relate special Lagrangians to stability conditions in Floer theory
\, but the precise notion of stability is subject to many interpretations.
I will focus on the exact case (Stein Calabi-Yau manifolds)\, and deal on
ly with almost calibrated Lagrangians. We will discuss how the existence o
f destabilising exact triangles obstructs special Lagrangians\, under some
additional assumptions\, using the technique of integration over moduli s
paces.\n
LOCATION:https://stable.researchseminars.org/talk/Freemath/82/
END:VEVENT
END:VCALENDAR