3CinG Annual Congress
Mon 20th-Thu 23rd Sep 2021 at Warwick
Organisers: Alessio Corti, Miles Reid
[Arrangements subject to change]
This a delayed annual congress of the EPSRC program grant
3CinG. We will run this as a hybrid meeting, with 6 or 7
speakers on Zoom, and a similar number of live talks in
Warwick, Zeeman Building MS.02. We will leave some slots in
the program blank for talks chosen on the spot (following
the Bonner Arbeitstagung tradition). If you wish to speak,
please bring along a draft and let us know.
The Zoom link was sent to the COW and to registered
participants on Sun 19th Sep. Anyone needing a reminder,
please let me know.
First talk: Mon 20th Sep at 12:00-1:00
Last talk: Thu 23rd Sep 2:00-3:00 [may be replaced by pub lunch]
Planned keynote speakers (possibly by video-link) include
Vasily Golyshev,
Mark Gross,
Paul Hacking
Paul Seidel,
Duco van Straten,
Umut Volgunes
We plan to feature 5 or 6 short talks by current or recent
PhD students on mornings of Tue 21st and Wed 22nd.
Most participants in the live event will be accommodated at
UoW Scarman House. Anyone interested in the live event,
please register via the Warwick MRC page
https://warwick.ac.uk/fac/sci/maths/research/events/2020-2021/annualcongress3cing
Attendance will be restricted to registered participants.
Restrictions due to University of Warwick public health
rules unfortunately mean that we cannot guarantee to accept
all registration requests. Talks will be live-streamed for
those unable to attend.
For details contact:
Alessio Corti
Miles Reid
Tentative timetable (subject to change):
(see below for titles)
Mon 20th Sep
12:00 Mark Gross
14:00 Duco van Straten
15:15 Paul Hacking
17:00 Alan Thompson (Loughborough)
Tue 21 Sep
10:00 LIU Shengxuan (Warwick)
10:45 Patience Ablett (Warwick)
11:30 JIANG Wei (Warwick)
14:00 Vasily Golyshev (Moscow)
15:15 Anne-Sophie Kaloghiros (Brunel)
17:00 Andrew Macpherson (Warwick)
18:30 Social dinner in Radcliffe
Wed 22 Sep
morning grad student talks
14:00 Umut Volgunes (Stanford, currently Moscow)
15:15 Paul Seidel (MIT)
17:00 Angelica Simonetti (DPMMS, Cambridge)
Thu 23 Sep
10:00 Al Kasprzy (Nottingham)
12:00 Hulya Arguz (Versailles)
Some of the titles
Mark Gross (DPMMS): Open FJRW theory and mirror symmetry for
Landau-Ginzburg models
(Fan-Jarvis-Ruan-Witten theory)
Duco van Straten (Mainz)
Title: A strange Calabi-Yau degeneration.
Abstract: If a Calabi-Yau threefold varies in a one-parameter
family and aquires some double points, a small resolution will
produce a rigid space. The local monodromy at such a 'conifold
transition' is of infinite order. In the talk I report on some
work done with S. Cynk (Krakow), which shows similar transitions
to rigid Calabi-Yaus are possible with monodromy of finite
order, in sharp distinction to what can happen for K3 surfaces.
Paul Hacking
Title: Mirror symmetry for Q-Fano 3-folds
Abstract: This is a report on work in progress with my student Cristian
Rodriguez. The mirror of a Q-Fano 3-fold with b_2=1 is a rigid K3
fibration over P^1 such that Hodge bundle is degree 1 and some power of
the monodromy at infinity is maximally unipotent. Although prior work
focussed on the maximally unipotent case (without base change), perhaps
a classification of such Picard--Fuchs equations is possible.
In the smooth case these fibrations were described explicitly by
Przyjalkowski, and Doran-Harder-Novoseltsev-Thompson showed that they
are given by etale covers of the (1-dimensional) moduli of rank 19 K3
surfaces. In the case of a single 1/2(1,1,1) singularity they are given
by rigid rational curves on the (2-dimensional) moduli of rank 18 K3
surfaces, and examples suggest they are Teichmuller curves in A_2 (via
the Shioda-Inose correspondence relating rank 18 K3s and abelian
surfaces), as studied by McMullen.
Vasily Golyshev (Moscow)
Title: On mixed Picard-Fuchs equations
I will give an update on recent work on variations of mixed Hodge
structure arising in mirror symmetry and their possible link to a B-SD
(Birch--Swinnerton-Dyer) type conjecture.
Anne-Sophie Kaloghiros,
Title: The Calabi problem for Fano 3-folds
Andrew Macpherson (Warwick)
Title: Why are correspondences ubiquitous?
Abstract: Many of the algebraic structures we construct from geometric
data are represented "motivically," that is, their structure constants
are obtained by pushing and pulling "coefficients" (e.g. functions,
sheaves) along diagrams like X <- W -> Y. In this quasi-survey talk, I
will explain how many of the convenient properties of the algebraic
categories we like to work in (e.g. vector spaces, dg-categories) are
already present in categories of correspondences themselves. This
explains their frequent appearance in the study of universal homology
theories.
Umut Varolgunes (Stanford, currently Moscow)
Title: Quantum cohomology as a deformation of symplectic cohomology
Abstract: Consider a positively monotone (Fano) closed symplectic
manifold M and a symplectic simple crossings divisor D in it. Assume
that the Poincare dual of the anti-canonical class is a positive
rational linear combination of the classes [D_i], where D_i are the
components of D with their symplectic orientation. A choice of such
coefficients, called the weights, (roughly speaking) equips M-D with a
Liouville structure. I will start by discussing results relating the
components of D with their symplectic orientation. A choice of such
coefficients, called the weights, (roughly speaking) equips M-D with a
Liouville structure. I will start by discussing results relating the
symplectic cohomology of M-D with quantum cohomology of M. These results
are particularly sharp when the weights are all at most 1 (hypothesis
A). Then, I will discuss 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 and Nick Sheridan.
Paul Seidel (MIT)
Title: Homological mirror symmetry and noncommutative linear
systems
Abstract: This will be an attempt to summarize what one might
expect about Homological Mirror Symmetry in the presence of an
anticanonical divisor... and the (much smaller, but more
reliable) subset of things I can prove about that situation.
Angelica Simonetti (DPMMS, Cambridge)
ZZ/2-equivariant smoothings of cusp singularities
LIU Shengxuan (Warwick)
Title: Stability condition on Calabi-Yau threefold of complete
intersection of quadratic and quartic hypersurfaces
Abstract: In this talk, I will first introduce the background of
Bridgeland stability condition. Then I will mention some existence
result of Bridgeland stability. Next I will prove the Bogomolov-Gieseker
type inequality of X_(2,4), Calabi-Yau threefold of complete
intersection of quadratic and quartic hypersufaces, by proving the
Clifford type inequality of the curve X_(2,2,2,4). Then this will
provide the existence of Bridgeland stability condition of X_(2,4).
Patience Ablett TBA
Gorenstein curves in codimension four
Whilst Gorenstein codimension three varieties are well
understood from Buchsbaum-Eisenbud's structure theorem, the
picture is less clear for codimension four. In this talk we
describe some constructions of stable curves corresponding
to the possible Betti tables for Artin Gorenstein algebras
of regularity and codimension four, as outlined in a paper
of Schenck, Stillman and Yuan [Calabi-yau threefolds in P^n
and Gorenstein rings, 2020, arXiv:2011.10871]. These
constructions use techniques from liaison theory and the
Tom and Jerry formats of Brown and Reid.
JIANG Wei
Wendelin Lutz (Imperial):
Title: Towards a geometric proof of the classification of T-polygons.
One formulation of mirror symmetry predicts (omitting a few adjectives)
a 1-1 correspondence between equivalence classes of certain lattice
polygons and deformation families of certain del Pezzo surfaces.
Lattice polygons corresponding to smooth Del Pezzo surfaces are called
T-polygons, and these have been classified by Kasprzyk-Nill-Prince using
combinatorial methods. I will sketch a new geometric proof of their
classification result.
Qaasim Shafi (Imperial)
Title: Quasimaps & Accordions
Abstract: Quasimaps provide an alternate curve counting
system to Gromov-Witten theory, which are related by
wall-crossing formulae. Relative (or logarithmic)
Gromov-Witten theory has proved useful for constructions in
mirror symmetry, as well as for determining ordinary
Gromov-Witten invariants via the degeneration formula.
Different versions of this theory rely on various
technologies, including expansions (or accordions) as well
as logarithmic structures. I’ll discuss how to use a hybrid
of these approaches to produce a proper moduli space
parametrising quasimaps relative a smooth divisor in any
genus.
12:00 Hulya Arguz (Versailles)
Title: Enumerative geometry and mirror symmetry for log Calabi--Yau pairs
Abstract: Given a log Calabi--Yau pair (X,D), consisting of a smooth
projective variety X together with a normal crossings anti-canonical
divisor D, we first provide a combinatorial algorithm for solving
the enumerative problem of computing rational stable maps to (X,D)
touching D at a single point. We then explain how to use the
solution to write explicit equations for mirrors to such pairs at
arbitrary dimensions. Part of this is joint work with Mark Gross.