IMPANGA is an algebraic geometry seminar organized by Piotr Achinger, Jarosław Buczyński,
and Michał Kapustka. In the academic year 2024/25, the seminar
meets twice per month for a one day session on Friday,
with two 60 min talks separated by a lunch break (11:00-12:00
and 13:30-14:30). IMPANGA meets in Room 403 at IMPAN
(unless stated otherwise).
IMPANGA was founded at IMPAN in 2000 by late Piotr Pragacz. See here for information on former meetings of IMPANGA
Upcoming meeting
Apr 11 (impanga 467)
Symmetric schemes, superfat points and associated tensors
Speaker: Stefano Canino (MIMUW) 11:00–12:00, IMPAN 403
Future meetings
Apr 25 (impanga 468)
- May 9 Art Waeterschoot
- May 23
- Jun 6 Jarosław Włodarczyk
Past meetings
Oct 18 (impanga 458)
Series of lectures on the Zariski multiplicity conjecture part IA short introduction to the Zariski multiplicity conjecture
Speaker: Christophe Eyral (IMPAN) 11:00–12:00, IMPAN 403
Oct 25 (impanga 459)
Series of lectures on the Zariski multiplicity conjecture part IIHeegaard Floer homologies for algebraic geometer
Speaker: Maciej Borodzik (IMPAN) 11:00–12:00, IMPAN 403
Equimultiplicity of μ-constant families
Speaker: Tomasz Pełka (MIMUW)13:30–14:30, IMPAN 403
Nov 15 (impanga 460)
Series of lectures on the Zariski multiplicity conjecture part IIIBi-Lipschitz equivalent cones with different degrees
Speaker: Zbigniew Jelonek (IMPAN) 11:00–12:00, IMPAN 403
A'Campo space: construction and applications.
Speaker: Tomasz Pełka (MIMUW)13:30–14:30, IMPAN 403
Nov 22 (impanga 461)
Degree of the subspace variety
Speaker: Pierpaola Santarsiero (University of Bologna) 11:00–12:00, IMPAN 403
Dec 06 (impanga 462)
Free plane curves in algebraic geometry
Speaker: Piotr Pokora (UKEN Kraków) 11:00–12:00, Kraków branch of
IMPAN, św. Tomasza 30/7 Kraków
I will present the recent developments on free
plane curves, mostly focusing on the problem of
constructing algebraic surfaces having large Picard
numbers and the so-called Numerical Terao's
Conjecture. Time permitting, I will deliver some
recent progress on Ziegler pairs of line arrangements.
Cactus scheme, catalecticant minors and singularities of secant varieties to high degree Veronese reembeddings.
Speaker: Jarosław Buczyński (IMPAN)13:30–14:30, Kraków branch of
IMPAN, św. Tomasza 30/7 Kraków
The r-th cactus variety of a subvariety X in a
projective space generalises secant variety of X and
it is defined using linear spans of finite schemes of
degree r. It's original purpose was to study the
vanishing sets of catalecticant minors. We propose
adding a scheme structure to the cactus variety and we
define it via relative linear spans of families of
finite schemes over a potentially non-reduced base. In
this way we are able to study the vanishing scheme of
the catalecticant minors. For X which is a
sufficiently large Veronese reembedding of projective
variety, we show that r-th cactus scheme and the zero
scheme of appropriate catalecticant minors agree on an
open and dense subset which is the complement of the
(r-1)-st cactus variety/scheme. As an application, we
can describe the singular locus of (in particular)
secant varieties to high degree Veronese varieties.
Based on a joint work with Hanieh Keneshlou.
Jan 10 (impanga 463)
K-stablity of Fano threefold hypersurfaces of index 1
Speaker: Livia Campo (University of Vienna) 11:00–12:00, IMPAN 403
The existence of Kaehler-Einstein metrics on
Fano 3-folds can be determined by studying lower
bounds of stability thresholds. An effective way to
verify such bounds is to construct flags of
point-curve-surface inside the Fano 3-folds. This
approach was initiated by Abban-Zhuang, and allows us
to restrict the computation of bounds for stability
thresholds only on flags. We employ this machinery to
prove K-stability of terminal quasi-smooth Fano 3-fold
hypersurfaces. This is deeply intertwined with the
geometry of the hypersurfaces: in fact, birational
rigidity and superrigidity play a crucial role. The
superrigid case had been attacked by Kim-Okada-Won. In
this talk I will discuss the K-stability of strictly
rigid Fano hypersurfaces via Abban-Zhuang Theory. This
is a joint work with Takuzo Okada.
A new technique for lower bounding the border rank
Speaker: Tomasz Mańdziuk (Texas A&M University)13:30–14:30, IMPAN 403
A fundamental problem in the theory of tensors
is establishing lower bounds for the border ranks of
explicit tensors. In the talk I will present a
technique for establishing lower bounds on border rank
based on border apolarity and I will discuss progress
concerning the border rank of the 3x3 matrix
multiplication tensor. The talk is based on a joint
work with Amy Huang, Austin Conner and J.M. Landsberg.
Jan 24 (impanga 464)
Hilbert scheme of 9 and 10 points and applications to secant varieties of pencils
Speaker: Maciej Gałązka (University of Trento) 11:00–12:00, IMPAN 403
We describe the irreducible components of the
Hilbert scheme of d points on affine space for d=9,
10. The main techniques we use are the variety of
commuting matrices and analyzing loci of local
algebras with a specific Hilbert function. As the
main consequence, we establish the equality of
cactus Grassmann and the secant Grassmann variety in
the corresponding cases. This is a joint project
with Hanieh Keneshlou and Klemen Sivic.
Harmonic polynomials and isotropic rank.
Speaker: Cosimo Flavi (MIMUW)13:30–14:30, IMPAN 403
The space of harmonic polynomials is the
kernel of the derivative action of a quadratic form
on the ring of polynomials. Each of its components
is an irreducible representation of the special
orthogonal group SOn and its structure is strictly
related to powers of quadratic forms. Every harmonic
polynomial can be written as a sum of powers of
isotropic linear forms. The minimum size of such
decompositions is called isotropic rank and we focus
on the determination of the generic isotropic rank.
This is a joint project with Cristiano Bocci,
Stefano Canino, and Enrico Carlini.
Mar 21 (impanga 465)
Hilbert scheme of points on plane curves
Speaker: Yuze Luan (IMPAN) 11:00–12:00, IMPAN 403
Denote a (possibly non-reduced, singular)
plane curve by C. The irreducible components of the
Hilbert scheme of n points on C are indexed by
partitions of n; all have dimension n; and their
multiplicities are given as a polynomial of the
parts of the corresponding partitions. We also
classify the irreducible components of the n, n+1
nest Hilbert scheme of points on the curve C. All
the components have the same dimension n+1 and are
indexed by partitions of n satisfying specific
combinatorial conditions.
Homotopy theory of schemes through the lens of condensed mathematics
Speaker: Marcin Lara (IMPAN)13:30–14:30, IMPAN 403
In this talk I will explain how the theory of
condensed mathematics allows one to revisit the
(étale) homotopy type of a scheme (going back to the
works of Grothendieck and Artin--Mazur) and work
with more general coefficients. I will mention some
benefits of this approach as well as some quirks.
The familarity with the condensed mathematics or the
pro-étale topology is not assumed: I will recall
some useful facts and keep the presentation on a
more intuitive level. This is based on a larger
collaborative project.
Mar 28 (impanga 466)
On the exceptional locus of O’Grady’s nonsymplectic resolutions
Speaker: Luigi Martinelli (Bielefeld University) 11:00–12:00, IMPAN 403
In this talk, we focus on some singular
moduli spaces of sheaves on a K3 surface. More
precisely, for any integer n > 1, we consider the
moduli space M(n) associated with the Mukai vector
2(1,0,1-n). Looking for new deformation classes of
hyper-Kähler manifolds, O’Grady constructed an
explicit resolution of every M(n). O’Grady’s
resolution is crepant and does give a hyper-Kähler
manifold only if n=2. If n>2, it turns out that
no crepant resolution exists for M(n), but one may
still look for a categorical crepant resolution. We
will report on the preliminary step in this
direction, which consists in a geometric analysis of
O’Grady’s resolution and of its exceptional locus.
A functorial approach to the stability of vector bundles
Speaker: Dario Weissmann (IMPAN)13:30–14:30, IMPAN 403
On a smooth projective curve the locus of
stable bundles that remain stable on all etale
Galois covers prime to the characteristic defines a
big open in the moduli space of stable bundles. In
particular, the bundles trivialized on some etale
Galois cover of degree prime to the characteristic
are not dense - in contrast to a theorem of Ducrohet
and Mehta stating that all etale trivializable
bundles are dense in positive characteristic. As an
application we study the closure of the prime to p
etale trivializable vector bundles. This closure is
closely related to a stratification of the moduli
space of stable vector bundles via their
decomposition behaviour on Galois covers of degree
prime to the characterstic. We obtain mostly sharp
dimension estimates for the closure of the prime to
p etale trivializable bundles as well as the
decomposition strata.