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).
To receive notifications about upcoming seminars join impanga-mailing-list@impan.pl using google account, or contact one of the organizers.
IMPANGA was founded at IMPAN in 2000 by late Piotr Pragacz. See here for information on former meetings of IMPANGA
Upcoming meeting
Jun 06 (impanga 471)
Resolution by torus actions
Speaker: Jarosław Włodarczyk (Purdue University) 11:00–12:00, IMPAN 403
Future meetings
IMPANGA will resume in October 2025.
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.
Apr 11 (impanga 467)
Symmetric schemes, superfat points and associated tensors
Speaker: Stefano Canino (MIMUW) 11:00–12:00, IMPAN 403
In a recent joint work together with M. V.
Catalisano, A. Gimigliano and M. Idà we introduce
the new class of m-symmetric schemes: an m-symmetric
scheme is a zero-dimensional subscheme X of P^n
supported at one point P and such that every line
through P intersects X with length m. In this talk
we will see some general aspects of the geometry of
these schemes with a special focus on m-superfat
points, i.e. m-symmetric schemes which are maximal
with respect to the inclusion. After that, we will
show how the knowledge of the geometry of these
schemes allows us to deduce new results on symmetric
and partially symmetric tensors. As an example, we
will see that the second osculating variety of a
Veronese surface is always contained in its fourth
secant variety.
Monodromy group of a Calabi-Yau threefold
Speaker: Tymoteusz Chmiel (UJ)13:30–14:30, IMPAN 403
Picard-Fuchs differential operator and its
monodromy representation are essential tools for
studying moduli spaces of Calabi-Yau threefolds. In
my talk I will introduce these concepts and discuss
several results concerning the monodromy group of a
one-parameter family of Calabi-Yau threefolds. In
particular, I will talk about the connection with
mirror symmetry, the field of definition of the
monodromy representation and arithmetic properties
of the monodromy group.
Apr 25 (impanga 468)
Inequalities for volume polynomials
Speaker: Mateusz Michałek (Universität Konstanz) 11:00–12:00, Kraków branch of
IMPAN
Hodge Index Theoem is a fundamental result in
algebraic geometry. It has remarkable applications
in combinatorics - by the work of June Huh it played
a key role in proving log concavity of the
coefficients of the chromatic polynomial of the
graph. Are there other inequalities in algebraic
geometry with possible applications in
combinatorics? In our talk we will report on recent
work with June Huh and Botong Wang on inequalities
coming from cohomology classes, going beyond
Lorentzian polynomials.
On Additivity of Border Rank and the Minimality of Schönhage’s Counterexample
Speaker: Filip Rupniewski (Sleepiz AG)13:30–14:30, Kraków branch of
IMPAN
Stated in 1969, the tensor rank additivity
conjecture states that the rank of a direct sum of
tensors equals the sum of the ranks of the
individual tensors. While the failure of additivity
for tensor rank remains an open problem—Shitov’s
non-constructive proof of the existence of a
counterexample contains a gap—the situation is
different for the additivity of border rank. The
smallest known counterexample, provided by Schönhage
(1981), is explicit and small enough to be written
on the blackboard. However, it is still unknown
whether this example, contained in the space
C4⊗C5⊗C7 of border rank 7, is minimal. In this talk,
I will give a brief overview of the border rank
additivity problem, highlighting the role of
Schönhage’s example. I will then discuss recent
progress aimed at determining whether it is possible
to find a smaller counterexample. This talk is based
on joint work with M. Gałązka and T. Mańdziuk.
May 9 (impanga 469)
Harmonic covers of skeleta and the different
Speaker: Art Waeterschoot (KU Leuven) 11:00–12:00, IMPAN 403
Any morphism of Berkovich’s nonarchimedean
analytic spaces is harmonic, i.e. preserves the
Laplace equation. At the level of skeleta, which are
dual intersection complexes of toroidal formal models,
one recovers harmonic morphisms of Z-affine “tropical”
complexes. The potential theory of pluricanonical
forms on such objects reveals a Riemann-Hurwitz
formula for skeleta, namely the Laplacian of the
different function coincides with the tropical
canonical divisor. I will present some applications to
arithmetic surfaces and wild quotient singularities.
SSM Thom polynomials of multisingularities
Speaker: Jakub Koncki (IMPAN)13:30–14:30, IMPAN 403
Thom polynomial is a tool used for
understanding the geometry of singular loci of maps.
To a singularity germ \eta we associate a polynomial
in infinitely many variables. Upon substituting these
variables with the Chern classes of the relative
tangent bundle of a stable map, we obtain the
fundamental class of the \eta-singular loci of the
given map. Thom polynomials have several
generalizations, including extension to
multisingularities, and polynomials that compute other
cohomological properties of the singular loci, such as
the Segre-Schwartz-MacPherson class. In the talk, I
will review these concepts and introduce the SSM-Thom
polynomials of multisingularities. I will present a
structure theorem for them that generalizes results of
Kazarian. The talk is based on a joint project with R.
Rimányi.