Algebra
and Geometry Seminar




Abstracts of talks 2016/2017

14
September 2016
Speaker (Institution)
Title
Abstract
Erdal Emsiz
(Pontificia Universidad Católica
de Chile)
Bethe
Ansatz for a finite qboson
system with boundary interactions
We construct an orthogonal basis of algebraic Bethe
Ansatz eigenfunctions for a finite qboson
system endowed with diagonal openend boundary interactions. The eigenfunctions are constructed by means of Sklyanin’s Quantum Inverse Scattering Method
formalism for open systems (based on the Quantum YangBaxter Equation
and the Reflection Equation). We show that these eigenfunctions
can be expressed explicitly in terms of Macdonald's spherical function
associated with the finite nonreduced root system BC_{n}
(also known as hyperoctahedral
HallLittlewood polynomials). We will also indicate how the above
model arises from the representation theory of a double affine Hecke algebra at critical level.
28
September 2016
Speaker (Institution)
Title
Abstract
Robin Walters (NEU Boston)
The
BernsteinSato polynomial of the Vandermonde
determinant and the Strong Monodromy Conjecture
The BernsteinSato polynomial, or bfunction, is an
important invariant in singularity theory, which is difficult to
compute in general. We describe a few different results towards
computing the bfunction of
the Vandermonde determinant X.
In 1989, Eric Opdam computed the bfunction
of
a related polynomial, and we use his result to produce a lower bound
for the bfunction of X. We use this lower bound to prove a conjecture of Budur,
Mustata, and Teitler
for the case of Weyl hyperplane arrangements, proving the Strong Monodromy Conjecture in this case. Secondly,
we use a result of Narvaez Macarro on the
duality of some Dmodules to show that the roots of this bfunction
of
X are symmetric about 1.
Finally, we use results about jumping coefficients together with Kashiwara's proof that the roots of a bfunction
are
rational in order to prove an upper bound for the bfunction of X, which we
conjecture is the correct formula.
Alberto Cattaneo (Zürich)
Perturbative
BVBFV theories on manifolds with boundary
According to Segal and Atiyah,
a quantum field theory on manifolds with boundary should be thought of
as, roughly speaking, the assignment of a vector space (space of
states) to the boundary and an element thereof (the state or the
evolution operator) to the bulk, in a way that is compatible with
gluing.
In this talk (based on joint work with P. Mnev and N. Reshetikhin) I
will describe how this has to be reformulated when working in
perturbation theory. In particular, I will discuss the perturbative
quantization of gauge theories on manifolds with boundary. It turns
out that, under suitable assumptions, the bulk symmetries, treated in
the BV formalism, naturally give rise to a cohomological
description of the reduced phase space (BFV formalism) in a correlated
way that can be quantized.
Rune Haugseng (Copenhagen)
The AKSZ
construction in derived algebraic geometry as an extended TQFT
The AKSZ construction, as implemented by PantevToënVaquiéVezzosi
in the context of derived algebraic geometry, gives a symplectic
structure on the derived stack of maps from an oriented compact
manifold to a symplectic derived stack. I
will describe how this gives rise to a family of extended topological
field theories valued in higher categories of symplectic
derived stacks, with the higher morphisms given by a notion of higher
Lagrangian correspondences.
This is joint work in progress with Damien Calaque and Claudia
Scheimbauer.
Martin A. Moskowitz (CUNY)
The index
of a lattice in its normalizer in certain Lie groups
We first deal with the rather general situation in which
the only positive conclusion is that [N_{G}(?):?]
is finite. Then we briefly discuss Hurwitz' theorem concerning compact
Riemann surface S of genus
g, where the analogue of
this index is estimated by 84g1
and where G=SL(2,R) and ? is the
fundamental group of S.
Then we turn to a construction and examination of a family of two step
simply connected solvable groups each of which contains many lattices
where one can calculate or estimate this index.
Nikolai Gordeev (Russian state pedagogical university)
Word maps
of simple algebraic groups
Let F_{m}
be the free group of rank m.
Then for any word w=w(x_{1},...,x_{m})? F_{m} and for any group G
one can define the word map G^{m}
? G by the formula: (g_{1},…,g_{m})
? w(g_{1},…,g_{m}). Word maps have been intensely studied over at least two
past decades in various
contexts.
In this talk we deal with the case where G=G(K) is the group of Kpoints
of
a simple linear algebraic group G
defined over a field K.
Here we consider the problem of surjectivity
of word maps and also some related questions.
9 November 2016 – Aula Consiglio, 15:0016:00
Viveca
Erlandsson (Aalto)
Counting curves on surfaces
Let S
be a surface of genus g
and r punctures, and c a (not
necessarily simple) closed curve on S.
Consider the set of curves in the mapping class group orbit of c.
Recently, Mirzakhani has shown that when S
is endowed with a hyperbolic metric, the cardinality of the subset
defined by the curves with length bounded by L
is asymptotic to a constant times L^{6g6+2r},
as L grows. In this talk
we discuss the same problem but where the length is measured with
respect to any Riemannian metric on the surface, as well as with
respect to the word length.
16 November 2016 – Aula Consiglio,
14:30
Florian Schätz (Luxembourg)
The
Eulerian idempotent in the lexicographic basis
The Eulerian idempotent is a canonical map from the free
algebra on generators x_{1},...,x_{n} to the space of Lie words
on x_{1},...,x_{n}.
Besides its importance in Lie theory, it also plays a central role in
the theory of linear ODEs, due to its relation to the Magnus
expansion. I will report on joint work in progress with Ruggero
Bandiera (“Sapienza” University of Rome),
whose main goal is to establish a (to the best of our knowledge) new
formula for the Eulerian idempotent. The derivation of this formula
relies on the notion of, and computations within, preLie algebras.
16 November 2016
– Aula Consiglio, 15:45
Valerio
Toledano
Laredo (NEU)
Yangians, quantum loop algebras and elliptic quantum groups
The Yangian Yg
and quantum loop algebra U_{q}(Lg)
of a complex semisimple Lie algebra g share very many similarities, and were long thought to
have the same representations, though no precise relation between them
existed until recently.
I will explain how to construct a faithful functor
from the finitedimensional representations of Yg
to those of U_{q}(Lg).
The functor is entirely explicit, and
governed by the monodromy of the abelian
difference equations determined by the commuting fields of the Yangian. It yields a meromorphic,
braided KazhdanLusztig equivalence
between finitedimensional representations of the Yg
and of U_{q}(Lg).
A similar construction yields a faithful functor
from representations of U_{q}(Lg)
to those of the elliptic quantum group E_{q,t}(g) corresponding to g. This allows in particular a classification of
irreducible finitedimensional representations of E_{q,tau}(g),
which was previously unknown.
This is joint work with Sachin
Gautam (Perimeter Institute & Ohio
State).
23 November 2016
Niels Kowalzig (Roma
“Sapienza”)
When Ext
is a BatalinVilkovisky algebra
We show under what conditions the complex computing
general Extgroups carries
the structure of a cyclic operad such
that Ext becomes a BatalinVilkovisky
algebra. This is achieved by transferring cyclic cohomology
theories for the dual of a (left) Hopf algebroid to the complex in question, which
asks for the notion of contramodules
introduced along with comodules by
EilenbergMoore half a century ago. Another crucial ingredient is an
explicit formula for the inverse of the HopfGalois
map on the dual, by which we illustrate recent categorical results and
answering a longstanding open question. As an application, we prove
that the Hochschild cohomology
of an associative algebra A is BatalinVilkovisky if A itself is
a contramodule over its enveloping
algebra A?A^{op}. This is, for example, the case for symmetric algebras
and Frobenius algebras with semisimple
Nakayama automorphism. We also recover
the construction for Hopf algebras.
Özlem Imamoglu
(ETH)
Modular cocycles and linking numbers
It is known that the 3manifold SL(2,Z)\SL(2,R) is
diffeomorphic to the complement of the trefoil knot in S^{3} . E. Ghys showed that the
linking number of the trefoil knot with a modular knot is given in
terms of the classical Dedekind symbol. The Dedekind symbol arose
historically in the transformation formula of the logarithm of
Dedekind’s eta function under SL(2,Z). In
this talk I will give a generalization of the Dedekind symbol
associated to a fixed modular knot and show its relation to the
linking numbers of two modular knots. This is joint work with W. Duke
and A. Toth.
7 December 2016 – Aula Consiglio,
15:0016:00
Damian Brotbek (Strasbourg)
On the hyperbolicity of general hypersurfaces
A smooth projective variety over the complex numbers is
said to be (Brody) hyperbolic if it doesn't contain any entire curve.
Kobayashi conjectured in the 70's that general
hypersurfaces of sufficiently large degree in P^{N} is hyperbolic. This conjecture was only proven recently
by Siu.
The purpose of this talk is to present a new proof of
this conjecture. The main idea of the proof, based on the theory of
jet differential equations, is to establish that a stronger property,
open in the Zariski topology, is satisfied for suitable deformations
of Fermat type hypersurfaces.
14 December 2016
– Aula Consiglio, 14:30
Sara
Perna
(Roma “Sapienza”)
Siegel
modular forms: some geometric applications
In this talk I will present some of the results of my
Ph.D. thesis.
I will show some geometric applications of the theory of
Siegel modular forms.
The first result I will present is a generalization of
Mukai's result about the existence of a degree 8 automorphism of the Igusa
quartic, a compactification of a moduli space of principally polarized
abelian varieties with some extra structure.
Although I will mostly talk about Siegel modular forms as
tools for the study of complex Abelian varieties and their moduli
spaces, they also represent an interesting and rich subject by
themselves in the theory of automorphic forms. Indeed I will give a
new construction of vectorvalued modular forms from scalarvalued
ones involving some multilinear algebra constructions. As an
application I will show the identity of two remarkable spaces of
vectorvalued modular forms. Finally I will give a new
characterization of the locus of decomposable principally polarized
abelian varieties through the image of the smooth 2torsion
points
on the theta divisor.
14 December 2016
– Aula Consiglio, 15:00
Paolo
Arcangeli
(Roma “Sapienza”)
A
CamachoSadtype index theorem for a couple of holomorphic selfmaps
Let M be an ndimensional complex
manifold and f,g two distinct holomorphic selfmaps of M. Suppose that f and g coincide on a globally
irreducible compact hypersurface S
of M. If one of the two
maps is a local biholomorphism in a
neighborhood of the regular part S'
of S and, if needed, S' sits
into M in a particular nice
way, then it is possible to define a 1dimensional
holomorphic
(possibly singular) foliation on S' and a partial holomorphic connection on the normal bundle of S' in M.
As a consequence, one can localize the (n1)th power of the first Chern
class of the line bundle [S]
on M canonically induced by S
and thus get an index theorem.
21 December 2016
– Aula Consiglio, 15:0015:45
Matteo
Braghiroli (Roma “Sapienza”)
Holomorphic
curves and covariantly constant spinors
on K3 surfaces
In this talk, I will present the main results of my PhD
thesis.
Let ? be a
Riemann surface and M a
compact, simply connected hyperKähler
manifold of real dimension 4, and let X
be an isometric immersion of ?
in M.
From a covariantly constant
spinor one can costruct a complex
structure on M that makes
it a K3 surface. Then, what I prove is that X
is a holomorphic map with respect to such structure on M
if and only if the spinor is annihilated by some projector associated
to X. From this fact we
recover the identification, wellknown in supersymmetric string
theory, of BPS states on a K3 with holomorphic vertical curves on its
twistor family.
11 January 2017 –
Aula Consiglio, 14:0014:45
Sergio
Ciamprone (Roma “Sapienza”)
Certain
braided weak Hopf C*algebras
associated to modular categories
The talk is a presentation of my Ph.D. thesis.
Semisimple quotient
categories arising from the representation theory of DrinfeldJimbo
quantum groups at roots of unity play a crucial role in many areas of
physics and mathematics. In this talk we will show how one can
construct in the type A case and for certain
roots of unity a family of quantum groupoids
whose representation theory is equivalent to these categories. The
construction was originally inspired by some work for sl_{2} of the early 90s in the physics literature and makes use
of a Hilbert space construction associated to the quotient category
due to Wenzl in the late 90s. These groupoids are weak Hopf
C*algebras, in a sense which is new in the literature. In light of
these facts, a generalization of the HaringOldenburg's reconstruction
theorem will be given. Finally, the quantum groupoids
introduced above will be presented by generators and relations in some
special cases. Most of the talk is based on a joint work with C. Pinzari.
Daniele Valeri (Tsinghua)
Algebraic
aspects of the ODE/IM correspondence
The ODE/IM correspondence is a conjectural and surprising
link between integrable quantum field
theories and monodromy data of certain
linear analytic ODEs associated to affine KacMoody
algebras.
In the present talk, I will briefly introduce the physical origin and
will describe the recent proof of the correspondence for the ground
state of the integrable model obtained in
collaboration with D. Masoero and A.
Raimondo (arXiv:1501.07421, arXiv:1511.00895). Then I will give some insights about the relation
between the correspondence for the excited states of the integrable
model and some aspects of the representation theory of Walgebras.
25 January 2017 – Aula Consiglio,
15:00
Selim Ghazouani (ENS Paris)
The
complex hyperbolic geometry of moduli spaces of flat tori
Generalizing an idea of Thurston, Veech
defines homogeneous structures on several moduli spaces of flat
surfaces with cone singularities. The specific case of tori provides
natural (noncomplete) complex hyperbolic structures of certain
complex manifolds.
We provide an interpretation of the metric completion of
these manifolds in terms of degenerations of the underlying flat
structures. This leads to
 on one hand, a natural compactification of the
associated moduli spaces of flat surfaces;
 on the other hand, a construction of complex hyperbolic
conemanifolds of finite volume, whose holonomy
are in a finite number of cases an arithmetic lattice.
This is a joint work with Luc Pirio.
1
February 2017
Speaker (Institution)
Title
Abstract
Vincent Pilaud (CNRS &
LIX, Polytechnique Paris)
Permutrees
Permutrees are
oriented and labeled trees satisfying certain local conditions around
each vertex. They gather under the same roof several combinatorial
families, including permutations, binary trees, and binary sequences.
The talk will present their combinatorial, geometric and
algebraic structure. In particular, we will show:
* the permutree lattice, which generalizes the weak
order on permutations, the Tamari lattice on binary trees, and the
bool an lattice on binary sequences;
* the permutreehedron, which generalizes the permutahedron, the associahedron,
and the cube;
* the permutree Hopf
algebra, which generalizes the MalvenutoReutenauer
Hopf algebra on permutations, the LodayRonco
Hopfalgebra on binary trees, and Solomon's
descent Hopf algebra on binary sequences.
This talk is based on a joint work with Viviane Pons
(LRI, Université Paris Sud).
Michal Kapustka (Zürich)
EPW cubes
and their degenerations
We will introduce a new construction of a complete family
of polarized IHS sixfolds of K3^{[3]}
type, of BeauvilleBogomolov degree q=4
and divisibility 2. The
construction is parallel to that of double EPW sextics
and the obtained varieties are called double EPW cubes. Studying their
degenerations we shall also provide a construction of a 19 dimensional
family of IHS fourfolds of K3^{[2]}
type, with q=4,
representing such manifolds admitting additionally nonsymplectic
involutions. The latter construction will be used to complete the
classification of IHS fourfolds of K3^{[2]}
type with automorphisms. In particular, we shall provide
geometric realisations of maximal dimensional families of IHS
fourfolds of K3^{[2]} type with involutions having invariant
lattices: U(2), U(2)+E_{8}(2) and U(2)+D_{4}(1).
The first part is joint work with Iliev,
G. Kapustka, Ranestad
and the second with Camere, G. Kapustka
and Mongardi.
22
February 2017
Speaker (Institution)
Title
Abstract
1 March 2017 – Aula Consiglio,
15:00
Alessandro
Ghigi (Pavia)
Stabilità
di
misure su varietà di Kähler
Presenterò
una
versione dell'applicazione momento valida per azioni di gruppi
riduttivi su spazi topologici privi di una struttura differenziabile.
Mostrerò
che
i criteri numerici per la stabilità valgono in questa generalità.
Infine considererò una azione di un gruppo riduttivo su una varietà kähleriana M
e mostrerò che la versione dell'applicazione momento appena descritta
si applica all'azione indotta sulle misure su M.
In
questo
modo si ottiene un criterio per la stabilità di una misura rispetto a
questa azione.
(Lavoro
in
collaborazione con Leonardo Biliotti.)
8 March 2017 – Aula Consiglio, 15:0016:00
Michèle Vergne (Paris 7)
Graded equivariant Todd class and the equivariant
index of elliptic operators.
Let D be an
elliptic operator acting on a compact manifold M. If G is a torus acting
on M,
with weight lattice ? and D is Ginvariant,
let m(?,D) be the dimension of
the space of solutions of D
with eigenvalue ?.
With De ConciniProcesi, we
determined the function ? ?
m(?) in terms of a multispline
function on the vector space generated by ?.
I will give a more precise formula for m(?)
in terms of the graded equivariant Todd
class.
Furthermore, if L
is a line bundle on a compact complex manifold, I will give an
asymptotic formula for the distribution ?
h^{0}(M,L^{k})(?)?_{?}/k
in terms of the graded equivariant Todd
class.
This generalizes the asymptotic EulerMac Laurin
formula for evaluating Riemann sums on polyhedra.
15 March 2017 – Aula Consiglio, 15:0016:00
Bruno
Klingler (Jussieu)
Chern's conjecture for special affine manifolds
An affine manifold X
(in the sense of differential geometry) is a differentiable manifold
admitting an atlas of charts with value in an affine space with
locally constant affine change of coordinates. Equivalently, it is a
manifold admitting a flat torsion free connection on its tangent
bundle. Around 1955 Chern asked if there
is any topological obstruction to the existence of an affine structure
on a compact manifold X. He conjectured that the Euler characteristic
e(TX) of any compact affine
manifold has to vanish. I will discuss this conjecture and a proof
when X is special affine (i.e. X is affine and moreover admits a parallel volume form).
Surprisingly (or not), the proof relies on algebraic methods coming
from hypercomplex geometry.
15 March 2017 – Aula Consiglio,
16:1517:15 – Joint with Mathematical Physics seminar
Guo Chuan Thiang
(Adelaide)
The
differential topology of semimetals
Abstract
29 March 2017 – Aula Consiglio,
15:0016:00 – Talk
cancelled!
5 April 2017 – Aula Consiglio, 15:00
Dmitri Panov (KCL)
Real line
arrangements with Hirzebruch property
A line arrangement of 3n lines in CP^{2} satisfies Hirzebruch
property if each line intersect others in n+1
points. Hirzebruch asked if all such
arrangements are related to finite complex reflection groups. We give
a positive answer to this question in the case when the line
arrangement in CP^{2} is real, confirming that there exist exactly four such
arrangements.
12 April 2017 – Aula Consiglio, 15:00
Fëdor
Bogomolov (NYU/HSE)
Symmetric
tensors and the geometry of subvarieties
of P^{N}
I will discuss the relation between the existence of
symmetric tensors with coefficients on smooth subvarieties
in a projective space with the properties of its tangent maps. For
subvarieties of small codimension the conjecture is that the existence
of sections in S^{m}(?^{1}?O(1)) for m?0 is equivalent to the existence of an embedding into a
union of quadrics.
19 April 2017 – Aula Consiglio,
15:00
Robert Auffarth (Universidad
de Chile)
Galois embeddings of abelian varieties and a
question raised by EkedahlSerre
For a smooth projective ndimensional variety X?P^{N}, let W be a
linear subspace of P^{N} of dimension Nn1
that is disjoint from X and
let ?_{W}:X?P^{N} be the linear projection associated to W.
A natural question to ask is: when does this projection
induce a Galois extension of function fields?
We will address this question in the case that X
is an abelian variety. Moreover, we will relate this discussion to a
question asked by Ekedahl and Serre
on Jacobian varieties that are isogenous
to the product of elliptic curves.
26 April 2017 – Aula Consiglio, 15:00
Stéphane Druel (CNRS
& Grenoble)
Singular
spaces with trivial canonical class
The BeauvilleBogomolov
decomposition theorem asserts that any compact Kähler
manifold with numerically trivial canonical bundle admits an étale
cover that decomposes into a product of a torus, an irreducible,
simplyconnected CalabiYau, and
holomorphic symplectic manifolds. With
the development of the minimal model program, it became clear that
singularities arise as an inevitable part of higher dimensional life.
I will present recent work in which we partly extend the
BeauvilleBogomolov decomposition theorem
to the singular setting.
3 May 2017 – Aula Consiglio, 15:00
Emanuele
Macrì
(NEU)
Derived
categories of cubic fourfolds and
noncommutative K3 surfaces
The derived category of coherent sheaves on a cubic
fourfold has a subcategory which can be thought as the derived
category of a noncommutative K3 surface. This subcategory was studied
recently in the work of Kuznetsov and
AddingtonThomas, among others. In this talk, I will present joint
work in progress with Bayer, Lahoz, Stellari and partially with Nuer, Perry, on
how to construct Bridgeland stability
conditions on this subcategory. This proves a conjecture by Huybrechts,
and it allows to start developing the moduli theory of semistable
objects in these categories, in an analogue way as for the classical
Mukai theory for (commutative) K3 surfaces. I will also discuss a few
applications of these results.
Daniel
LabardiniFragoso (UNAM)
Algebras
associated to surfaces with orbifold
points
FeliksonShapiroTumarkin have shown that surfaces with marked
points and orbifold points of order 2
give rise to cluster algebras. They have done so by associating skewsymmetrizable matrices to the triangulations
of such surfaces, and by showing that flips of triangulations are
compatible with FominZelevinsky's
mutations of matrices. In this talk I will sketch a construction of
'species with potential' that Jan Geuenich
and myself have given for these triangulations in the hope of
producing a representationtheoretic approach to the corresponding
skewsymmetrizable cluster algebras
similar to the approach given by DerksenWeymanZelevinsky
for skewsymmetric cluster algebras via quiver representations.
17 May 2017 – Aula Consiglio, 15:00
Edoardo
Sernesi (Roma 3)
Syzygy
schemes of a canonical curve
It is possible to associate certain "syzygy schemes" to
the minimal resolution of a projective curve. Not much is known about
them.
I will give an overview of known results in the case of
canonical curves and report on recent results obtained in
collaboration with M. Aprodu and A.
Bruno.
24 May 2017 – Aula Consiglio, 15:0016:00
Emmanuel Letellier (Paris 7)
Computing
the Poincaré polynomial of character
varieties
In this talk I will review some
work with Hausel and
RodriguezVillegas on the computation of the Poincaré
polynomial of character varieties (moduli space of representations of
fundamental group of punctured Riemann surfaces into GL(n,C)) using arithmetic
geometry and the character table of GL(n)
over
finite fields.
31 May 2017 – Aula Consiglio,
15:0016:00
Jerzy Weyman (UConn)
Finite
free resolutions and KacMoody Lie
algebras
Let us recall that a format (r_{n},…,r_{1})
of a free complex F_{?}=[0?F_{n}?F_{n1}?…?F_{0}?0]
over a commutative Noetherian ring R
is the sequence of ranks r_{i}_{
}of the ith
differential d_{i}.
We will assume that rk(F_{i})=r_{i}+r_{i+1}.
We say that an acyclic complex
F^{gen}_{
}of a given format over a given ring R^{gen}^{
}is generic if for
every complex G_{?}
of this format over a Noetherian ring S
there exists a homomorphism f:
R^{gen}?S such that G=F^{gen}?_{Rgen}S.
For complexes of length 2 the existence of the generic acyclic complex was established by Hochster and Huneke
in the 1980's. It is a normalization of the ring giving a generic
complex (two matrices with composition zero and rank conditions).
I will discuss the ideas going into the proof of the
following result.
Associate to a triple of ranks (r_{3},r_{2},r_{1}) a triple (p,q,r)=(r_{3}+1,r_{2}1,r_{1}+1).
Associate to (p,q,r)
the graph T_{p,q,r}
(three arms of lengths p1,
q1, r1
attached to the central vertex). Then there exists a Noetherian
generic ring R^{gen}
for this format if and only if T_{p,q,r} is a Dynkin
graph. In other cases one can construct in a uniform way a
nonNoetherian generic ring R^{gen},
which deforms to a ring carrying an action of the KacMoody
Lie
algebra corresponding to the graph T_{p,q,r}.
7
June 2017  Aula Consiglio, 15:0016:00
Giovanni Cerulli Irelli (Roma "Sapienza")
Cellular
decomposition of quiver Grassmannians
We show that every quiver Grassmannian associated with a
representation of a quiver Dynkin or affine admits a cellular
decomposition. We also show that quiver Grassmannians associated with
rigid representations of an arbitrary acyclic quiver have property
(S).
This is a joint project (still in progress) with F.
Esposito, H. Franzen and M. Reineke.
14 June 2017 –
Aula Consiglio, 15:0016:00
Nikolaos Tziolas (Cyprus)
Automorphisms of smooth canonically polarized surfaces in positive
characteristic
Let X be a
smooth canonically polarized surface defined over an algebraically
closed field of characteristic p>0. In this talk I will present
some results about the geometry of X
in the case when the automorphism scheme
Aut(X) of X is not smooth, or
equivalently X has
nontrivial global vector fields.
This is a
situation that appears only in positive characteristic and is
intimately related to the structure of the moduli stack of canonically
polarized surfaces in positive characteristic because the smoothness
of the automorphism scheme is the
obstruction for the moduli stack to be DeligneMumford,
something
that is always true in characteristic zero but not in general in
positive characteristic. One of the results that will be presented in
this talk is that smooth canonically polarized surfaces with nonsmooth
automorphism scheme and “small” invariants
are algebraically simply connected and uniruled.
14 June 2017 –
Aula TBA, 16:0017:00
Stephane
Gaussent (St. Etienne)
A
Macdonald formula for KacMoody groups
In this talk, I will report on a joint work with Nicole BardyPanse and Guy Rousseau.
The Macdonald formula that will be discussed is the one giving the image of the Satake isomorphism between the spherical Hecke algebra and the algebra of Winvariant functions on the coweight lattice of a maximal torus in a KacMoody group over a local field. To establish the formula, on the one hand, we use the action of the affine IwahoriHecke algebra defined via its BernsteinLusztig presentation. On the other hand, we compute the image of the Satake isomorphism using Hecke paths in the standard apartment of the masure associated to the situation, where the masure is some generalization of the BruhatTits building.
I will start by recalling some classical facts about the
theory for simple algebraic groups and then move on to the general
setting of KacMoody groups over local fields.
Tuesday 20 June
2017 – Aula Consiglio, 14:3015:30
Frédéric Campana (Lorraine)
Birational
stability of the orbifold cotangent bundle
We show that a foliation on a projective complex manifold is algebraic with rationally connected (closure of) leaves exactly when its minimal slope with respect to some movable class is positive. This extends and strengthens former classical results by Y. Miyaoka and BogomolovMcQuillan. Applications to foliations, hyperbolicity (a converse to a result of J.P. Demailly) and moduli will be mentioned.
This is a joint work with Mihai Paun, partly based on a former joint work with T. Peternell.
21 June 2017 –
Aula Consiglio, 15:0016:00
Bart
Van
Steirteghem (CUNY)
Momentum
polytopes of multiplicity free Hamiltonian manifolds
Generalizing T. Delzant's classification of toric
symplectic manifolds, F. Knop has shown that multiplicity free
Hamiltonian manifolds are classified by their momentum polytope and
generic isotropy group.
In this talk I will explain how the theory of (smooth affine)
spherical varieties can be used to give a combinatorial
characterization of the momentum polytopes of these manifolds.
This is joint work with G. Pezzini.
Radu Laza (SUNY at Stony Brook)
Some
remarks on degenerations of hyperkähler manifolds
The key tool for understanding degenerations of K3
surfaces is the KulikovPerssonPinkham theorem (a semistable
degeneration of K3 surfaces can be modified to have trivial canonical
bundle). Recent advances in the minimal model program (with essential
further contributions from Fujino) give an analogous result on higher
dimensional hyperkähler
manifolds. In this talk, I will explore some geometric consequences of
this result (e.g. a simplification of some proofs of deformation type
for certain hyperkähler
constructions, and some results on the dual complex of a semistable
degeneration of hyperkählers).
This is a report on joint work with J. Kollár, G. Saccà, and C.
Voisin.
Fosco Loregian (SISSA)
Homotopical
algebra is not concrete
We generalize Freyd's wellknown result that "homotopy is
not concrete" offering a general method to show that under certain
assumptions on a model category M its homotopy category
ho(M) cannot be concrete with respect to the universe
where M is assumed to be locally small. This result is
part of an attempt to understand more deeply the relation between
(some parts of) set theory and (some parts of) abstract homotopy
theory.
12 July
2017
Speaker (Institution)
Title
Abstract
19 July
2017
Speaker (Institution)
Title
Abstract