Algebra and Geometry Seminar



Abstracts of talks 2016/2017



14 September 2016

Speaker (Institution)






21 September 2016

Erdal Emsiz (Pontificia Universidad Católica de Chile)

Bethe Ansatz for a finite q-boson system with boundary interactions


We construct an orthogonal basis of algebraic Bethe Ansatz eigenfunctions for a finite q-boson system endowed with diagonal open-end boundary interactions. The eigenfunctions are constructed by means of Sklyanin’s Quantum Inverse Scattering Method formalism for open systems (based on the Quantum Yang-Baxter 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 non-reduced root system BCn (also known as hyperoctahedral Hall-Littlewood 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)







5 October 2016

Robin Walters (NEU Boston)

The Bernstein-Sato polynomial of the Vandermonde determinant and the Strong Monodromy Conjecture


The Bernstein-Sato polynomial, or b-function, is an important invariant in singularity theory, which is difficult to compute in general. We describe a few different results towards computing the b-function of the Vandermonde determinant X. In 1989, Eric Opdam computed the b-function of a related polynomial, and we use his result to produce a lower bound for the b-function 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 D-modules to show that the roots of this b-function of X are symmetric about -1. Finally, we use results about jumping coefficients together with Kashiwara's proof that the roots of a b-function are rational in order to prove an upper bound for the b-function of X, which we conjecture is the correct formula.




12 October 2016

Alberto Cattaneo (Zürich)

Perturbative BV-BFV 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.



19 October 2016

Rune Haugseng (Copenhagen)

The AKSZ construction in derived algebraic geometry as an extended TQFT

The AKSZ construction, as implemented by Pantev-Toën-Vaquié-Vezzosi 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.




26 October 2016 – Room H

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 [NG(?):?] 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 84g-1 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.



2 November 2016

Nikolai Gordeev (Russian state pedagogical university)

Word maps of simple algebraic groups


Let Fm be the free group of rank m. Then for any word w=w(x1,...,xm)? Fm and for any group G one can define the word map Gm ? G by the formula: (g1,…,gm) ? w(g1,…,gm). 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 K-points 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, 15:00-16:00

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 L6g-6+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 x1,...,xn to the space of Lie words on x1,...,xn. 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, pre-Lie 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 Uq(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 finite-dimensional representations of Yg to those of Uq(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 Kazhdan-Lusztig equivalence between finite-dimensional representations of the Yg and of Uq(Lg).

A similar construction yields a faithful functor from representations of Uq(Lg) to those of the elliptic quantum group Eq,t(g) corresponding to g. This allows in particular a classification of irreducible finite-dimensional 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 Batalin-Vilkovisky algebra


We show under what conditions the complex computing general Ext-groups carries the structure of a cyclic operad such that Ext becomes a Batalin-Vilkovisky 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 Eilenberg-Moore half a century ago. Another crucial ingredient is an explicit formula for the inverse of the Hopf-Galois map on the dual, by which we illustrate recent categorical results and answering a long-standing open question. As an application, we prove that the Hochschild cohomology of an associative algebra A is Batalin-Vilkovisky if A itself is a contramodule over its enveloping algebra A?Aop. This is, for example, the case for symmetric algebras and Frobenius algebras with semisimple Nakayama automorphism. We also recover the construction for Hopf algebras.




30 November 2016

Özlem Imamoglu (ETH)

Modular cocycles and linking numbers


It is known that the 3-manifold SL(2,Z)\SL(2,R)  is diffeomorphic to the complement of the trefoil knot in S3 . 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, 15:00-16:00

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 PN 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 vector-valued modular forms from scalar-valued ones involving some multi-linear algebra constructions. As an application I will show the identity of two remarkable spaces of vector-valued modular forms. Finally I will give a new characterization of the locus of decomposable principally polarized abelian varieties through the image of the smooth 2-torsion points on the theta divisor.



14 December 2016 – Aula Consiglio, 15:00

Paolo Arcangeli (Roma “Sapienza”)

A Camacho-Sad-type index theorem for a couple of holomorphic self-maps


Let M be an n-dimensional complex manifold and f,g two distinct holomorphic self-maps 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 1-dimensional 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 (n-1)-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, 15:00-15:45

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 hyper-Kähler 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, well-known in super-symmetric string theory, of BPS states on a K3 with holomorphic vertical curves on its twistor family.





11 January 2017 – Aula Consiglio, 14:00-14:45

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 Drinfeld-Jimbo 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 sl2 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 Haring-Oldenburg'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. 




18 January 2017

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 Kac-Moody 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 W-algebras.





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 (non-complete) 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 cone-manifolds 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)







8 February 2017

Vincent Pilaud (CNRS & LIX, Polytechnique Paris)



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 Malvenuto-Reutenauer Hopf algebra on permutations, the Loday-Ronco 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).




15 February 2017

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 Beauville-Bogomolov 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 non-symplectic 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)+E8(-2) and U(2)+D4(-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)







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, 15:00-16:00

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 G-invariant, let m(?,D) be the dimension of  the space of solutions of D with eigenvalue ?.

With De Concini-Procesi, 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 ? h0(M,Lk)(?)??/k in terms of the graded equivariant Todd class.

This generalizes the asymptotic Euler-Mac Laurin formula for evaluating Riemann sums on polyhedra.




15 March 2017 – Aula Consiglio, 15:00-16:00

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, 16:15-17:15 – Joint with Mathematical Physics seminar

Guo Chuan Thiang (Adelaide)

The differential topology of semimetals







29 March 2017 – Aula Consiglio, 15:00-16:00 – 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 CP2 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 CP2 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 PN


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 Sm(?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 Ekedahl-Serre


For a smooth projective n-dimensional variety X?PN, let W be a linear subspace of PN of dimension N-n-1 that is disjoint from X and let ?W:X?PN 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 Beauville-Bogomolov 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, simply-connected Calabi-Yau, 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 Beauville-Bogomolov decomposition theorem to the singular setting.




3 May 2017 – Aula Consiglio, 15:00

Emanuele Macrì (NEU)

Derived categories of cubic fourfolds and non-commutative 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 non-commutative K3 surface. This subcategory was studied recently in the work of Kuznetsov and Addington-Thomas, 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.




10 May 2017

Daniel Labardini-Fragoso (UNAM)

Algebras associated to surfaces with orbifold points


Felikson-Shapiro-Tumarkin have shown that surfaces with marked points and orbifold points of order 2 give rise to cluster algebras. They have done so by associating skew-symmetrizable matrices to the triangulations of such surfaces, and by showing that flips of triangulations are compatible with Fomin-Zelevinsky'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 representation-theoretic approach to the corresponding skew-symmetrizable cluster algebras similar to the approach given by Derksen-Weyman-Zelevinsky for skew-symmetric 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, 15:00-16:00

Emmanuel Letellier (Paris 7)

Computing the Poincaré polynomial of character varieties


In this talk I will review some  work with Hausel and Rodriguez-Villegas 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, 15:00-16:00

Jerzy Weyman (UConn)

Finite free resolutions and Kac-Moody Lie algebras


Let us recall that a format (rn,…,r1) of a free complex F?=[0?Fn?Fn-1?…?F0?0] over a commutative Noetherian ring R is the sequence of ranks ri of the i-th differential di. We will assume that rk(Fi)=ri+ri+1. We say that an acyclic  complex Fgen of a given format over a given ring Rgen is generic if for every complex G? of this format over a Noetherian ring S there exists a homomorphism f: Rgen?S such that G=Fgen?RgenS.

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 (r3,r2,r1) a triple (p,q,r)=(r3+1,r2-1,r1+1). Associate to (p,q,r) the graph Tp,q,r (three arms of lengths p-1, q-1, r-1 attached to the central vertex). Then there exists a Noetherian generic ring Rgen for this format if and only if Tp,q,r is a Dynkin graph. In other cases one can construct in a uniform way a non-Noetherian generic ring Rgen, which deforms to a ring carrying an action of the Kac-Moody Lie algebra corresponding to the graph Tp,q,r.




7 June 2017 - Aula Consiglio, 15:00-16:00

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, 15:00-16:00

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 Deligne-Mumford, 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, 16:00-17:00

Stephane Gaussent (St. Etienne)

A Macdonald formula for Kac-Moody groups


In this talk, I will report on a joint work with Nicole Bardy-Panse 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 W-invariant functions on the coweight lattice of a maximal torus in a Kac-Moody group over a local field. To establish the formula, on the one hand, we use the action of the affine Iwahori-Hecke algebra defined via its Bernstein-Lusztig 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 Bruhat-Tits 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 Kac-Moody groups over local fields.




Tuesday 20 June 2017 – Aula Consiglio, 14:30-15:30

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 Bogomolov-McQuillan. 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, 15:00-16:00

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.





28 June 2017

Radu Laza (SUNY at Stony Brook)

Some remarks on degenerations of hyperkähler manifolds


The key tool for understanding degenerations of K3 surfaces is the Kulikov-Persson-Pinkham theorem (a semi-stable 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 semi-stable degeneration of hyperkählers).
This is a report on joint work with J. Kollár, G. Saccà, and C. Voisin.




5 July 2017

Fosco Loregian (SISSA)

Homotopical algebra is not concrete


We generalize Freyd's well-known 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)







19 July 2017

Speaker (Institution)