Symposium on singularities and their topology
Date: Hannover, 1417 July 2014
Talks will take place in the main building of the University (Welfengarten 1). Room F309
Speakers include:
 Enrique Artal
 Wim Veys
 Anatoly Libgober
 Mathias Schulze
 Christian Sevenheck
 Eleonore Faber
 Mihai Tibar
 Vincent Florens
 Ursula Ludwig
 Alejandro Melle
 Duco van Straten
Talks:
Enrique Artal: On the topology of line arrangements II The invariant introduced in Florens' talk is related with some twisted intersection forms which are helpful in the study of characteristic varieties of line arrangements; this study can be extended almost wordbyword to the case of rational arrangements. This is part of joint work with Vincent Florens and Benoît GuervilleBallé 
Wim Veys: Bounds for padic exponential sums and logcanonical thresholds In joint work with Raf Cluckers, we propose a conjecture for exponential sums which generalizes both a conjecture by Igusa and a local variant by Denef and Sperber, in particular, it is without the homogeneity condition on the polynomial in the phase, and with new predicted uniform behavior. The exponential sums have summation sets consisting of integers modulo p^m lying padically close to y, and the proposed bounds are uniform in p, y, and m. We give evidence for the conjecture, by showing uniform bounds in p, y, and in some values for m. On the way, we prove new bounds for logcanonical thresholds which are closely related to the bounds predicted by the conjecture. 
Anatoly Libgober: Elliptic genus of singularities. I will discuss elliptic genus of orbifolds, elliptic genus of singularities and their iterrelation (LandauGinzburgCalabi Yau correspondence). Mathematical generalizations (corresponding to phases of N=2 theories) will also be discussed. 
Mathias Schulze: Derivations of negative degree and a generalized Euler sequence Jonathan Wahl gave the following cohomological characterization of projective space: Let X be a smooth complex projective variety and L an ample line bundle on X. If the tangent sheaf 
Christian Sevenheck: Hyperplane sections of free divisors and discriminants and potential applications in mirror symmetry. About 10 years ago Buchweitz and Mond introduced socalled linear free divisors.They appear in particular as discriminants of quiver representations and yield many new examples of free divisors.The special and simplest case of the normal crossing divisor has an interpretation as LandauGinzburg model in mirror symmetry. We describe how to extend this construction to other discriminants, describe the Hodge theoretic properties of these functions and give some speculations on their appearence in mirror symmetry. 
Eleonore Faber: Noncommutative resolutions and the global spectrum of commutative rings Motivated by algebraic geometry, one studies noncommutative analogs of resolutions of singularities. In short, a noncommutative resolution of a commutative ring R is an endomorphism ring of a certain Rmodule of finite global dimension. However, it is not clear which finite values of global dimensions are possible, even for rings R of low Krulldimension. This leads us to consider the socalled global spectrum of a commutative ring, that is, the set of all possible global dimensions of endomorphism rings of CohenMacaulaymodules. In this talk we discuss several approaches to noncommutative resolutions of singularities, namely, Van den Bergh's noncommutative crepant resolution and the approach of DaoIyamaTakahashiVial. Then we study their relevance for nonnormal rings, especially the question, under which conditions a noncommutative resolution exists. In particular, we consider the problem of the existence of noncommutative resolutions of free divisors. Finally, we will address some questions connected with the global spectrum. This is joint work with H. Dao and C. Ingalls. 
Mihai Tibar On the topology of singular hypersurfaces We explain some new results based on the use of nongeneric Lefschetz pencils or on the study of nonisolated singularities, where the central role is played by the monodromy and its variation. 
Vincent Florens: On the topology of line arrangements The boundary of a tubular neighborhood of a line arrangement is a graph 3manifold, whose structure is determined by the combinatorics of the arrangement. We construct a new topological invariant of arrangements, derived from the inclusion map of this boundary manifold into the exterior. This invariant can be easily computed from a wiring diagram that encodes the braid monodromy of the arrangement. As an application, we present some new examples of Zariski pairs. Joint work with E.Artal, B.Guerville and a part with M.Marco. 
Ursula Ludwig: Witten deformation using stratified Morse functions and Gromov’s trick. The Witten deformation, proposed by Witten in the 80’s, is an analytic proof of the Morse inequalities for compact manifolds and smooth Morse functions. The proof uses the deformation of the de Rham complex via the given Morse function f : M → R. The main idea in generalising the socalled Witten deformation to singular spaces is to deform the complex of L2forms instead of the de Rham complex. In this talk I will focus on deformations using socalled admissible Morse functions. Those comprise in particular the example of stratified Morse functions in the sense of the theory developed by Goresky and MacPherson on a singular complex curve. In the beginning of the talk, I will recall the Witten deformation for smooth compact manifolds and smooth Morse functions. 
Alejandro Melle: The generalized higher order Euler characteristics

Duco van Straten: A resurgent Weylalgebra Abstract: The theory of plane curve singularities in the symplectic (p,q)plane has a natural extension to the study of a version of "noncommutative singularity theory" where one uses a formal Heisenbergalgebra with relation pqqp=h. In the talk I will describe aspects of an attempt to understand the divergences that appear naturally. 
Remke Kloosterman Using Alexander polynomials in algebraic geometry We revisit Dimca's method to compute the Alexander polynomial of a hypersurface in $\Ps^n$ with only isolated quasihomogeneous singularities. We present a variant of Dimca's method, which we use to prove several other results. First, we use this method to relate the Alexander polynomial of a plane curve with ADE singularities with the MordellWeil rank of an isotrivial fibration of hyperelliptic Jacobians. Then we show that a hypersurface with nonconstant Alexander polynomial and only isolated quasihomogeneous singularities has a non $T$smooth equianalytic deformation space. Moreover, for a finite set of points $\Sigma$ in $\Ps^n$ and an integer $m\geq n$, we give a lower bound for the degree of a form $f$ such that $f=0$ has isolated singularities and the multiplicity of $f$ at each point of $\Sigma$ is at least $m$ 
Xia Liao: normal crossing property for quasihomogeneous free divisors The notion of normal crossing divisor is fundamental in algebraic geometry. However, its definition involves a choice of local analytic coordinate system. It is a natural question to ask whether normal crossing divisors can be characterized by a purely algebraic condition. Eleonore 
Christian Gorzel: The maximizing simple sextics with an elliptic component Persson proved that the irreducible maximizing sextics are rational curves. By Yang's work, we know that there are 519 combinations of simple singularities for maximizing sextics. 
Jesse Kass: CoxeterDynkin diagrams for simple curve singularities The simple curve singularities were classified by Giusti and FrühbisKrüger, and in important cases, CoxeterDynkin diagrams were described by Alpert, Ebeling, EbelingGuseĭnZade, and Mondvan Straten. I will extend this work by describing CoxeterDynkin diagrams for all simple curve singularities. The technique demonstrates an unexpected connection between c.i. singularities in 4space and space curve singularities in 3space. 
Alexey Basaelev: Mirror symmetry for the singularities with the group action From the point of view of singularity theory mirror symmetry is the correspondence between Kyoji Saito's flat structure of a singularity and GromovWitten theory of the certain variety. This setting was generalized by physicists who have proposed an generalized mirror conjecture that involves not only a singularity but also a symmetry group of it. In the talk we present particular example of the mirror symmetry of this kind. 
Mathias Zach: The topology of CohenMacaulay codimension 2 singularities We present a way to compute the vanishing cycles of isolated CohenMacaulay codimension 2 singularities. This is done by exploiting its matrix structure to construct a second family from every deformation in which we reduce to complete intersections. 
Schedule:
Monday :
Registration from 14
Faber 15  16
van Straten 16:15  17:15
Basalaev 17:45  18:15
Tuesday:
Sevenheck 9  10
Libgober 10:30  11:30
Kloostermann 11:45  12:15
Veys 15  16
Ludwig 16:30  17:30
Conference dinner 19:00 or later
Wednesday:
Florens 9  10
Tibar 10:30  11:30
Gorzel 11:45  12:15
Artal 1516
Zach 16:30  17
Kass 17  17:30
Thursday:
Schulze 9  10
Liao 10:15  10:45
Melle 11:15  12:15
For registration or any other related question, contact Miguel Marco miguelmath.unihannover.de
Organizers:
 Wolfgang Ebeling ebelingmath.unihannover.de
 Anne Fruhbis Krueger annemath.unihannover.de
 Michael Lönne loennemath.unihannover.de
 Miguel Marco miguelmath.unihannover.de
Participants:
 Enrique Artal
 Christian Barz
 Alexey Basalaev
 Wolfgang Ebeling
 Eleonore Faber
 Vincent Florens
 Anne Fruhbis Krueger
 Patrick Graf
 Christian Gorzel
 Sabir GuseinZade
 Helmut Hamm
 Jesse Kass
 Remke Kloosterman
 Xia Liao
 Anatoly Libgober
 Wenfei Liu
 Michael Lönne
 Ignacio Luengo
 Ursula Ludwig
 Miguel Marco
 Alejandro Melle
 Julio Moyano
 Matteo Penegini
 Mathias Schulze
 Christian Sevenheck
 Duco van Straten
 Mihai Tibar
 Orsola Tommasi
 Davide Veniani
 Wim Veys
 Matthias Zach
Lodging:
This is a list of recommended hotels.
www.hotelsavoy.de
Hotel Savoy Hannover
Schlosswenderstr. 10
D30159 Hannover
Manager: Marcel Lagershausen
Phone:0049 (0) 5111674870
Fax: 0049 (0) 51116748710
email: info@hotelsavoy.de
www.hotelschlafgut.de
Hotel im Werkhof
Kniestraße 33, 30167 Hannover
Phone: 0049 511 353560
email: booking@hotelschlafgut.de
www.mith.de
Hotel Gästehaus am Herrenhäuser Garten
Herrenhäuser Kirchweg 17
30167 Hannover
url www.mith.de
email hotel@mith.de
Tel +49 (0)511 70072 0
www.loccumerhof.de
Hotel LOCCUMER HOF
GmbH & Co KG*
Kurt Schumacher Straße 14/16
30159 Hannover
Tel: +49 . 511 . 12 64  0
Fax: +49 . 511 . 13 11 92
EMail: info@loccumerhof.de