Weekly Bulletin

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Monday, 27 March
Time Speaker Title Location
09:30 - 10:30 Prof. Dr. Daniel Huybrechts
Universität Bonn
Conference: Cycles and Moduli
Kuznetsov's K3 category and the global Torelli theorem for cubic fourfolds
HG G 19.1 
11:00 - 12:00 Dr. Arend Bayer
The University of Edinburgh
Conference: Cycles and Moduli
Bridgeland stability on Kuznetsov components, and applications 
HG G 19.1 
Abstract: I will present a construction of stability conditions on Kuznetsov's semi-orthogonal component of derived categories of Fano threefolds, and on cubic fourfolds, along with applications to Torelli-type questions.This is based on joint work with Lahoz, Macri and Stellari, and some of the applications on joint work in progress also with Nuer and Perry.
14:30 - 15:30 Dr. Georg Oberdieck
Massachusetts Institute of Technology
Conference: Cycles and Moduli
Enumerative geometry of elliptic fibrations and modular forms 
HG G 19.1 
Abstract: Led by physics arguments Huang, Katz and Klemm conjectured that curve counting invariants of elliptic Calabi-Yau threefolds form Jacobi forms. On the mathematics side the origin of the modularity is becoming clearer. Part of the modularity arises from sheaf theory. Fourier-Mukai transforms with respect to the Poincare line bundle of the fibration yield modular constraints. The other part has origins in Gromov-Witten theory. I will explain how this philosophy leads to a proof that the generating series of Gromov-Witten invariants of the product of a K3 surface and an elliptic curve (with respect to primitive classes on the K3) is the reciprocal of the Igusa cusp form, a Siegel modular form. The sheaf theory part is joint work with Junliang Shen, the Gromov-Witten part is joint work with Aaron Pixton.
16:00 - 17:00 Dr. Dimitri Zvonkine
Institut de Mathématiques de Jussieu
Conference: Cycles and Moduli
Plugging r=0 into the space of r-th roots 
HG G 19.1 
Abstract: Consider a complex curve C endowed with line bundle L whose r-th tensor power is the trivial or the canonical line bundle. The moduli space of pairs (C,L) is a ramified covering of the moduli space Mbar_{g,n} of algebraic curves. It carries several natural cohomology classes whose projections to Mbar_{g,n} turn out to be polynomial in r. We will state several theorems and conjectures that relate the constant term of this polynomial (obtained by plugging r=0) to the Poincaré dual cohomology classes of important geometric loci in Mbar_{g,n}. This is joint work with F. Janda, R. Pandharipande, and A. Pixton.
Tuesday, 28 March
Time Speaker Title Location
09:30 - 10:30 Prof. Dr. Jérémy Blanc
Universität Basel
Conference: Cycles and Moduli
Automorphisms of P^1-bundles on rational surfaces 
HG G 19.1 
Abstract: In this talk, I will speak about the connected component of automorphisms of P^1-bundles over rational surfaces. It turns out that this study is reduced to the case of minimal rational surfaces, i.e. Hirzebruch surfaces and the projective plane. Then, one has a large family of decomposable P^1-bundles (projectivisations of decomposable P^1-bundles) and some interesting two other countable families, namely Umemura bundles and Schwarzenberger bundles. This work is done using the action of automorphisms of Hirzebruch surfaces on the moduli space of P^1-bundles on it. Joint work with Andrea Fanelli and Ronan Terpereau.
11:00 - 12:00 Dr. Stefan Schreieder
Universität Bonn
Conference: Cycles and Moduli
Generic vanishing and minimal cohomology classes on abelian fivefolds 
HG G 19.1 
Abstract: We classify generic vanishing subschemes of principally polarised abelian varieties in dimension five, showing that they exist only on Jacobians of curves and intermediate Jacobians of cubic threefolds, and confirming a conjecture of Pareschi and Popa in this case. Our result is implied by a more general statement about subvarieties of minimal cohomology class whose sum is a theta divisor. This is joint work with Casalaina-Martin and Popa.
14:30 - 15:30 Prof. Dr. Qizheng Yin
Beijing University
Conference: Cycles and Moduli
Gromov-Witten theory, cycles on moduli of K3's, and cycles on hyper-Kähler's 
HG G 19.1 
Abstract: Using virtual class techniques in Gromov-Witten theory, we obtain a decomposition of the small diagonal for the universal family of K3 surfaces, thus generalizing a theorem of Beauville and Voisin. The universal decomposition plays a key role in the proof of the Marian-Oprea-Pandharipande conjecture on the tautological ring of the moduli of K3 surfaces. This is joint work with Rahul Pandharipande. If time permits, I will also speculate possible uses of Gromov-Witten virtual classes in studying cycles on hyper-Kähler varieties. varieties, and sketch the proof. Furthermore, we will mention that for K3$^{[2]}$-type, every big and nef line bundle becomes base point free on a generic deformation.
15:15 - 16:15 Prof. Dr. Melanie Rupflin
University of Oxford
Analysis Seminar
Title T.B.A.
HG G 43 
16:00 - 17:00 Prof. Dr. Dan Petersen
University of Copenhagen
Conference: Cycles and Moduli
Tautological classes with twisted coefficients 
HG G 19.1 
Abstract: Let Mg, for g≥2, be the moduli space of smooth curves of genus g. Mumford defined a subring R(Mg) of the Chow ring CH(Mg) called the tautological ring. I explain how to associate to any irreducible algebraic representation of Sp(2g) a relative Chow motive Vλ over Mg, and how to define a tautological subgroup R(Mg,Vλ) inside CH(Mg,Vλ). Computing R(Mg,Vλ) for all λ is equivalent to computing the tautological rings of all fibered powers of the universal curve over Mg simultaneously. We are able to completely determine R(Mg,Vλ) for all λ when g is at most 4. A particular consequence is that the tautological rings of all fibered powers of the universal curve over Mg satisfy Poincaré duality in these genera. This was previously known only in genus 2. We also obtain results about conjectural failures of Poincaré duality for g ≥ 5; specifically, we can show that if certain cycles related to modified diagonals on products of very general curves are nonzero in Chow, then Poincaré duality fails in the tautological ring. (Joint with Mehdi Tavakol and Qizheng Yin.)
17:15 - 18:30 Mihaly Barasz
Nilcons
Zurich Graduate Colloquium (uzh)
What is... the prisoner's dilemma?
KO2  F 150
Wednesday, 29 March
Time Speaker Title Location
09:30 - 10:30 Prof. Dr. Kieran O'Grady
Università degli Studi di Roma "La Sapienza"
Conference: Cycles and Moduli
Moduli of hyperelliptic K3's of degree 4 and VGIT. 
HG G 19.1 
Abstract: This is a report on joint work with Radu Laza. The moduli space of hyperelliptic K3's of degree 4 may be identified with an 18-dimensional locally symmetric variety of Type IV, that we denote by F(18). The generic hyperelliptic K3 of degree 4 is a double cover of P^1\times P^1, branched over (4,4) smooth curve. There is a birational period map from the GIT quotient of the space of (4,4) divisors on P^1\times P^1 to the Baily-Borel compactification F(18)^{*}, which is very far from being regular. Starting from Looijenga's pioneering work on new compactifications defined by arrangements in Type IV BSD's, we have given a very precise conjectural decomposition of the period map into a composition of flips and divisorial contractions. One way of proving our part of our assertions is to do VGIT on the space of (4,4) divisors on P^1\times P^1.
10:15 - 12:00 Prof. Dr. Eitan Tadmor 
ETH Zurich, Switzerland
Nachdiplomvorlesung
Self-organized dynamics. From emerging consensus to hydrodynamic flocking
HG G 43 
11:00 - 12:00 Prof. Dr. Zhiyuan Li
Fudan University
Conference: Cycles and Moduli
Algebraic cycles on moduli space of polarized hyperkahler manifolds 
HG G 19.1 
Abstract: We define the tautological ring on moduli space of polarized hyperhahler manifolds, which is largely motivated from the work of Marian, Oprea and Pandharipande on moduli space of K3 surfaces. We will talk about the properties of the tautological ring and give some conjectural descriptions such as the tautological conjecture. We will provide some evidence towards these conjectures. This is a joint work of Nicolas Bergeron.
14:30 - 15:30 Prof. Dr. Joseph Ayoub
Universität Zürich
Conference: Cycles and Moduli
Hodge theory for the conservativity conjecture
HG G 19.1 
15:00 - 16:00 Dr. Buket Oezkaya
Sabanci Univercity
Arbeitsgemeinschaft in Codierungstheorie und Kryptographie (uzh)
On Linear Complementary-Dual Multinegacirculant Codes
Y27  H 28
15:45 - 16:45 Alexandre Martin
Universität Wien
Geometry Seminar
On the acylindrical hyperbolicity of certain Artin groups 
HG G 43 
Abstract: Acylindrical hyperbolicity is a far-reaching generalisation of the notion of relative hyperbolicity that encompasses many classes of groups of interest in geometry and geometric group theory. In this talk, I will present a powerful but easy to apply criterion to show the acylindrical hyperbolicity of certain groups acting on CAT(0) cube complexes. As an application, I will explain how such a criterion can be used to show the acylindrical hyperbolicity of certain Artin groups. (Joint work with Indira Chatterji)
16:00 - 17:00 Allison N. Beemer
University of Nebraska-Lincoln
Arbeitsgemeinschaft in Codierungstheorie und Kryptographie (uzh)
A Multidimensional Network Framework for Trapping Set Analysis
Y27  H 28
16:00 - 17:00 Prof. Dr. Marc Levine
Universität Duisburg-Essen
Conference: Cycles and Moduli
The intrinsic stable normal cone and motivic virtual fundamental classes 
HG G 19.1 
Abstract: We describe how to use motivic stable homotopy theory and the Grothendieck six functor formalism to construct a general theory of the intrinsic normal cone and virtual fundamental classes for perfect obstruction theories. This gives a uniform treatment of these constructions for arbitrary cohomology theories living in the motivic stable homotopy category, including algebraic cycles, algebraic K-theory and algebraic cobordism, as well as the oriented cycles of Barge-Morel-Fasel. This last theory makes possible an enumerative geometry with values in quadratic forms.
16:15 - 17:15 Prof. Dr. Mathias Fink
ESPCI Paris
Zurich Colloquium in Applied and Computational Mathematics
Wave Control and Holography with Time Transformations 
Y27  H 25
Abstract: Because time and space play a similar role in wave propagation, wave control can be achieved or by manipulating spatial boundaries or by manipulating time boundaries. Here we emphasize the role of time boundaries manipulation. We show that sudden changes of the medium properties generate instant wave sources that emerge instantaneously from the entire wavefield and can be used to control wavefield and to revisit the holographic principles and the way to create time-reversed waves. Experimental demonstrations of this approach with water waves will be presented and the extension of this concept to acoustic and electromagnetic waves will be discussed. More sophisticated time manipulations can also be studied in order to extend the concept of photonic crystals and wave localization in the time domain.
17:15 - 18:15 Nicolas Matte Bon
ETH Zürich
Seminar on Stochastic Processes
Extensive amenability of group actions 
Y27  H 12
Abstract: A group is amenable if the spectral radius of any symmetric random walk on it is equal to one. This is only one among the many equivalent characterisations of this property, that make it play a role in many aspects of group theory. Nevertheless, deciding wether a group is amenable or not can be a difficult problem. Extensive amenability is a property of group actions, first considered by Juschenko and Monod, that leads to a method to prove amenability of groups. I will explain this property and give a a probabilistic reformulation of it, then explain this method and illustrate it by proving amenability of some groups of interval exchange transformations. Finally I will highlight the current limits of this method and some related open questions. Talk based on a joint work with Juschenko, Monod, and de la Salle.
Thursday, 30 March
Time Speaker Title Location
09:15 - 11:00 Prof. Dr. Richard Schoen 
ETH Zurich, Switzerland
Nachdiplomvorlesung
Topics in scalar curvature
HG G 43 
09:30 - 10:30 Prof. Dr. Dragos Oprea
University of California, San Diego
Conference: Cycles and Moduli
Segre classes and tautological relations over the moduli of K3s 
HG G 19.1 
Abstract: I will discuss the K-trivial case of a conjecture of Lehn regarding the top Segre classes of tautological vector bundles over the Hilbert scheme of points. The method involves the study of the virtual geometry of certain Quot schemes via equivariant localization. In addition, when the surface varies in moduli, the same method applied to the relative Quot schemes yields relations intertwining the k-classes over the moduli space of K3s and the Noether-Lefschetz loci. This is based on joint work with Alina Marian and Rahul Pandharipande.
11:00 - 12:00 Ulrike Rieß
Universität Bonn
Conference: Cycles and Moduli
Base loci of big and nef line bundles on irreducible symplectic varieties 
HG G 19.1 
Abstract: In this talk, we present results on base loci of big and nef line bundles on irreducible symplectic varieties, which were motivated by Mayer's remarkable statements for K3 surfaces. We focus on conditions for the existence of base divisors for big and nef line bundles on certain irreducible symplectic varieties, and sketch the proof. Furthermore, we will mention that for K3$^{[2]}$-type, every big and nef line bundle becomes base point free on a generic deformation.
13:30 - 14:30 Prof. Dr. Alessandro Chiodo
Institut de Mathématiques de Jussieu
Conference: Cycles and Moduli
Néron models and genus-one double ramification cycles via Picard functors 
HG G 19.1 
Abstract: Néron models of Jacobians are naturally described via Picard functors. Over a discrete valuation ring, this can be obtained by Raynaud's theorem via a quotient of the non-separated Picard functor. We can also present a direct approach within the separated functor Pic0 of twisted curves. Recently Holmes extended Raynaud's approach on a base scheme of dimension greater than one and was able to provide in this way a universal Néron model over moduli of curves. This construction admits several applications (e.g. the study of limit linear series by Biesel and Holmes). It also allows a new definition of the Double Ramification locus (DR) parametrizing curves equipped with a principal divisor. In collaboration with Holmes, we compute this cycle in genus one and match the formula of Janda, Pandharipande, Pixton and Zvonkine.
15:00 - 16:00 Prof. Dr. Gavril Farkas
Humboldt-Universität zu Berlin
Conference: Cycles and Moduli
The Prym-Green Conjecture on the resolution of paracanonical curves
HG G 19.1 
15:15 - 16:15 Robert Seiringer
IST Austria
Talks in Mathematical Physics
Stability of quantum many-body systems with point interactions 
HG G 43 
Abstract: We present a proof that a system of N fermions interacting with an additional particle via point interactions is stable if the ratio of the mass of the additional particle to the one of the fermions is larger than some critical m∗. The value of m∗ is independent of N and turns out to be less than 1. This fact is of relevance for the stability of fermionic gases in the unitary limit. We also present a rigorous version of the Tan relations valid for all wave functions in the domain of the Hamiltonian of this model.
17:15 - 18:15 Fred Espen Benth 
University of Oslo
Talks in Financial and Insurance Mathematics
Cointegration in continuous-time for factor models 
HG G 43 
Abstract: Based on some empirical evidence and stochastic models from the freight market, we propose a framework for cointegration in continuous-time. We study forward pricing, relevant in commodity markets, and how cointegration in the spot market affects the forward markets. We share some thoughts on particular cases like CARMA, polynomial and Levy stationary processes. Finally, we propose a notion of cointegration for infinite dimensional processes. The presentation is based on joint work with Andre Suess (Barcelona and Zuerich).
Friday, 31 March
Time Speaker Title Location
14:15 - 15:15 Prof. Dr. Yiannis Petridis
University College London
Number Theory Seminar
Arithmetic Statistics of modular symbols 
HG G 43 
Abstract: Mazur, Rubin, and Stein have recently formulated a series of conjectures about statistical properties of modular symbols in order to understand central values of twists of elliptic curve L-functions. Two of these conjectures relate to the asymptotic growth of the first and second moments of the modular symbols. In joint work with Morten S. Risager we prove these on average using analytic properties of Eisenstein series twisted with modular symbols. We also prove another conjecture predicting the Gaussian distribution of normalized modular symbols ordered according to the size of the denominator of the cusps.
16:30 - 17:45 Jason van Zelm
University of Liverpool
Algebraic Geometry and Moduli Seminar
Nontautological bielliptic cycles 
HG G 43 
Abstract: Tautological classes are geometrically defined classes in the Chow ring of the moduli space of curves which are particularly well understood. The classes of many known geometrically defined loci were proven to be tautological. A bielliptic curve is a curve with a 2-to-1 map to an elliptic curve. In this talk we will build on an idea of Graber and Pandharipande to show that the closure of the locus of bielliptic curves in the moduli space of stable curves of genus g is non-tautological when g is at least 12.

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28.03.2017
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