Departement Mathematik

Algebraic geometry and moduli seminar

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Frühjahrssemester 2017

Datum / Zeit Referent:in Titel Ort
22. Februar 2017
13:30-15:00 		Dr. Hyenho Lho
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel GW/SQ wall crossing I
Referent:in, Affiliation Dr. Hyenho Lho, ETH Zürich
Datum, Zeit 22. Februar 2017, 13:30-15:00
Ort HG G 43
Abstract We will study the wall crossing formula between Gromov-Witten invariant and Stable Quotient invariant for all genus. This formula which is recently proved for very general cases by Ciocan-Fontanine and Kim cover large class of target spaces. In a series of lectures, we will study this formula eventually enlarging the class of target spaces from Fano to Calabi-Yau.
GW/SQ wall crossing Iread_more
HG G 43
24. Februar 2017
16:00-17:15 		Dr. Enrica Floris
Universität Basel
Details

Algebraic Geometry and Moduli Seminar

Titel Invariance of plurigenera for foliations on surfaces
Referent:in, Affiliation Dr. Enrica Floris, Universität Basel
Datum, Zeit 24. Februar 2017, 16:00-17:15
Ort HG G 43
Abstract Recently, Brunella and McQuillan proved some of the main results of birational geometry in the setup of foliations on surfaces. In this talk, we will discuss to which extent the theorem of Invariance of Plurigenera is true for foliations on surfaces. This is a joint work with Paolo Cascini.
Invariance of plurigenera for foliations on surfacesread_more
HG G 43
1. März 2017
13:30-15:00 		Dr. Hyenho Lho
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel GW/SQ wall crossing II
Referent:in, Affiliation Dr. Hyenho Lho, ETH Zürich
Datum, Zeit 1. März 2017, 13:30-15:00
Ort HG G 43
Abstract We will study the wall crossing formula between Gromov-Witten invariant and Stable Quotient invariant for all genus. This formula which is recently proved for very general cases by Ciocan-Fontanine and Kim cover a large class of target spaces. In series of lectures, we will study this formula eventually enlarging the class of target spaces from Fano to Calabi-Yau.
GW/SQ wall crossing IIread_more
HG G 43
3. März 2017
16:00-17:15 		Pierrick Bousseau
Imperial College London
Details

Algebraic Geometry and Moduli Seminar

Titel DT invariants from holomorphic curves
Referent:in, Affiliation Pierrick Bousseau, Imperial College London
Datum, Zeit 3. März 2017, 16:00-17:15
Ort HG G 43
Abstract I will first describe a general analogy between DT invariants of 3-Calabi-Yau categories and holomorphic disks in holomorphic symplectic varieties, and reinterpret the Gromov-Witten/Kronecker correspondence in this context. In some specific case, I will then explain a conjectural extension of this result relating refined DT invariants and holomorphic curves of higher genus. Finally, I plan to give a sketch of proof of this extended correspondence.
DT invariants from holomorphic curvesread_more
HG G 43
8. März 2017
13:30-15:00 		Dr. Hyenho Lho
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel GW/SQ wall crossing III
Referent:in, Affiliation Dr. Hyenho Lho, ETH Zürich
Datum, Zeit 8. März 2017, 13:30-15:00
Ort HG G 43
Abstract We will study the wall crossing formula between Gromov-Witten invariant and Stable Quotient invariant for all genus. This formula which is recently proved for very general cases by Ciocan-Fontanine and Kim cover a large class of target spaces. In series of lectures, we will study this formula eventually enlarging the class of target spaces from Fano to Calabi-Yau.
GW/SQ wall crossing IIIread_more
HG G 43
15. März 2017
13:30-15:00 		Dr. Hyenho Lho
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel GW/SQ wall crossing IV
Referent:in, Affiliation Dr. Hyenho Lho, ETH Zürich
Datum, Zeit 15. März 2017, 13:30-15:00
Ort HG G 43
Abstract We will study the wall crossing formula between Gromov-Witten invariant and Stable Quotient invariant for all genus. This formula which is recently proved for very general cases by Ciocan-Fontanine and Kim cover a large class of target spaces. In series of lectures, we will study this formula eventually enlarging the class of target spaces from Fano to Calabi-Yau.
GW/SQ wall crossing IVread_more
HG G 43
17. März 2017
16:00-17:15 		Prof. Dr. Filippo Viviani
Roma III
Details

Algebraic Geometry and Moduli Seminar

Titel The cohomology of the Hilbert schemes and of the compactified Jacobians of a singular curve
Referent:in, Affiliation Prof. Dr. Filippo Viviani, Roma III
Datum, Zeit 17. März 2017, 16:00-17:15
Ort HG G 43
Abstract We generalize the classical MacDonald formula for smooth curves to reduced curves with planar singularities. More precisely, we show that the cohomologies of the Hilbert schemes of points on a such a curve are encoded in the cohomologies of the fine compactified Jacobians of its connected subcurves, via the perverse Leray filtration. This is a joint work with Luca Migliorini and Vivek Shende.
The cohomology of the Hilbert schemes and of the compactified Jacobians of a singular curve read_more
HG G 43
22. März 2017
13:30-15:00 		Dr. Tyler Kelly
University of Cambridge
Details

Algebraic Geometry and Moduli Seminar

Titel A toric Orlov theorem via Landau-Ginzburg models
Referent:in, Affiliation Dr. Tyler Kelly, University of Cambridge
Datum, Zeit 22. März 2017, 13:30-15:00
Ort HG G 43
Abstract Orlov's theorem defines and proves that any smooth Fano (resp. general type) hypersurface in projective n-space has a subcategory (resp. supercategory) in its bounded derived category of coherent sheaves that is a Fractional Calabi-Yau category. We prove this is the case for a certain class of toric complete intersections. The method to find this is by studying a Landau-Ginzburg model associated to the toric complete intersection and then using geometric invariant theory. We will try to focus on studying a few motivating examples from previous literature. This work is joint with David Favero (Alberta).
A toric Orlov theorem via Landau-Ginzburg modelsread_more
HG G 43
24. März 2017
16:00-17:15 		Dr. Olivier Benoist
Université de Strasbourg
Details

Algebraic Geometry and Moduli Seminar

Titel Sums of squares on real uniruled varieties
Referent:in, Affiliation Dr. Olivier Benoist, Université de Strasbourg
Datum, Zeit 24. März 2017, 16:00-17:15
Ort HG G 43
Abstract It is a classical theorem of Pfister that a non-negative rational function on a real algebraic variety of dimension n is a sum of 2^n squares. In this talk, we will investigate improvements on this bound under additional geometric hypotheses. Here is an example of the results we will explain: in the function field of a real uniruled threefold without real points, -1 is a sum of 4 squares. This is partly joint work with Olivier Wittenberg.
Sums of squares on real uniruled varietiesread_more
HG G 43
* 31. März 2017
16:30-17:45 		Jason van Zelm
University of Liverpool
Details

Algebraic Geometry and Moduli Seminar

Titel Nontautological bielliptic cycles
Referent:in, Affiliation Jason van Zelm, University of Liverpool
Datum, Zeit 31. März 2017, 16:30-17:45
Ort 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.
Nontautological bielliptic cyclesread_more
HG G 43
* 11. April 2017
13:00-14:15 		Prof. Dr. Sergey Shadrin
University of Amsterdam
Details

Algebraic Geometry and Moduli Seminar

Titel The tautological ring of M_{g,n} via Pandharipande-Pixton-Zvonkine r-spin relations
Referent:in, Affiliation Prof. Dr. Sergey Shadrin, University of Amsterdam
Datum, Zeit 11. April 2017, 13:00-14:15
Ort HG G 19.1
Abstract We use relations in the tautological ring of the moduli spaces \bar{M}_{g,n} derived by Pandharipande, Pixton, and Zvonkine from the Givental formula for the r-spin Witten class in order to obtain some restrictions on the dimensions of the tautological rings of the open moduli spaces M_{g,n}. In particular, we give a new proof for the result of Looijenga (for n=1) and Buryak et al. (for n>= 2) that dim R^{g-1}(M_{g,n})<= n. We also give a new proof of the result of Looijenga (for n=1) and Ionel (for arbitrary n>= 1) that R^i(M_{g,n})=0 for i>= g and give some estimates for the dimension of R^i(M_{g,n}) for $i<= g-2.
The tautological ring of M_{g,n} via Pandharipande-Pixton-Zvonkine r-spin relationsread_more
HG G 19.1
26. April 2017
13:30-15:00 		Dr. Clément Dupont
Université de Montpellier
Details

Algebraic Geometry and Moduli Seminar

Titel Brown's moduli spaces of curves and the gravity operad
Referent:in, Affiliation Dr. Clément Dupont , Université de Montpellier
Datum, Zeit 26. April 2017, 13:30-15:00
Ort HG G 43
Abstract We will introduce Brown’s moduli spaces, which parametrize genus zero curves. The original motivation is arithmetic and lies in the algebro-geometric study of multiple zeta values. In this talk we will see how these spaces fit in the study of the operadic structures underlying the moduli spaces of genus zero curves. More precisely, we will explain the proof of two essentially equivalent results: the purity of the Hodge structure on the cohomology of Brown’s moduli spaces, and the freeness of the non symmetric operad underlying Getzler’s gravity operad. This is joint work with Bruno Vallette.
Brown's moduli spaces of curves and the gravity operadread_more
HG G 43
5. Mai 2017
16:00-17:15 		Dr. Honglu Fan
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Gromov-Witten theory of projective bundles
Referent:in, Affiliation Dr. Honglu Fan, ETH Zürich
Datum, Zeit 5. Mai 2017, 16:00-17:15
Ort HG G 43
Abstract Originally motivated by the crepant transformation conjecture for ordinary flops, we tried to study how much can characteristic classes determine the Gromov-Witten theory of projective bundles. I will talk about an easy example and our results. If there is time, I will also discuss some further ideas.
Gromov-Witten theory of projective bundlesread_more
HG G 43
10. Mai 2017
13:30-15:00 		Dr. Nicola Tarasca
University of Georgia
Details

Algebraic Geometry and Moduli Seminar

Titel Hyperelliptic loci in moduli spaces of curves
Referent:in, Affiliation Dr. Nicola Tarasca, University of Georgia
Datum, Zeit 10. Mai 2017, 13:30-15:00
Ort HG G 43
Abstract In this talk, I will discuss some recent results in the enumerative geometry of subvarieties of moduli spaces of curves. In joint work with Dawei Chen, we study the extremality of loci of hyperelliptic curves with marked Weierstrass points inside cones of effective classes of high codimension. I will present a formula for classes of loci of genus-two curves with marked Weierstrass points as result of an ongoing work with Renzo Cavalieri. These are among the first results toward the study of cones of higher codimensional effective classes.
Hyperelliptic loci in moduli spaces of curvesread_more
HG G 43
12. Mai 2017
16:00-17:15 		Prof. Dr. Alexander Kuznetsov
Steklov Mathematical Institute
Details

Algebraic Geometry and Moduli Seminar

Titel Derived categories of families of sextic del Pezzo surfaces
Referent:in, Affiliation Prof. Dr. Alexander Kuznetsov, Steklov Mathematical Institute
Datum, Zeit 12. Mai 2017, 16:00-17:15
Ort HG G 43
Abstract I will give a description of the derived category of coherent sheaves on a flat family of normal sextic del Pezzo surfaces with du Val singularities.
Derived categories of families of sextic del Pezzo surfacesread_more
HG G 43
17. Mai 2017
13:30-15:00 		Junliang Shen
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Derived categories of K3 surfaces, O'Grady's filtration, and Hyperkähler varieties
Referent:in, Affiliation Junliang Shen, ETH Zürich
Datum, Zeit 17. Mai 2017, 13:30-15:00
Ort HG G 43
Abstract We discuss the connections among derived categories of K3 surfaces, O'Grady's filtration on Chow groups, and zero cycles on certain Hyperkähler varieties. First, we show that the second Chern class of any object in the derived category of a K3 surface lies in a suitable piece of O'Grady's filtration. This solves and generalizes a conjecture by O'Grady, and provides new structures on derived categories of K3 surfaces. Second, we introduce a conjecture concerning stable objects in derived categories of K3 surfaces and zero cycles on their moduli spaces. We show that our results and conjecture lead to a natural candidate of the Beauville-Voisin filtration for zero cycles on these moduli spaces (which are Hyperkähler varieties of K3^[n]-type). In particular, we will discuss its connection with Voisin's recent proposal via constant cycle subvarieties. This is based on a joint work with Qizheng Yin and Xiaolei Zhao.
Derived categories of K3 surfaces, O'Grady's filtration, and Hyperkähler varietiesread_more
HG G 43
19. Mai 2017
16:00-17:15 		Prof. Dr. Andrei Okounkov
Columbia University
Details

Algebraic Geometry and Moduli Seminar

Titel Quasimap counts and integral solutions of the quantum Knizhnik-Zamolodchikov equations
Referent:in, Affiliation Prof. Dr. Andrei Okounkov, Columbia University
Datum, Zeit 19. Mai 2017, 16:00-17:15
Ort HG G 43
Abstract I will review the appearance of qKZ and related difference equations in the enumerative K-theory of quasimaps to Nakajima varieties and explain, following a joint paper with Mina Aganagic, how a correspondence between descendent and relative enumerative constraints translates into Mellin-Barnes integral formulas for solutions. The example of the Hilbert schemes of points in C^2 will be emphasized throughout the talk.
Quasimap counts and integral solutions of the quantum Knizhnik-Zamolodchikov equationsread_more
HG G 43
24. Mai 2017
13:30-15:00 		Dr. Nicola Tarasca
Univ. of Georgia
Details

Algebraic Geometry and Moduli Seminar

Titel K-classes of Brill-Noether loci and a determinantal formula
Referent:in, Affiliation Dr. Nicola Tarasca, Univ. of Georgia
Datum, Zeit 24. Mai 2017, 13:30-15:00
Ort HG G 43
Abstract I will present a formula for the Euler characteristic of the structure sheaf of Brill-Noether loci of linear series on curves with prescribed vanishing at marked points. The formula recovers the classical Castelnuovo number in the zero-dimensional case, and previous results of Eisenbud-Harris, Pirola, Chan-López-Pflueger-Teixidor in the curve case. The result follows from a new determinantal formula for the K-theory class of certain degeneracy loci of maps of flag bundles. This is joint work with Dave Anderson and Linda Chen.
K-classes of Brill-Noether loci and a determinantal formularead_more
HG G 43
23. Juni 2017
16:00-17:15 		Dr. Hyenho Lho
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Vanishing condition on the GW invariants of P1^n
Referent:in, Affiliation Dr. Hyenho Lho, ETH Zürich
Datum, Zeit 23. Juni 2017, 16:00-17:15
Ort HG G 43
Abstract We will prove some vanishing conditions of Gromov-Witten invariants of product of projective lines.
Vanishing condition on the GW invariants of P1^nread_more
HG G 43
* 27. Juni 2017
13:30-14:45 		Dr. Georg Oberdieck
MIT
Details

Algebraic Geometry and Moduli Seminar

Titel Holomorphic anomaly equations for elliptic fibrations
Referent:in, Affiliation Dr. Georg Oberdieck, MIT
Datum, Zeit 27. Juni 2017, 13:30-14:45
Ort HG G 19.2
Abstract The Gromov-Witten potentials of an elliptic curve are known to be quasi-modular forms and to satisfy a holomorphic anomaly equation (HAE), a recursive formula for the derivative with respect to the second Eisenstein series. We explain a conjectural HAE for general elliptic fibrations and present some evidence along the way. This is joint work with Aaron Pixton.
Holomorphic anomaly equations for elliptic fibrationsread_more
HG G 19.2
* 27. Juni 2017
15:15-16:30 		Dr. Qingtao Chen
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Recent progress of various Volume Conjectures for links as well as 3-manifolds
Referent:in, Affiliation Dr. Qingtao Chen, ETH Zürich
Datum, Zeit 27. Juni 2017, 15:15-16:30
Ort HG G 19.2
Abstract The original Volume Conjecture of Kashaev-Murakami-Murakami predicts a precise relation between the asymptotics of the colored Jones polynomials of a knot in S^3 and the hyperbolic volume of its complement. I will discuss two different directions that lead to generalizations of this conjecture. The first direction concerns different quantum invariants of knots, arising from the colored SU(n) (with the colored Jones polynomial corresponding to the case n = 2). I will first display subtle relations between congruence relations (inspired by large N duality relating Chern-Simons gauge theory and Gromov-Witten theory), cyclotomic expansions and the original Volume Conjecture for colored Jones polynomials of knots. I will then generalize this point of view to the colored SU(n) invariant of knots. Certain congruence relations for colored SU(n) invariants, discovered in joint work with K. Liu, P. Peng and S. Zhu, lead us to formulate cyclotomic expansions and a Volume Conjecture for these colored SU(n) invariants. If time permits, I will briefly discuss similar ideas for the superpolynomials that arise in HOMFLY-PT homology. Another direction for generalization involves the Witten-Reshetikhin-Turaev and (modified) Turaev-Viro quantum invariants of 3-manifolds. In a joint work with T. Yang, we formulated a new Volume Conjecture for the asymptotics of these 3-manifolds invariants evaluated at certain roots of unit, and numerically checked it for many examples. I would like report current situation of these new conjectures, which include my new work with Jun Murakami. Interestingly, this conjecture uses roots of unity that are different from the one usually considered in literature. This may indicate that the understanding of this new phenomenon requires new physical and geometric interpretations that go beyond the usual quantum Chern-Simons theory.
Recent progress of various Volume Conjectures for links as well as 3-manifoldsread_more
HG G 19.2

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