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Frühjahrssemester 2024

Datum / Zeit Referent:in Titel Ort
* 12. Februar 2024
17:30-19:00 		Felix Thimm
Univ. of Oslo
Details

Algebraic Geometry and Moduli Seminar

Titel The 3-fold K-theoretic DT/PT vertex correspondence
Referent:in, Affiliation Felix Thimm, Univ. of Oslo
Datum, Zeit 12. Februar 2024, 17:30-19:00
Ort Zoom
Abstract Donaldson-Thomas (DT) and Pandharipande-Thomas (PT) invariants are two curve counting invariants for 3-folds. In the Calabi-Yau case, a correspondence between the numerical DT and PT invariants has been conjectured by Pandharipande and Thomas and proven by Bridgeland and Toda using wall-crossing. For equivariant K-theoretically refined invariants, the DT/PT correspondence reduces to a DT/PT correspondence of equivariant K-theoretic vertices. In this talk I will explain our proof of the equivariant K-theoretic DT/PT vertex correspondence using a K-theoretic version of Joyce's wall-crossing setup. An important technical tool is the construction of a symmetized pullback of a symmetric perfect obstruction theory on the orginial DT and PT moduli stacks to a symmetric almost perfect obstruction theory on auxiliary moduli stacks. This is joint work with Henry Liu and Nick Kuhn.
The 3-fold K-theoretic DT/PT vertex correspondence read_more
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* 20. Februar 2024
13:30-15:00 		Dr. Sam Canning
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Non-tautological cycles on the moduli space of smooth curves
Referent:in, Affiliation Dr. Sam Canning, ETH Zürich
Datum, Zeit 20. Februar 2024, 13:30-15:00
Ort ITS
Abstract It is more difficult to find non-tautological algebraic cycles on moduli spaces of smooth curves than on moduli spaces of stable curves. In fact, there were only 11 known pairs (g,n) for which M_{g,n} was known to have a non-tautological algebraic cycle, due to Graber--Pandharipande and van Zelm. I will explain how to produce non-tautological algebraic cycles in infinitely many more cases. In particular, M_g has non-tautological algebraic cycles whenever g is at least 16. This is joint work with V. Arena, E. Clader, R. Haburcak, A. Li, S.C. Mok, and C. Tamborini.
Non-tautological cycles on the moduli space of smooth curvesread_more
ITS
23. Februar 2024
16:00-17:30 		Prof. Dr. Sheldon Katz
Univ. of Illinois and FIM
Details

Algebraic Geometry and Moduli Seminar

Titel The generating function of Euler characteristics of Hilbert schemes of points on a supermanifold
Referent:in, Affiliation Prof. Dr. Sheldon Katz, Univ. of Illinois and FIM
Datum, Zeit 23. Februar 2024, 16:00-17:30
Ort HG G 43
Abstract In this talk, I extend well-known results on the generating function of Euler characteristics of Hilbert schemes of points from complex manifolds to complex supermanifolds. These are two-variable generating functions in general: since functions on a zero dimensional subscheme of a supermanifold are Z_2-graded, there is an even degree and an odd degree. For supermanifolds of a given superdimension (n|m), the generating function can be expressed in terms of the corresponding generating function for C^{n|m}, which can in turn be computed by an analogue of box-counting. These basic generating functions are worked in low superdimension and can be expressed as rational functions of two variables.
The generating function of Euler characteristics of Hilbert schemes of points on a supermanifoldread_more
HG G 43
* 4. März 2024
15:00-16:30 		Dr. Sam Canning
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Tautological projection on the moduli space of abelian varieties
Referent:in, Affiliation Dr. Sam Canning, ETH Zürich
Datum, Zeit 4. März 2024, 15:00-16:30
Ort ITS
Abstract I will show that every cycle on the moduli space of abelian varieties decomposes canonically as a sum of a tautological and non-tautological class. The key input is the vanishing of the top Chern class of the Hodge bundle when restricted to the boundary of any toroidal compactification. This is joint work with Molcho, Oprea, and Pandharipande.
Tautological projection on the moduli space of abelian varietiesread_more
ITS
6. März 2024
13:30-15:00 		Aitor Iribar Lopez
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Twisted products in the moduli space of abelian varieties
Referent:in, Affiliation Aitor Iribar Lopez, ETH Zürich
Datum, Zeit 6. März 2024, 13:30-15:00
Ort HG G 43
Abstract In the moduli space of principally polarized abelian varieties, it is natural to consider the loci determined by those varieties that are not simple. I will give a description of the irreducible components of these loci, and explain how to obtain their projection to the tautological ring of A_g (as recently developed by Canning, Molcho, Oprea and Pandharipande), using the theory of toroidal compactifications of Siegel domains. Then I will discuss some connections to the enumerative geometry of curves.
Twisted products in the moduli space of abelian varietiesread_more
HG G 43
* 11. März 2024
15:00-16:30 		Prof. Dr. Ran Tessler
Weizmann Institute
Details

Algebraic Geometry and Moduli Seminar

Titel The amplituhedron: tilings and cluster adjacency
Referent:in, Affiliation Prof. Dr. Ran Tessler, Weizmann Institute
Datum, Zeit 11. März 2024, 15:00-16:30
Ort ITS
Abstract The amplituhedron is a geometric object discovered by Arkani-Hamed and Tranka (2013) in their study of planar N=4 Super Yang Mills scattering amplitudes. In my talk I will describe this object, its properties, and the recent resolutions of two major conjectures in the field: the BCFW triangulation conjecture and the cluster adjacency conjecture for BCFW tiles. Based on joint works with C. Even-Zohar, T. Lakrec, M. Parisi, M. Sherman-Bennett and L. Williams.
The amplituhedron: tilings and cluster adjacencyread_more
ITS
13. März 2024
13:30-15:00 		Prof. Dr. Ran Tessler
Weizmann Institute
Details

Algebraic Geometry and Moduli Seminar

Titel Open FJRW theory in genus 0 and mirror symmetry
Referent:in, Affiliation Prof. Dr. Ran Tessler, Weizmann Institute
Datum, Zeit 13. März 2024, 13:30-15:00
Ort HG G 43
Abstract We define the g=0 open FJRW theory for (W,G) where W is a Fermat polynomial and G is its maximal symmetry group. We calculate all disk invariants, and classify the wall crossing group. We prove mirror symmetry with Saito's B-model.Based on joint works with Mark Gross and Tyler Kelly.
Open FJRW theory in genus 0 and mirror symmetryread_more
HG G 43
15. März 2024
16:00-17:30 		Prof. Dr. Albrecht Klemm
Universität Bonn
Details

Algebraic Geometry and Moduli Seminar

Titel Symplectic invariants on Calabi-Yau 3 folds, modularity and stability
Referent:in, Affiliation Prof. Dr. Albrecht Klemm, Universität Bonn
Datum, Zeit 15. März 2024, 16:00-17:30
Ort HG G 43
Abstract We discuss techniques to calculate symplectic invariants on CY 3-folds M, namely Gromov-Witten (GW) invariants, Pandharipande-Thomas (PT) invariants, and Donaldson-Thomas (DT) invariants. Physically the latter are closely related to BPS brane bound states in type IIA string compactifications on M. We focus on the rank r_6=1 DT invariants that count D6-D2-D0 brane bound states related to PT- and high genus GW invariants, which are calculable by mirror symmetry and topological string B-model methods modulo certain boundary conditions, and the rank zero DT invariants that count rank r_4=1 D4-D2-D0 brane bound states. It has been conjectured by Maldacena, Strominger, Witten and Yin that the latter are governed by an index that has modularity properties to due S-duality in string theory and extends to a mock modularity index of higher depth for r_4>1. Again the modularity allows to fix the at least the r_4=1 index up to boundary conditions fixing their polar terms. Using Wall crossing formulas obtained by Feyzbakhsh certain PT invariants close to the Castelnouvo bound can be related to the r_4=1,2 D4-D2-D0 invariants. This provides further boundary conditions for topological string B-model approach as well as for the D4-D2-D0 brane indices. The approach allows to prove the Castenouvo bound and calculate the r_6=1 DT- invariants or the GW invariants to higher genus than hitherto possible.
Symplectic invariants on Calabi-Yau 3 folds, modularity and stabilityread_more
HG G 43
20. März 2024
13:30-15:00 		Dr. Chiara Meroni
ETH-ITS
Details

Algebraic Geometry and Moduli Seminar

Titel The algebra of convex hulls
Referent:in, Affiliation Dr. Chiara Meroni, ETH-ITS
Datum, Zeit 20. März 2024, 13:30-15:00
Ort HG G 43
Abstract Convex hulls and their boundaries are complicated but relevant objects in convex geometry and optimization. However, there is an algebraic technique to study the convex hull of a real variety. The goal is to understand which varieties contribute to the boundary. I will explain this general method and then focus on the case of smooth surfaces in four-dimensional space, in particular Veronese, Del Pezzo, and Bordiga surfaces.
The algebra of convex hullsread_more
HG G 43
* 15. April 2024
17:30-19:00 		Dr. Miguel Moreira
MIT
Details

Algebraic Geometry and Moduli Seminar

Titel The cohomology ring of moduli spaces of 1-dimensional sheaves on CP2
Referent:in, Affiliation Dr. Miguel Moreira, MIT
Datum, Zeit 15. April 2024, 17:30-19:00
Ort Zoom
Abstract The cohomology of moduli spaces of 1-dimensional sheaves, together with a special filtration called the perverse filtration, can be used to give an intrinsic definition of (refined) Gopakumar-Vafa invariants. While there are methods to calculate the Betti numbers of these moduli spaces in low degree, understanding the perverse filtration is more challenging. One way to compute it is to fully determine the cohomology ring. In this talk I will explain an approach to describing the cohomology rings of moduli spaces and moduli stacks in terms of generators and relations, which allowed us to determine them for curve classes up to degree 5 (for moduli spaces) and 4 (for moduli stacks). I will explain the P=C conjecture, which is an analogue of the P=W conjecture in a Fano and compact setting. This is joint work with Yakov Kononov, Woonam Lim and Weite Pi.
The cohomology ring of moduli spaces of 1-dimensional sheaves on CP2read_more
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17. April 2024
13:30-15:00 		Prof. Dr. Danilo Lewanski
University of Trieste
Details

Algebraic Geometry and Moduli Seminar

Titel A fair amount of weighted intersection numbers summing up to zero
Referent:in, Affiliation Prof. Dr. Danilo Lewanski, University of Trieste
Datum, Zeit 17. April 2024, 13:30-15:00
Ort HG G 43
Abstract Via virtual localisation techniques, Johnson, Pandharipande and Tseng proved that the integral of the Hodge class over the moduli space of admissible covers vanishes under certain sufficient technical conditions: either strong negativity or negativity together with boundedness would suffice. What happens when these conditions are lifted? The answer (in a certain setting) was provided in previous work with Borot, Do, Karev and Moskovsky: the vanishing of a single summand gets replaced by the vanishing of the sum of many. This was achieved as a byproduct of the topological recursion procedure. By deformation techniques in topological recursion, other three families of these relations arose, two of which genus dependent. Based on joint work with Gaëtan Borot and Maksim Karev, tested thanks to the admcycles Sage package.
A fair amount of weighted intersection numbers summing up to zeroread_more
HG G 43
19. April 2024
16:00-17:30 		Dr. Julia Schneider
Universität Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Birational maps of Severi-Brauer surfaces, with applications to Cremona groups of higher rank
Referent:in, Affiliation Dr. Julia Schneider, Universität Zürich
Datum, Zeit 19. April 2024, 16:00-17:30
Ort HG G 43
Abstract We describe the group of birational transformations of a non-trivial Severi-Brauer surface over a perfect field, proving that if it contains a point of degree 6, then it is not generated by elements of finite order. We then use this result to study Mori fibre spaces over the field of complex numbers and deduce that the Cremona group of rank at least 4 admits any group (of cardinality at most $|\mathbb{C}|$) as a quotient. Moreover, we prove that the 3-torsion in the abelianization of the Cremona group of rank at least 4 is uncountable. This is based on a joint work with J. Blanc and E. Yasinsky.
Birational maps of Severi-Brauer surfaces, with applications to Cremona groups of higher rankread_more
HG G 43
24. April 2024
13:30-15:00 		Prof. Dr. Alessio Sammartano
Politecnico di Milano
Details

Algebraic Geometry and Moduli Seminar

Titel Components and singularities of Hilbert schemes of points
Referent:in, Affiliation Prof. Dr. Alessio Sammartano, Politecnico di Milano
Datum, Zeit 24. April 2024, 13:30-15:00
Ort HG G 43
Abstract The Hilbert scheme of points in affine n-dimensional space parametrizes finite subschemes of a given length. It is smooth and irreducible if n is at most 2, singular and reducible if n is at least 3. Understanding its irreducible components, their singularities and birational geometry, has long been an inaccessible problem. In this talk, I will describe substantial progress on this problem achieved in recent years. In particular, I will focus on the discovery of elementary components, Murphy’s law up to retraction, and the problem of rationality of components. This is based on works of Joachim Jelisiejew and on a joint work of Gavril Farkas, Rahul Pandharipande, and myself.
Components and singularities of Hilbert schemes of pointsread_more
HG G 43
26. April 2024
16:00-17:30 		Aitor Iribar Lopez
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel Morphisms between Hermitian domains and applications to enumerative geometry
Referent:in, Affiliation Aitor Iribar Lopez, ETH Zürich
Datum, Zeit 26. April 2024, 16:00-17:30
Ort HG G 43
Abstract In the 80's Mumford and his collaborators developed the theory of compactifications of bounded symmetric domains, which included moduli spaces of K3 and abelian varieties. We will go through that theory and explain how some functorial properties of these compactifications can be applied to some modern problems, like tautological projections of Shimura varieties, or obtaining relations in the Chow ring of certain period domains for weight 2 VHS.
Morphisms between Hermitian domains and applications to enumerative geometryread_more
HG G 43
3. Mai 2024
16:00-17:30 		Alessio Cela
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Titel The integral Chow ring of the moduli stack of Prym pairs of genus 2
Referent:in, Affiliation Alessio Cela, ETH Zürich
Datum, Zeit 3. Mai 2024, 16:00-17:30
Ort HG G 43
Abstract I will explain how to compute the integral Chow ring of the moduli stack R_2 of Prym pairs of genus 2.
The integral Chow ring of the moduli stack of Prym pairs of genus 2read_more
HG G 43
* 13. Mai 2024
17:30-19:00 		Dr. Ian Cavey
University of Illinois U-C
Details

Algebraic Geometry and Moduli Seminar

Titel Verlinde series for Hirzebruch surfaces
Referent:in, Affiliation Dr. Ian Cavey, University of Illinois U-C
Datum, Zeit 13. Mai 2024, 17:30-19:00
Ort Zoom
Abstract Verlinde series are generating functions of Euler characteristics of line bundles on the Hilbert schemes of points on a surface. Formulas for Verlinde series were determined for surfaces with K=0 by Ellingsrud, Göttsche, and Lehn. More recently, Göttsche and Mellit determined Verlinde series for surfaces with K^2=0, and gave a conjectural formula in the general case. In this talk, I will give a formula for the Euler characteristics of line bundles on the Hilbert schemes of points on CP1 x CP1, and a combinatorial (but less explicit) formula for ample line bundles on the Hilbert schemes of points on Hirzebruch surfaces. By structural results of Ellingsrud, Göttsche, and Lehn, this determines the Verlinde series for all surfaces. The proof is based on a new combinatorial description of the equivariant Verlinde series for the affine plane.
Verlinde series for Hirzebruch surfacesread_more
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15. Mai 2024
13:30-15:00 		Prof. Dr. Francois Greer
Michigan State University
Details

Algebraic Geometry and Moduli Seminar

Titel Quasi-modular special cycles
Referent:in, Affiliation Prof. Dr. Francois Greer, Michigan State University
Datum, Zeit 15. Mai 2024, 13:30-15:00
Ort HG G 43
Abstract A classical theorem of Kudla and Millson states that the cohomology classes of Noether-Lefschetz loci in a moduli space of K3-type Hodge structures form the coefficients of a modular form. We investigate how well this theorem survives upon passing to a smooth compactification. As an application, we sketch a counterexample to the Severi Problem for rational surfaces.
Quasi-modular special cycles read_more
HG G 43
17. Mai 2024
16:00-17:30 		Prof. Dr. Pierrick Bousseau
University of Georgia
Details

Algebraic Geometry and Moduli Seminar

Titel The KSBA moduli space of stable log Calabi-Yau surfaces
Referent:in, Affiliation Prof. Dr. Pierrick Bousseau, University of Georgia
Datum, Zeit 17. Mai 2024, 16:00-17:30
Ort HG G 43
Abstract The KSBA moduli space, introduced by Kollár--Shepherd-Barron, and Alexeev, is a natural generalization of "the moduli space of stable curves" to higher dimensions. It parametrizes stable pairs (X,B), where X is a projective algebraic variety satisfying certain conditions and B is a divisor such that KX+B is ample. This moduli space is described concretely only in a handful of situations: for instance, if X is a toric variety and B=D+\epsilon C, where D is the toric boundary divisor and C is an ample divisor, it is shown by Alexeev that the KSBA moduli space is a toric variety. Generally, for a log Calabi-Yau variety (X,D) consisting of a projective variety X and an anticanonical divisor D, with B=D+ε C where C is an ample divisor, it was conjectured by Hacking-Keel-Yu that the KSBA moduli space is still toric (up to passing to a finite cover). In joint work with Alexeev and Arguz, we prove this conjecture for all log Calabi-Yau surfaces. This uses tools from the minimal model program, log smooth deformation theory, mirror symmetry and punctured log Gromov-Witten theory.
The KSBA moduli space of stable log Calabi-Yau surfacesread_more
HG G 43
* 24. Mai 2024
14:30-15:30 		Prof. Dr. Sabrina Pauli
TU Darmstadt
Details

Algebraic Geometry and Moduli Seminar

Titel Quadratically enriched tropical correspondence theorems
Referent:in, Affiliation Prof. Dr. Sabrina Pauli, TU Darmstadt
Datum, Zeit 24. Mai 2024, 14:30-15:30
Ort ITS
Abstract In the talk I will explain that thanks to methods from A^1-homotopy theory, more precisely recent work of Kass-Levine-Solomon-Wickelgren, it now makes sense to perform weighted counts of plane rational curves of degree d through a point configuration of 3d-1 points over an arbitrary field k, and these curve counts are valued in the Grothendieck-Witt ring GW(k) of quadratic forms over the field k, generalizing Welschinger's invariants for k the real numbers. I will present tropical correspondence theorems for these GW(k)-valued counts, identifying these counts with the count of tropical curves counted with some multiplicity. This is based on joint work with Jaramillo Puentes and forthcomi ng work by Markwig-Jaramillo Puentes-Röhrle.
Quadratically enriched tropical correspondence theoremsread_more
ITS
24. Mai 2024
16:00-17:00 		Dr. Sam Molcho
Aarhus University
Details

Algebraic Geometry and Moduli Seminar

Titel Tautological relations for degenerating abelian varieties
Referent:in, Affiliation Dr. Sam Molcho, Aarhus University
Datum, Zeit 24. Mai 2024, 16:00-17:00
Ort HG G 43
Abstract The moduli space of dimension g principally polarized abelian varieties has a system of nice -- toroidal -- compactifications. I will explain how semistable degenerations of abelian varieties endow each of these compactifications with a tautological ring, and I will discuss methods to obtain relations in these rings.
Tautological relations for degenerating abelian varietiesread_more
HG G 43
26. Juni 2024
13:30-15:00 		Dr. Carl Lian
Tufts University
Details

Algebraic Geometry and Moduli Seminar

Titel Enumerativity of fixed-domain Gromov-Witten invariants
Referent:in, Affiliation Dr. Carl Lian, Tufts University
Datum, Zeit 26. Juni 2024, 13:30-15:00
Ort HG G 19.1
Abstract It is well-understood that Gromov-Witten (GW) invariants often fail to be enumerative. For example, when r is at least 3, the higher-genus GW invariants of P^r fail to count smooth curves in projective space in any transparent sense. The situation seems to be better when one fixes the complex structure of the domain curve. It was originally speculated that if X is a Fano variety, then the "fixed-domain" GW count of curves of sufficiently large degree passing through the maximal number of general points is enumerative. I will discuss some positive and negative results in this direction, focusing on the case of hypersurfaces. The most recent results are joint with Roya Beheshti, Brian Lehmann, Eric Riedl, Jason Starr, and Sho Tanimoto, and build on earlier work with Rahul Pandharipande and Alessio Cela.
Enumerativity of fixed-domain Gromov-Witten invariantsread_more
HG G 19.1
28. Juni 2024
14:30-16:00 		Dr. Younghan Bae
Utrecht University
Details

Algebraic Geometry and Moduli Seminar

Titel Fourier transform and the class of Abel-Jacobi sections
Referent:in, Affiliation Dr. Younghan Bae, Utrecht University
Datum, Zeit 28. Juni 2024, 14:30-16:00
Ort ITS
Abstract After the work of Beauville and Deninger-Murre, Fourier transformation plays an important role to study the Chow group of abelian schemes. Arinkin extended the Fourier transformation to the relative compactified Jacobian of a family of integral local planar curves. In this talk, I will explain how Arinin’s Fourier transform can be used to compute the class of Abel-Jacobi sections on the relative Jacobian over the moduli space of integral nodal curves. This result partially recovers Pixton’s formula of Abel-Jacobi section proven by Bae-Holmes-Pandharipande-Schmitt-Schwarz. This is a joint work in progress with S. Molcho.
Fourier transform and the class of Abel-Jacobi sectionsread_more
ITS

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