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Autumn Semester 2022

Date / Time Speaker Title Location
* 26 September 2022
17:30-18:45 		Prof. Dr. Jim Bryan
University of British Columbia
Details

Algebraic Geometry and Moduli Seminar

Title A theory of Gopakumar-Vafa invariants for orbifold CY 3-folds
Speaker, Affiliation Prof. Dr. Jim Bryan, University of British Columbia
Date, Time 26 September 2022, 17:30-18:45
Location Zoom
Abstract We define integer valued invariants of an orbifold Calabi-Yau threefold X with transverse ADE orbifold points. These invariants contain equivalent information to the Gromov-Witten invariants of X and are related by a Gopakumar-Vafa like formula which may be regarded as a universal multiple cover / degenerate contribution formula for orbifold Gromov-Witten invariants. We also give sheaf theoretic definitions of our invariants. As examples, we give formulas for our invariants in the case of a (local) orbifold K3 surface. These new formulas generalize the classical Yau-Zaslow and Katz-Klemm-Vafa formulas. This is joint work with S. Pietromonaco.
A theory of Gopakumar-Vafa invariants for orbifold CY 3-foldsread_more
Zoom
28 September 2022
13:30-15:00 		Dr. Samir Canning
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title New results on the Chow and cohomology rings of moduli spaces of stable curves I
Speaker, Affiliation Dr. Samir Canning, ETH Zürich
Date, Time 28 September 2022, 13:30-15:00
Location HG G 43
Abstract I will explain some new results showing that the Chow and cohomology rings of moduli spaces of stable curves in relatively low genus and low number of marked points are isomorphic and equal to the tautological ring. These computations involve both concrete geometric techniques in order to explicitly study various strata in the moduli spaces and more abstract techniques relating the computations in the Chow ring to those in cohomology. This part is joint work with Hannah Larson. Next, I will explain a surprising extended application of these results to the vanishing of the eleventh cohomology of moduli spaces of pointed stable curves of genus g at least 2. This part is joint work with Hannah Larson and Sam Payne.
New results on the Chow and cohomology rings of moduli spaces of stable curves Iread_more
HG G 43
30 September 2022
16:00-17:30 		Dr. Yohan Brunebarbe
Université de Bordeaux
Details

Algebraic Geometry and Moduli Seminar

Title Hyperbolicity in presence of a large local system
Speaker, Affiliation Dr. Yohan Brunebarbe, Université de Bordeaux
Date, Time 30 September 2022, 16:00-17:30
Location HG G 43
Abstract Serge Lang has proposed several influential conjectures relating different notions of hyperbolicity for proper complex algebraic varieties. For example, he asked whether the locus swept out by entire curves coincides with the locus swept out by subvarieties not of general type. I will explain that some of these conjectures (including the one above) are true for varieties admitting a large complex local system.
Hyperbolicity in presence of a large local systemread_more
HG G 43
* 3 October 2022
17:30-18:45 		Dr. Woonam Lim
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Virasoro constraints in sheaf theory and vertex algebras
Speaker, Affiliation Dr. Woonam Lim, ETH Zürich
Date, Time 3 October 2022, 17:30-18:45
Location
Zoom
Abstract In enumerative geometry, Virasoro constraints first appeared in the context of moduli of stable curves and maps. These constraints provide a rich set of conjectural relations among Gromov-Witten descendent invariants. Recently, the analogous constraints were formulated in several sheaf theoretic contexts; stable pairs on 3-folds, Hilbert scheme of points on surfaces, higher rank sheaves on surfaces with only (p,p)-cohomology. In joint work with A. Bojko, M. Moreira, we extend and reinterpret Virasoro constraints in sheaf theory using Joyce's vertex algebra. This new interpretation yields a proof of Virasoro constraints for curves and surfaces with only (p,p) cohomology by means of wall-crossing formulas.
Virasoro constraints in sheaf theory and vertex algebrasread_more

Zoom
5 October 2022
13:30-15:00 		Dr. Samir Canning
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title New results on the Chow and cohomology rings of moduli spaces of stable curves II
Speaker, Affiliation Dr. Samir Canning, ETH Zürich
Date, Time 5 October 2022, 13:30-15:00
Location HG G 43
Abstract I will explain some new results showing that the Chow and cohomology rings of moduli spaces of stable curves in relatively low genus and low number of marked points are isomorphic and equal to the tautological ring. These computations involve both concrete geometric techniques in order to explicitly study various strata in the moduli spaces and more abstract techniques relating the computations in the Chow ring to those in cohomology. This part is joint work with Hannah Larson. Next, I will explain a surprising extended application of these results to the vanishing of the eleventh cohomology of moduli spaces of pointed stable curves of genus g at least 2. This part is joint work with Hannah Larson and Sam Payne.
New results on the Chow and cohomology rings of moduli spaces of stable curves IIread_more
HG G 43
7 October 2022
15:30-17:00 		Prof. Dr. Carel Faber
University of Utrecht
Details

Algebraic Geometry and Moduli Seminar

Title Polynomial point counts and odd cohomology vanishing on moduli spaces of stable curves
Speaker, Affiliation Prof. Dr. Carel Faber, University of Utrecht
Date, Time 7 October 2022, 15:30-17:00
Location HG G 43
Abstract I will discuss joint work with Jonas Bergström and Sam Payne. Arbarello and Cornalba have shown that H^1, H^3, and H^5 vanish for the moduli spaces of stable n-pointed curves of genus g. We show that H^7 and H^9 vanish as well. It is known that H^{11} doesn't vanish in general, so the result is sharp. To obtain this result, we need the vanishing for genus 4 and n at most 3. We actually determine the full cohomology in these cases. The main method is approximate counts over finite fields. I will also discuss the connection with recent results of Canning, Larson, and Payne.
Polynomial point counts and odd cohomology vanishing on moduli spaces of stable curvesread_more
HG G 43
12 October 2022
13:30-15:00 		Dr. Samir Canning
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title New results on the Chow and cohomology rings of moduli spaces of stable curves III
Speaker, Affiliation Dr. Samir Canning, ETH Zürich
Date, Time 12 October 2022, 13:30-15:00
Location HG G 43
Abstract I will explain some new results showing that the Chow and cohomology rings of moduli spaces of stable curves in relatively low genus and low number of marked points are isomorphic and equal to the tautological ring. These computations involve both concrete geometric techniques in order to explicitly study various strata in the moduli spaces and more abstract techniques relating the computations in the Chow ring to those in cohomology. This part is joint work with Hannah Larson. Next, I will explain a surprising extended application of these results to the vanishing of the eleventh cohomology of moduli spaces of pointed stable curves of genus g at least 2. This part is joint work with Hannah Larson and Sam Payne.
New results on the Chow and cohomology rings of moduli spaces of stable curves IIIread_more
HG G 43
14 October 2022
16:00-17:30 		Prof. Dr. Y.-P. Lee
Academia Sinica (Taiwan)
Details

Algebraic Geometry and Moduli Seminar

Title QK = GV, two integral invariants on Calabi-Yau 3-folds
Speaker, Affiliation Prof. Dr. Y.-P. Lee, Academia Sinica (Taiwan)
Date, Time 14 October 2022, 16:00-17:30
Location HG G 43
Abstract On Calabi--Yau threefolds there are two types of integral invariants, quantum K-invariants and Gopakumar--Vafa invariants. In this talk, I will explain a joint project (with You-Cheng Chou) which aims to show that the quantum K-invariants and Gopakumar invariants are equivalent. At genus zero, this is a conjecture by Jockers--Mayr and Garoufalidis--Scheidegger (for the quintic), and a proof of the JMGS conjecture will be presented.
QK = GV, two integral invariants on Calabi-Yau 3-foldsread_more
HG G 43
15 October 2022
11:30-12:30 		Weite Pi
Yale University
Details

Algebraic Geometry and Moduli Seminar

Title Moduli of 1-dimensional sheaves on the projective plane: cohomology, perversity, and BPS invariants
Speaker, Affiliation Weite Pi, Yale University
Date, Time 15 October 2022, 11:30-12:30
Location HG G 43
Abstract The moduli spaces of one-dimensional sheaves on CP2 are first studied by Carlos Simpson and Le Potier, and they admit a Hilbert-Chow morphism to a projective base that behaves like a completely integrable system. Following a proposal of Maulik-Toda, one should be able to obtain certain BPS invariants from this morphism. In this talk, we investigate the cohomology ring structure of these moduli spaces. We will derive a minimal set of tautological generators for the cohomology ring, and discuss how they are related, through the key notion of perversity, to the curve counting invariants for local CP2. Based on joint work with Junliang Shen, and with Junliang Shen and Yakov Kononov in progress.
Moduli of 1-dimensional sheaves on the projective plane: cohomology, perversity, and BPS invariantsread_more
HG G 43
21 October 2022
16:00-17:30 		Prof. Dr. Danilo Lewanski
University of Trieste
Details

Algebraic Geometry and Moduli Seminar

Title A spin on the GW/H correspondence
Speaker, Affiliation Prof. Dr. Danilo Lewanski, University of Trieste
Date, Time 21 October 2022, 16:00-17:30
Location HG G 43
Abstract We address a spin version of the GW/H correspondence. The conjecture has a well-defined statement and one of the motivations behind it is that spin curves contain useful information for the GW theory of Kähler surfaces. In the original GW/H correspondence, Hurwitz numbers provide substantial structure to the GW side. For instance, they enjoy integrability of the 2D Toda type, they have a clear formulation in the Fock space and the ELSV formula is known. Moreover, the ELSV formula is compatible via localisation with the GW side. One could investigate similar questions for spin Hurwitz numbers. We provide some of the answers and prove the correspondence in the case of spin equivariant P^1.Based on completed work and on work in progress with A. Giacchetto, R. Kramer, A. Sauvaget.
A spin on the GW/H correspondence read_more
HG G 43
* 24 October 2022
17:30-18:45 		Dr. Dhruv Ranganathan
Cambridge University
Details

Algebraic Geometry and Moduli Seminar

Title Logarithmic enumerative geometry for curves and surfaces
Speaker, Affiliation Dr. Dhruv Ranganathan, Cambridge University
Date, Time 24 October 2022, 17:30-18:45
Location Zoom
Abstract I will discuss ongoing work with Davesh Maulik in which we formulate a generalization of the GW/DT conjectures to the setting of simple normal crossings pairs. When the divisor in the pair is smooth, the formulation of the conjecture necessitates the study of the cohomology of the Hilbert scheme of points on a surface. The formulation of the logarithmic GW/DT conjecture requires new geometry coming from a logarithmic Hilbert scheme of points. We prove a strengthened logarithmic degeneration formula on both sides of the correspondence and prove that the new conjectures are compatible with the old ones via degeneration. I’ll discuss this circle of ideas, and explain which parts of the conjectures are within reach.
Logarithmic enumerative geometry for curves and surfacesread_more
Zoom
26 October 2022
13:30-15:00 		Dr. Fenglong You
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Relative and orbifold Gromov-Witten theory
Speaker, Affiliation Dr. Fenglong You, ETH Zürich
Date, Time 26 October 2022, 13:30-15:00
Location HG G 43
Abstract In this series of talks, I will summarize some recent progress on degenerations and mirror symmetry. The first talk is to relate relative Gromov--Witten theory with absolute orbifold Gromov--Witten theory. The second talk is about structures in relative Gromov--Witten theory. The third talk is about relative mirror symmetry and applications.
Relative and orbifold Gromov-Witten theoryread_more
HG G 43
28 October 2022
16:00-17:30 		Prof. Dr. Andrew Kresch
Universität Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Specialization of rationality
Speaker, Affiliation Prof. Dr. Andrew Kresch, Universität Zürich
Date, Time 28 October 2022, 16:00-17:30
Location HG G 43
Abstract An important problem in algebraic geometry is the study of rationality of algebraic varieties. I will describe progress on the understanding of rationality in families of smooth projective varieties. This includes the specialization of rationality in families, the existence of families of smooth projective varieties with varying rationality, and associated invariants. Extensions will also be described, e.g., to the orbifold setting.
Specialization of rationalityread_more
HG G 43
* 7 November 2022
17:30-18:45 		Prof. Dr. Davesh Maulik
MIT
Details

Algebraic Geometry and Moduli Seminar

Title The P=W conjecture for GL(n)
Speaker, Affiliation Prof. Dr. Davesh Maulik, MIT
Date, Time 7 November 2022, 17:30-18:45
Location Zoom
Abstract The P=W conjecture, first proposed by de Cataldo-Hausel-Migliorini in 2010, gives a link between the topology of the moduli space of Higgs bundles on a curve and the Hodge theory of the corresponding character variety, using non-abelian Hodge theory. In this talk, I will explain this circle of ideas and discuss a recent proof of the conjecture for GL(n) (joint with Junliang Shen).
The P=W conjecture for GL(n)read_more
Zoom
9 November 2022
13:30-15:00 		Dr. Fenglong You
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Structures in relative Gromov-Witten theory
Speaker, Affiliation Dr. Fenglong You, ETH Zürich
Date, Time 9 November 2022, 13:30-15:00
Location HG G 43
Abstract In this series of talks, I will summarize some recent progress on degenerations and mirror symmetry. The first talk is to relate relative Gromov--Witten theory with absolute orbifold Gromov--Witten theory. The second talk is about structures in relative Gromov--Witten theory. The third talk is about relative mirror symmetry and applications.
Structures in relative Gromov-Witten theoryread_more
HG G 43
11 November 2022
16:00-17:30 		Ivan Yakovlev
Université de Bordeaux
Details

Algebraic Geometry and Moduli Seminar

Title Contribution of n-cylinder square-tiled surfaces to Masur-Veech volume of H(2g-2)
Speaker, Affiliation Ivan Yakovlev, Université de Bordeaux
Date, Time 11 November 2022, 16:00-17:30
Location HG G 43
Abstract The minimal stratum H(2g-2) of the Hodge bundle over the moduli space of complex curves admits a natural volume form called the Masur--Veech volume. The total mass with respect to this volume, called the Masur--Veech volume, is of great importance in combinatorics, geometry and dynamics on Riemann surfaces. Zorich showed how to express the Masur--Veech volume as the asymptotic count of so-called square-tiled surfaces. Sauvaget found an explicit formula for the generating series of the Masur--Veech volumes of H(2g-2) via an orthogonal approach using intersection theory. We prove a refinement of Sauvaget formula via Zorich combinatorial approach. This refinement involves counting square-tiled surfaces with a fixed number of cylinders. It relies ultimately on the study of counting functions for certain families of metric ribbon graphs (equivalently -- double Hurwitz numbers with a single non-completed cycle). The top-degree terms of these counting functions turn out to be polynomials whose coefficients have a simple combinatorial description. Our result raises the question of intersection-theoretic interpretation of the volume contributions and of the coefficients of these polynomials.
Contribution of n-cylinder square-tiled surfaces to Masur-Veech volume of H(2g-2)read_more
HG G 43
* 21 November 2022
17:30-18:45 		Zhiyu Liu
Zhejiang University (Hangzhou)
Details

Algebraic Geometry and Moduli Seminar

Title Castelnuovo bound and Gromov-Witten invariants of the quintic 3-fold
Speaker, Affiliation Zhiyu Liu, Zhejiang University (Hangzhou)
Date, Time 21 November 2022, 17:30-18:45
Location Zoom
Abstract One of the most challenging problems in geometry and physics is to compute higher genus Gromov-Witten invariants of compact Calabi-Yau 3-folds, such as the famous quintic 3-fold. I will briefly describe how physicists compute Gromov-Witten invariants of the quintic 3-fold up to genus 53, using five mathematical conjectures. Three of them have been already proved, and one of the remaining two conjectures has been solved in some genus. I will explain how to prove the last open one, called the Castelnuovo bound, which predicts the vanishing of Gopakumar-Vafa invariants for a given degree at sufficiently high genus. This talk is based on the joint work with Yongbin Ruan.
Castelnuovo bound and Gromov-Witten invariants of the quintic 3-foldread_more
Zoom
23 November 2022
13:30-15:00 		Maximilian Schimpf
Universität Bonn
Details

Algebraic Geometry and Moduli Seminar

Title PT theory of elliptic 3-folds, quasi-Jacobi forms, and holomorphic anomaly equations
Speaker, Affiliation Maximilian Schimpf, Universität Bonn
Date, Time 23 November 2022, 13:30-15:00
Location HG G 43
Abstract It is a well-known consequence of mirror symmetry that curve counting invariants of Calabi-Yau varieties should be "modular" in some sense. However, finding the proper notion of modularity has proven difficult in general and so far can only be done in various special cases e.g. elliptic curve, K3, quintic threefold. One might suspect that modularity also holds if one does curve counting on a family of Calabi-Yau varieties instead. Indeed this seems to work for elliptic threefolds in which case PT theory seems to be the most natural thing to study. In this case we conjecture that one gets quasi-Jacobi forms of certain weight that satisfy certain holomorphic anomaly equations, which we can make precise but not yet prove. Further, we introduce pi-stable pairs which seem to be even better behaved and should be related to ordinary PT theory via a wall-crossing formula similar to the DT/PT correspondence. We also present several examples for which our conjectures hold. This is joint work with Georg Oberdieck.
PT theory of elliptic 3-folds, quasi-Jacobi forms, and holomorphic anomaly equationsread_more
HG G 43
25 November 2022
16:00-17:30 		Dr. Leo Herr
University of Leiden
Details

Algebraic Geometry and Moduli Seminar

Title The rhizomic topology
Speaker, Affiliation Dr. Leo Herr, University of Leiden
Date, Time 25 November 2022, 16:00-17:30
Location HG G 43
Abstract What is a sheaf on a log scheme X? If we take the ordinary etale topology, we ignore the log structure. Taking the log etale topology, even the structure "sheaf" O_X is not a sheaf! The same goes for M_X and bar M_X. We introduce a new "rhizomic" topology on log schemes coarser than the log etale topology. Will this be enough? Time permitting, we will also discuss log intersection theory and a riddle about log jet spaces.
The rhizomic topologyread_more
HG G 43
30 November 2022
13:30-15:00 		Dr. Carl Lian
HU Berlin
Details

Algebraic Geometry and Moduli Seminar

Title Geometric Tevelev degrees of P^r
Speaker, Affiliation Dr. Carl Lian, HU Berlin
Date, Time 30 November 2022, 13:30-15:00
Location HG G 43
Abstract We will discuss a complete computation of the geometric Tevelev degrees of projective spaces, in terms of Schubert calculus. That is, we enumerate maps from a general pointed curve to a projective space of any dimension passing through the appropriate number of general points on the target. Previously, the answers were known for covers of the projective line, or for maps of sufficiently large degree (in which case the answers agree with virtual counts in Gromov-Witten theory). The proof employs the moduli space of complete collineations in an essential way, and also goes through a result of Klyachko on torus orbit closures in the Grassmannian.
Geometric Tevelev degrees of P^rread_more
HG G 43
2 December 2022
16:00-17:30 		Dr. Sergej Monavari
EPF Lausanne
Details

Algebraic Geometry and Moduli Seminar

Title Double nested Hilbert schemes and stable pair invariants
Speaker, Affiliation Dr. Sergej Monavari, EPF Lausanne
Date, Time 2 December 2022, 16:00-17:30
Location HG G 43
Abstract Hilbert schemes of points on a smooth projective curve are simply symmetric powers of the curve itself; they are smooth and we know essentially everything about them. We propose a variation by studying double nested Hilbert schemes of points, which parametrize flags of 0-dimensional subschemes satisfying certain nesting conditions dictated by Young diagrams. These moduli spaces are almost never smooth but admit a virtual structure à la Behrend-Fantechi. We explain how this virtual structure plays a key role in (re)proving the correspondence between Gromov-Witten invariants and stable pair invariants for local curves, and say something on their K-theoretic refinement.
Double nested Hilbert schemes and stable pair invariantsread_more
HG G 43
7 December 2022
13:30-15:00 		Prof. Dr. Dimitri Zvonkine
Versailles and CNRS
Details

Algebraic Geometry and Moduli Seminar

Title Quantum Hall effect via the Grothendieck-Riemann-Roch formula
Speaker, Affiliation Prof. Dr. Dimitri Zvonkine, Versailles and CNRS
Date, Time 7 December 2022, 13:30-15:00
Location HG G 43
Abstract We will explain how the fractional quantum Hall effect on a Riemann surface of genus g can be studied using algebraic geometry. The wave functions of charged particles have a semi-phenomenological description by Laughlin states. These states form a holomorphic vector bundle over a Picard group of the Riemann surface. The Chern characters of this vector bundle can be computed by the Grothendieck-Riemann-Roch formula. The mathematical part of the talk involves Grothendieck-Riemann-Roch computations for a universal line bundle on the symmetric power of a smooth curve over its Picard group. This is joint work with Semyon Klevtsov.
Quantum Hall effect via the Grothendieck-Riemann-Roch formularead_more
HG G 43
9 December 2022
16:00-17:30 		Dr. Adam Afandi
Universität Münster
Details

Algebraic Geometry and Moduli Seminar

Title An Ehrhart theory for tautological intersection numbers
Speaker, Affiliation Dr. Adam Afandi, Universität Münster
Date, Time 9 December 2022, 16:00-17:30
Location HG G 43
Abstract Ehrhart polynomials are counting functions for integer lattice points in dilates of polyhedral objects. In this talk, I'll explain how these polynomials arise when computing tautological intersection numbers on the moduli space of pointed stable curves. In particular, it turns out that tautological intersection numbers can be organized into evaluations of Ehrhart polynomials of partial polytopal complexes. The proof of this result primarily relies on a theorem of Breuer, which classifies Ehrhart polynomials of partial polytopal complexes. At the end of the talk, I'll discuss various ways one can try to generalize this Ehrhart phenomenon.
An Ehrhart theory for tautological intersection numbersread_more
HG G 43
14 December 2022
13:30-15:00 		Dr. Maximilian Schimpf
Universität Bonn
Details

Algebraic Geometry and Moduli Seminar

Title The local PT theory of CP1 relative to two ends
Speaker, Affiliation Dr. Maximilian Schimpf, Universität Bonn
Date, Time 14 December 2022, 13:30-15:00
Location HG G 43
Abstract In this work in progress we follow Monavari's approach (see his talk above)and further determine the fixed locus of the PT moduli space of an arbitrary local curve - we find that it's reduced of pure dimension and its virtual cycle agrees with its fundamental cycle. From this one obtains surprising results about PT of C^2 x P^1 relative to 0 and infinity. This is perhaps the most important 3-fold for PT theory since it governs all the other ones via degeneration. On this basis we conjecture explicit formulas for part of its PT theory with the expectiation that there exist similar formulas for the rest as well - however it's not clear how easily one can guess and prove them. We also elaborate on several consequences that such formulas would have.
The local PT theory of CP1 relative to two endsread_more
HG G 43
20 January 2023
15:00-16:00 		Dr. Arkadij Bojko
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Equivariant Segre and Verlinde series for quot-schemes I
Speaker, Affiliation Dr. Arkadij Bojko, ETH Zürich
Date, Time 20 January 2023, 15:00-16:00
Location HG G 43
Abstract Motivated by strange duality, Johnson predicted a correspondence between the Segre and the Verlinde series in the case of a Hilbert scheme of points on a surface. This was soon after proved by Marian-Oprea-Pandharipande and motivated an analogous result in the case of punctual quot-schemes of trivial vector bundles on curves and surfaces. In my work, I have observed that this mysterious correspondence holds even after allowing more general vector bundles, and I extended it to Calabi-Yau fourfolds. Combining it with a natural-looking symmetry between Segre and Verlinde series, respectively, lead to a 12-fold correspondence of these invariants in 1,2, and 4 dimensions. However, very little was known about the equivariant versions of these results. In this talk, I will give an overview of our joint project with J. Huang which addresses multiple open questions by either giving complete theorems proving the correspondences or formulating conjectures supported by empirical evidence.
Equivariant Segre and Verlinde series for quot-schemes Iread_more
HG G 43
20 January 2023
16:00-17:00 		Jiahui Huang
ETH Zürich
Details

Algebraic Geometry and Moduli Seminar

Title Equivariant Segre and Verlinde series for quot-schemes II
Speaker, Affiliation Jiahui Huang, ETH Zürich
Date, Time 20 January 2023, 16:00-17:00
Location HG G 43
Abstract As a continuation of the previous lecture, this talk will outline the proofs of the theorems previously mentioned. I will mainly focus on surfaces and describe the proof of a universal series expression for the equivariant Segre and Verlinde invariants. This is done by relating them to their non-equivariant version of projective toric surfaces. In the case of K-trivial surfaces, a simpler expression can then be obtained for the reduced invariants. Using combinatorial tools introduced by L. Gottsche and A. Mellit, some of the universal series can be computed explicitly. I shall also display some computer calculations for Calabi-Yau 4-folds that support the conjectures previously mentioned. These statements can be considered as 4-D analogues to the results on surfaces.
Equivariant Segre and Verlinde series for quot-schemes IIread_more
HG G 43

Notes: red marked events are important and events marked with an asterisk (*) indicate that the time and/or location are different from the usual time and/or location.

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