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Spring Semester 2023

Date / Time Speaker Title Location
* 1 February 2023
13:30-15:00 		Dr. Fenglong You
ETH Zürich
Event Details

Algebraic Geometry and Moduli Seminar

Title Relative mirror symmetry and the proper Landau-Ginzburg potential
Speaker, Affiliation Dr. Fenglong You, ETH Zürich
Date, Time 1 February 2023, 13:30-15:00
Location ITS
Abstract Following Givental, enumerative mirror symmetry can be stated as a relation between genus zero Gromov-Witten invariants and period integrals. I will talk about a relative version of mirror symmetry that relates genus zero relative Gromov-Witten invariants of smooth pairs and relative periods. Then I will talk about how to use it to compute the mirror proper Landau-Ginzburg potentials of smooth log Calabi—Yau pairs.
Relative mirror symmetry and the proper Landau-Ginzburg potentialread_more
ITS
* 6 February 2023
14:00-15:30 		Dr. Hyeonjun Park
KIAS Korea
Event Details

Algebraic Geometry and Moduli Seminar

Title Virtual pullbacks in Donaldson-Thomas theory of Calabi-Yau 4-folds
Speaker, Affiliation Dr. Hyeonjun Park, KIAS Korea
Date, Time 6 February 2023, 14:00-15:30
Location ITS
Abstract In this talk, I will introduce a virtual pullback formula between Oh-Thomas virtual cycles for moduli spaces of sheaves on Calabi-Yau 4-folds. I will explain a natural compatibility condition between obstruction theories which provides the formula. In the perspective of derived algebraic geometry, this compatibility condition can be understood as Lagrangian correspondences of (-2)-shifted symplectic derived schemes. The two main applications are the Lefschetz principle and the Pairs/Sheaves correspondence. In particular, these prove various conjectures in DT4 theory under some assumptions. Examples include (1) the Cao-Kool conjecture on tautological Hilbert scheme invariants, (2) the Cao-Kool-Monavari conjecture on DT/PT correspondence, and (3) the Cao-Maulik-Toda conjecture on genus zero Gopakumar-Vafa type invariants.
Virtual pullbacks in Donaldson-Thomas theory of Calabi-Yau 4-foldsread_more
ITS
* 7 February 2023
13:30-15:00 		Dr. Fenglong You
ETH Zürich
Event Details

Algebraic Geometry and Moduli Seminar

Title Relative quantum cohomology under birational transformations
Speaker, Affiliation Dr. Fenglong You, ETH Zürich
Date, Time 7 February 2023, 13:30-15:00
Location ITS
Abstract I will talk about how relative quantum cohomology, defined by Tseng-You and Fan-Wu-You, varies under birational transformations. Relation with FJRW theory and extremal transitions of absolute Gromov--Witten theory will also be discussed.
Relative quantum cohomology under birational transformationsread_more
ITS
10 March 2023
16:00-17:30 		Prof. Dr. Daniel Huybrechts
Event Details

Algebraic Geometry and Moduli Seminar

Title Twisting K3 surfaces
Speaker, Affiliation Prof. Dr. Daniel Huybrechts,
Date, Time 10 March 2023, 16:00-17:30
Location HG G 43
Abstract I’ll explain why and how to twist K3 surfaces, how to control these twists in terms of Hodge theory and how to view families of twisted K3 surfaces geometrically. The Brauer group and the associated Brauer family give rise to families that behave very much like twistor spaces.
Twisting K3 surfacesread_more
HG G 43
15 March 2023
13:30-15:00 		Prof. Dr. Marcos Marino
Université de Genève
Event Details

Algebraic Geometry and Moduli Seminar

Title Resurgence and asymptotics in Gromov-Witten theory
Speaker, Affiliation Prof. Dr. Marcos Marino, Université de Genève
Date, Time 15 March 2023, 13:30-15:00
Location HG G 43
Abstract The generating functions of genus g Gromov-Witten invariants of Calabi-Yau threefolds lead to factorially divergent series, when the genus is large. Finding the precise asymptotics of these series is an interesting question. The theory of resurgence of Jean Ecalle associates a very rich structure to a factorially divergent series, involving a collection of “trans-series”, which in particular makes it possible to obtain the precise asymptotics. Determining the resurgent structure of generating functions in Gromov-Witten theory is a difficult problem, and in this talk I will present some partial results and conjectures on this structure, based on trans-series solutions of the holomorphic anomaly equations. As a consequence of these results, I will formulate precise conjectures for the asymptotics of the generating functions of the quintic CalabiYau, and for the asymptotics of fixed degree orbifold Gromov-Witten invariants of C^3/Z_3.
Resurgence and asymptotics in Gromov-Witten theoryread_more
HG G 43
17 March 2023
16:00-17:30 		Alessio Cela
ETH Zürich
Event Details

Algebraic Geometry and Moduli Seminar

Title Fixed-domain curve counts for blow-ups of projective space
Speaker, Affiliation Alessio Cela, ETH Zürich
Date, Time 17 March 2023, 16:00-17:30
Location HG G 43
Abstract I will explain some new results about the problem of counting pointed curves of fixed complex structure in blow-ups of projective space at general points. The geometric and virtual Gromov-Witten counts in genus 0 and in higher genus for large degree agree in the Fano (and some (-K)-nef) examples, but not in general. For toric blow-ups, geometric counts can be expressed in terms of integrals on products of Jacobians and symmetric products of the domain curves, and evaluated explicitly in genus 0 and in the case of Bl_q(P^r). Formulas for the the virtual counts in the case of the blow-up of P^r at one point can also be computed via the quantum cohomology ring.
Fixed-domain curve counts for blow-ups of projective spaceread_more
HG G 43
* 20 March 2023
17:30-18:45 		Prof. Dr. Longting Wu
SUSTech (Shenzhen)
Event Details

Algebraic Geometry and Moduli Seminar

Title All-genus WDVV recursion, quivers, and BPS invariants
Speaker, Affiliation Prof. Dr. Longting Wu, SUSTech (Shenzhen)
Date, Time 20 March 2023, 17:30-18:45
Location Zoom
Abstract Let D be a smooth rational ample divisor in a smooth projective surface X. In this talk, we will present a simple uniform recursive formula for (primary) Gromov-Witten invariants of O_X(-D). The recursive formula can be used to determine such invariants for all genera once some initial data is known. The proof relies on a correspondence between all-genus Gromov–Witten invariants and refined Donaldson–Thomas invariants of acyclic quivers. In particular, the corresponding BPS invariants are expressed in terms of Betti numbers of moduli spaces of quiver representations. This is a joint work with Pierrick Bousseau.
All-genus WDVV recursion, quivers, and BPS invariantsread_more
Zoom
22 March 2023
13:30-15:00 		Prof. Dr. Renzo Cavalieri
Colorado State Univ.
Event Details

Algebraic Geometry and Moduli Seminar

Title Tropical contributions to enumerative geometry of target dimension 1, Part I
Speaker, Affiliation Prof. Dr. Renzo Cavalieri, Colorado State Univ.
Date, Time 22 March 2023, 13:30-15:00
Location HG G 43
Abstract This cycle of talks wants to highlight how ideas from tropical geometry have contributed not only to the solution, but also to the development of enumerative geometric problems regarding moduli spaces of curves, and maps from curves to curves. We will spend a little of time reviewing the origins of this story, i.e. the development of tropical Hurwitz numbers as combinatorial analogues for the classical Hurwitz numbers. We will discuss a more recent interpretation that views tropical Hurwitz numbers as the natural computation for the intersection number of the double ramification cycle with an element of the log Chow ring of the moduli space of curves (called in this case the branch polynomial, as it is presented as a piecewise polynomial function on the moduli spaces of tropical curves) which is determined by the tropical moduli space of covers of the projective line. We will see that from the tropical perspective analogous piecewise polynomial functions may be associated to $k$-DR cycles (cycles arising from spaces of twisted pluri-differentials), thus giving rise to $k$-analogues of Hurwitz numbers (called leaky Hurwitz numbers) that enjoy many of the algebro-combinatorial properties of Hurwitz numbers - such as piecewise polynomiality and wall crossings. We will present some work in progress which intends to incorporate descendants into these pictures. Tropical algorithms are developed that give rise to some intruiguingly simple formulas in the case when one point is fully ramified. The material presented is based on many years of joint work with several people, including Paul Johnson, Hannah Markwig, Dhruv Ranganathan and Johannes Schmitt.
Tropical contributions to enumerative geometry of target dimension 1, Part Iread_more
HG G 43
24 March 2023
15:00-16:15 		Dr. Sam Canning
ETH Zürich
Event Details

Algebraic Geometry and Moduli Seminar

Title Moduli of K3 surfaces of degree 2
Speaker, Affiliation Dr. Sam Canning, ETH Zürich
Date, Time 24 March 2023, 15:00-16:15
Location HG G 43
Abstract The intersection theory of the moduli space of K3 surfaces polarized by a lattice is a subject of recent interest because of its deep connections with a wide variety of mathematics, including the intersection theory of moduli spaces of curves and the study of modular forms. Oprea and Pandharipande conjectured that the tautological rings of these moduli spaces of K3 surfaces are highly structured in a way that mirrors the picture for the moduli space of curves. I will explain how to compute the Chow ring of the moduli space of degree 2 quasipolarized K3 surfaces, which consequently proves the conjecture in this case. This is joint work with Dragos Oprea and Rahul Pandharipande.
Moduli of K3 surfaces of degree 2read_more
HG G 43
24 March 2023
16:15-17:30 		Prof. Dr. Dragos Oprea
UC San Diego
Event Details

Algebraic Geometry and Moduli Seminar

Title On the cohomology of tautological bundles over Quot schemes of curves
Speaker, Affiliation Prof. Dr. Dragos Oprea, UC San Diego
Date, Time 24 March 2023, 16:15-17:30
Location HG G 43
Abstract We consider tautological bundles and their exterior and symmetric powers over the Quot scheme of zero dimensional quotients over the projective line. We prove several results regarding the vanishing of their higher cohomology, and we describe the spaces of global sections via tautological constructions. This is based on joint work with Alina Marian, Shubham Sinha and Steven Sam.
On the cohomology of tautological bundles over Quot schemes of curvesread_more
HG G 43
29 March 2023
13:30-15:00 		Prof. Dr. Renzo Cavalieri
Colorado State University
Event Details

Algebraic Geometry and Moduli Seminar

Title Tropical contributions to enumerative geometry of target dimension 1, Part II
Speaker, Affiliation Prof. Dr. Renzo Cavalieri, Colorado State University
Date, Time 29 March 2023, 13:30-15:00
Location HG G 43
Abstract This cycle of talks wants to highlight how ideas from tropical geometry have contributed not only to the solution, but also to the development of enumerative geometric problems regarding moduli spaces of curves, and maps from curves to curves. We will spend a little of time reviewing the origins of this story, i.e. the development of tropical Hurwitz numbers as combinatorial analogues for the classical Hurwitz numbers. We will discuss a more recent interpretation that views tropical Hurwitz numbers as the natural computation for the intersection number of the double ramification cycle with an element of the log Chow ring of the moduli space of curves (called in this case the branch polynomial, as it is presented as a piecewise polynomial function on the moduli spaces of tropical curves) which is determined by the tropical moduli space of covers of the projective line. We will see that from the tropical perspective analogous piecewise polynomial functions may be associated to $k$-DR cycles (cycles arising from spaces of twisted pluri-differentials), thus giving rise to $k$-analogues of Hurwitz numbers (called leaky Hurwitz numbers) that enjoy many of the algebro-combinatorial properties of Hurwitz numbers - such as piecewise polynomiality and wall crossings. We will present some work in progress which intends to incorporate descendants into these pictures. Tropical algorithms are developed that give rise to some intruiguingly simple formulas in the case when one point is fully ramified. The material presented is based on many years of joint work with several people, including Paul Johnson, Hannah Markwig, Dhruv Ranganathan and Johannes Schmitt.
Tropical contributions to enumerative geometry of target dimension 1, Part IIread_more
HG G 43
5 April 2023
13:30-15:00 		Prof. Dr. Renzo Cavalieri
Colorado State University
Event Details

Algebraic Geometry and Moduli Seminar

Title Tropical contributions to enumerative geometry of target dimension 1, Part III
Speaker, Affiliation Prof. Dr. Renzo Cavalieri, Colorado State University
Date, Time 5 April 2023, 13:30-15:00
Location HG G 43
Abstract This cycle of talks wants to highlight how ideas from tropical geometry have contributed not only to the solution, but also to the development of enumerative geometric problems regarding moduli spaces of curves, and maps from curves to curves. We will spend a little of time reviewing the origins of this story, i.e. the development of tropical Hurwitz numbers as combinatorial analogues for the classical Hurwitz numbers. We will discuss a more recent interpretation that views tropical Hurwitz numbers as the natural computation for the intersection number of the double ramification cycle with an element of the log Chow ring of the moduli space of curves (called in this case the branch polynomial, as it is presented as a piecewise polynomial function on the moduli spaces of tropical curves) which is determined by the tropical moduli space of covers of the projective line. We will see that from the tropical perspective analogous piecewise polynomial functions may be associated to $k$-DR cycles (cycles arising from spaces of twisted pluri-differentials), thus giving rise to $k$-analogues of Hurwitz numbers (called leaky Hurwitz numbers) that enjoy many of the algebro-combinatorial properties of Hurwitz numbers - such as piecewise polynomiality and wall crossings. We will present some work in progress which intends to incorporate descendants into these pictures. Tropical algorithms are developed that give rise to some intruiguingly simple formulas in the case when one point is fully ramified. The material presented is based on many years of joint work with several people, including Paul Johnson, Hannah Markwig, Dhruv Ranganathan and Johannes Schmitt.
Tropical contributions to enumerative geometry of target dimension 1, Part IIIread_more
HG G 43
* 5 April 2023
15:30-17:00 		Miguel Moreira
ETH Zürich
Event Details

Algebraic Geometry and Moduli Seminar

Title The cohomology ring is not χ-invariant
Speaker, Affiliation Miguel Moreira, ETH Zürich
Date, Time 5 April 2023, 15:30-17:00
Location ITS
Abstract This talk will be about the moduli space M_{d, χ} of stable 1-dimensional sheaves on the projective plane. The cohomology of these moduli spaces is conjecturally related to the enumerative geometry of local P^2. This relation predicts in particular that the (intersection) Betti numbers of M_{d, χ} do not depend on χ, which has been proven by Maulik-Shen. A natural question is whether the cohomology ring is also χ-invariant. In this talk I will answer that question negatively: except for possibly finitely many exceptional cases, the ring cohomology determines χ up to some trivial symmetries. In particular this shows that those spaces are typically not homeomorphic (previously they were only known to be non-isomorphic as algebraic varieties). This is based on joint work with W. Lim and W. Pi.
The cohomology ring is not χ-invariantread_more
ITS
* 1 May 2023
17:30-18:45 		Prof. Dr. Sam Payne
UT Austin
Event Details

Algebraic Geometry and Moduli Seminar

Title Cohomology groups of moduli spaces of curves
Speaker, Affiliation Prof. Dr. Sam Payne, UT Austin
Date, Time 1 May 2023, 17:30-18:45
Location Zoom
Abstract Algebraic geometry endows the cohomology groups of moduli spaces of curves with additional structures, such as (mixed) Hodge structures and Galois representations. Standard conjectures from arithmetic, regarding analytic continuations of L-functions attached to these Galois representations, lead to striking predictions, by Chenevier and Lannes, about which such structures can appear. I will survey recent results unconditionally confirming several of these predictions and studying patterns in the appearances of motives of low weight. The latter are governed by the operadic structures induced by tautological morphisms and the cohomology of graph complexes. Based on joint work with Jonas Bergström and Carel Faber; with Sam Canning and Hannah Larson; with Melody Chan and Søren Galatius; and with Thomas Willwacher.
Cohomology groups of moduli spaces of curvesread_more
Zoom
3 May 2023
13:30-15:00 		Prof. Dr. Vivek Shende
UC Berkeley and Univ. of Southern Denmark
Event Details

Algebraic Geometry and Moduli Seminar

Title Skein valued curve counting
Speaker, Affiliation Prof. Dr. Vivek Shende, UC Berkeley and Univ. of Southern Denmark
Date, Time 3 May 2023, 13:30-15:00
Location HG G 43
Abstract We explain how to invariantly count holomorphic curves of all genera with Lagrangian boundary conditions in Calabi-Yau 3-folds. In the process we discover a natural geometric occurence of the HOMFLYPT skein relations, and prove the Ooguri-Vafa conjecture relating the HOMFLYPT invariant of a knot to the count of curves ending on a certain associated Lagrangian (the knot conormal transplanted to the resolved conifold).
Skein valued curve countingread_more
HG G 43
5 May 2023
16:00-17:30 		Prof. Dr. Vivek Shende
UC Berkeley and Uniersity of Southern Denmark
Event Details

Algebraic Geometry and Moduli Seminar

Title Skein valued mirror symmetry
Speaker, Affiliation Prof. Dr. Vivek Shende, UC Berkeley and Uniersity of Southern Denmark
Date, Time 5 May 2023, 16:00-17:30
Location HG G 43
Abstract We show how, at least in some class of examples ("Reeb-positive"), the all-genus skein-valued curve count on a non-compact Lagrangian (e.g. a Harvey-Lawson brane in a toric CY3) is annihilated by an operator equation which is a skein-valued quantization of the mirror curve. As an application we prove the all-color version of the Ooguri-Vafa conjecture mentioned above.
Skein valued mirror symmetryread_more
HG G 43
10 May 2023
13:30-15:00 		Prof. Dr. Dhruv Ranganathan
Cambridge University
Event Details

Algebraic Geometry and Moduli Seminar

Title Brill-Noether theory for curves in an algebraic torus
Speaker, Affiliation Prof. Dr. Dhruv Ranganathan, Cambridge University
Date, Time 10 May 2023, 13:30-15:00
Location HG G 43
Abstract Brill-Noether theory is a rich subject dating back to the late 19th century. It governs the geometry of the space of maps from curves to projective space, such as the dimensions of its irreducible components and the dimensions of their images in the moduli space of curves. Logarithmic geometry suggests an alternative geometry: the space of rational maps from smooth pointed curves to an algebraic torus, known in some circles as the interior of the higher double ramification cycle. I will explain how to use logarithmic and tropical techniques to gain access to the geometry of this space, and prove “Brill-Noether existence” results. These specialise in a transparent fashion to classical results of Kempf, Kleiman, Laksov, as well as the recent Hurwitz-Brill-Noether direction pioneered by K. Cook-Powell, E. Larson, H. Larson, D. Jensen, and I. Vogt. The talk is based on work with D. Jensen.
Brill-Noether theory for curves in an algebraic torusread_more
HG G 43
12 May 2023
16:00-17:30 		Dr. Sam Molcho
ETH Zürich
Event Details

Algebraic Geometry and Moduli Seminar

Title Grothendieck-Riemann-Roch for twisted bundles
Speaker, Affiliation Dr. Sam Molcho, ETH Zürich
Date, Time 12 May 2023, 16:00-17:30
Location HG G 43
Abstract The Brill-Noether classes w_{g,d}^r are virtual fundamental classes associated to the Brill-Noether loci W_{g,d}^r in the universal Jacobian Pic^d(C_{g,n}/M_{g,n}), parametrizing curves with line bundles that have at least r+1 linearly independent sections. Pulling back to M_{g,n} via Abel-Jacobi sections produces tautological classes, which can be calculated by Grothendieck-Riemann-Roch. Extending those classes to the compactification \bar{M}_{g,n} is however not straightforward: the right extensions live naturally on blowups of \bar{M}_{g,n}, or, equivalently, in logCH(\bar{M}_{g,n}). Consequently, their calculation is also subtle. In this talk, I will discuss a general formula that allows to calculate these classes. The formula is close in the spirit of Mumford's GRR calculation, but with combinatorial corrections required. I will then discuss the connection of the calculation with relations in the tautological ring, to the limited extent that I understand them. This is joint work with Alex Abreu and Nicola Pagani.
Grothendieck-Riemann-Roch for twisted bundlesread_more
HG G 43
24 May 2023
13:30-15:00 		Prof. Dr. Dhruv Ranganathan
Cambridge University
Event Details

Algebraic Geometry and Moduli Seminar

Title Enumerative geometry for curves in an algebraic torus
Speaker, Affiliation Prof. Dr. Dhruv Ranganathan, Cambridge University
Date, Time 24 May 2023, 13:30-15:00
Location HG G 43
Abstract I will discuss various aspects of the enumerative geometry of curves in an algebraic torus, formulated as the logarithmic enumerative geometry of a toric pair. I will explain how logarithmic double ramification cycles can be used to give a complete, albeit complex, solution to the logarithmic GW theory of all toric varieties, relative to their full toric boundary. I will then explain what happens in various special geometries when this solution can be made explicit. One simplification leads very quickly to traditional tropical correspondence theorems, recovering work of Mikhalkin, Nishinou-Siebert, and others. Another simplification leads to tropical refined curve counting, recovering work of Bousseau via integrable systems techniques. I will then explain how the logarithmic GW/DT conjectures (aka the LMNOP conjectures) come into the story via “triple double” ramification cycles. The talk is based on joint work with A. Urundolil Kumaran and D. Maulik, and touches upon forthcoming work of P. Kennedy-Hunt, Q. Shafi, and A. Urundolil-Kumaran.
Enumerative geometry for curves in an algebraic torusread_more
HG G 43
* 24 May 2023
16:15-17:30 		Prof. Dr. Dan Abramovich
Brown University
Event Details

Algebraic Geometry and Moduli Seminar

Title The Chow ring of a weighted blowup
Speaker, Affiliation Prof. Dr. Dan Abramovich, Brown University
Date, Time 24 May 2023, 16:15-17:30
Location Y27 H 25
Abstract The Chow groups of a blowup of a smooth variety along a smooth subvariety are described in Fulton's book using Grothendieck's "key formula", involving the Chow groups of the blown up variety, the center of blowup, and the Chern classes of its normal bundle. If interested in weighted blowups, one expects everything to generalize directly. This is in hindsight correct, except that at every turn there is an interesting and delightful surprise, shedding light on the original formulas for usual blowups, especially when one wants to pin down the integral Chow ring of a stack theoretic weighted blowup. As an application, one obtains a quick derivation of a formula, due to Di Lorenzo-Pernice-Vistoli and Inchiostro, of the Chow ring of the moduli space \bar{M}_{1,2}.
The Chow ring of a weighted blowupread_more
Y27 H 25
26 May 2023
16:00-17:30 		Dr. Michel van Garrel
University of Birmingham
Event Details

Algebraic Geometry and Moduli Seminar

Title Geometry of enumerative mirror symmetry
Speaker, Affiliation Dr. Michel van Garrel, University of Birmingham
Date, Time 26 May 2023, 16:00-17:30
Location HG G 43
Abstract Given a log Calabi-Yau pair (Y,D), the intrinsic mirror symmetry construction of Gross-Siebert builds the mirror family X of (Y,D) as a geometric generating function of the genus 0 punctured Gromov-Witten invariants of (Y,D). String theory loosely predicts that period integrals on X equal generating functions of genus 0 log Gromov-Witten invariants of (Y,D). In this joint work with Helge Ruddat and Bernd Siebert, we verify this prediction for pairs (Y,D) with Y a smooth Fano variety and D a smooth anticanonical divisor, and for insertions curve classes on D. A key to this is that insertions of (Y,D) determine Lagrangians of X via tropical geometry.
Geometry of enumerative mirror symmetryread_more
HG G 43
31 May 2023
13:30-15:00 		Prof. Dr. Aaron Pixton
University of Michigan
Event Details

Algebraic Geometry and Moduli Seminar

Title Admissible covers and stable maps
Speaker, Affiliation Prof. Dr. Aaron Pixton, University of Michigan
Date, Time 31 May 2023, 13:30-15:00
Location HG G 43
Abstract Given a space parametrizing branched covers of smooth curves (with some given genus, degree, and ramification profile data), there are two well-known compactifications - the admissible covers of Harris and Mumford and the stable maps of (relative) Gromov-Witten theory. Both of these compactifications give rise to cycles on moduli spaces of stable curves. I will describe work in progress giving a way to translate between the cycles produced by the two compactifications. Part of this talk presents joint work with Q. Zhao.
Admissible covers and stable mapsread_more
HG G 43
14 June 2023
13:30-15:00 		Dr. Hannah Larson
Harvard
Event Details

Algebraic Geometry and Moduli Seminar

Title The embedding theorem in Hurwitz-Brill-Noether theory
Speaker, Affiliation Dr. Hannah Larson, Harvard
Date, Time 14 June 2023, 13:30-15:00
Location HG G 43
Abstract Brill--Noether theory studies the maps of general curves to projectivespaces. The embedding theorem of Eisenbud and Harris states that a general degree d map C to P^r is an embedding when r is at least 3. Hurwitz--Brill--Noether theory starts with a curve C already equipped with a fixed map C to P^1 (which often forces C to be special) and then studies the maps of C to other projective spaces. In this setting, the appropriate analogue of the invariants d and r is a finer invariant called the splitting type. Our embedding theorem determines the splitting types \vec{e} such that a general map of splitting type \vec{e} is an embedding. This is joint work with Kaelin Cook--Powel, Dave Jensen, Eric Larson, and Isabel Vogt.
The embedding theorem in Hurwitz-Brill-Noether theoryread_more
HG G 43
12 July 2023
13:30-15:00 		Prof. Dr. Hsian-Hua Tseng
Ohio State University
Event Details

Algebraic Geometry and Moduli Seminar

Title Virasoro constraints for toric bundles
Speaker, Affiliation Prof. Dr. Hsian-Hua Tseng, Ohio State University
Date, Time 12 July 2023, 13:30-15:00
Location HG G 43
Abstract Virasoro constraints are conjectural differential equations satisfied by generating functions of descendant Gromov-Witten invariants of Kahler manifolds/orbifolds. In this talk, we will begin with reviewing Givental's formulation of these constraints. We will then discuss the following result, which is a joint work with T. Coates and A. Givental: For a toric bundle E-> B, Virasoro constraints hold for E if and only if they hold for B.
Virasoro constraints for toric bundlesread_more
HG G 43
18 August 2023
16:00-17:30 		Prof. Dr. Qizheng Yin
Beijing University
Event Details

Algebraic Geometry and Moduli Seminar

Title Abelian fibrations, Perverse = Chern, and multiplicativity
Speaker, Affiliation Prof. Dr. Qizheng Yin, Beijing University
Date, Time 18 August 2023, 16:00-17:30
Location ITS
Abstract The perverse filtration captures interesting homological information of algebraic maps. Recent studies of integrable systems (e.g. Hitchin systems, Beauville-Mukai systems) suggest two common features of the perverse filtration of abelian fibrations: 1) the perverse filtration is multiplicative with respect to the cup product; 2) the perversity of tautological classes is governed by the Chern degree. In this talk, I will explain a unified approach to both 1) and 2) for a natural class of abelian fibrations, namely fibrations in compactified Jacobians. I will discuss several ingredients from (coherent) derived categories, K-theory/Chow theory, and constructible categories, as well as some applications of our result. Joint work in progress with Davesh Maulik and Junliang Shen.
Abelian fibrations, Perverse = Chern, and multiplicativityread_more
ITS

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